Hello and welcome to Town Meeting TV's coverage of Town Meeting Day 2023. My name's Bobby Lucia and I'll be your host for today's program, which is one in a series of forums that we'll be hosting an advance of Town Meeting Date this year. And in our forum series we invite candidates, municipal officials, and other folks in the area to unpack the items and races that you'll see up and down your ballot this year. As part of our coverage on the Burlington Ballot on Town Meeting Day, today we're focused on a ballot initiative to establish a community control board to oversee the Burlington Police Department. If passed by Burlington voters, and then by the Vermont legislature and the governor, this initiative would create a board of seven to nine Burlington residents chosen by local non-profit leaders, a city councilor, and the mayor, and the board would be charged with investigating incidents of excessive force and other misconduct and making disciplinary decisions including the dismissal of officers and or the police chief. And this question made it onto the ballot through a citizen petition, which garnered the necessary 2000 or so signatures required to reach the ballot. And as a city, charter change, as I mentioned, if it does pass, it also has to pass the Vermont legislature and be signed by the governor to take effect. And so to better understand this ballot initiative today, with us we have Milo Grant, who is a longtime Burlington resident and who currently serves on the Burlington Police Commission. So Milo, thank you so much for joining us today. Thank you so much for having me. So Milo, we'll dive into the initiative shortly, but first, why don't you tell us just a bit about the Burlington Police Commission and what your role is on that body and what that group is charged with? Certainly. Thank you. So I do first want to say that I am here speaking as a citizen who serves on the special committee to review policing policies and currently serves on the police commission. I am not speaking on behalf of the police commission as a whole because the police commission as a whole has not made any statement on the ballot item. I'm just talking about what my experiences have been. With regards to the police commission itself, what we've been doing since I've been on the commission, which the last two and a half years, we've changed some things. In particular, something I think that most people can relate to is a re-examination of the complaints process and also a inviting in additional resources such as NACOL, the National Association for Law Enforcement Oversight. National Association Community Oversight of Law Enforcement, thank you, sorry. And getting advice from that organization and other resources to say what's the best thing that we can do for Burlingtonians who file complaints against our police department and what does that process look like? So when I first started, we didn't actually see the complaints. We were told about them. So we didn't really know what they were. So now we actually see the complaints. We can see the original written complaints. And then there was the whole process about, well, who confirms that a complaint's been received? What type of deliberation should there be? Who then confirms what information is relayed to the complainant? Things like that that weren't always happening before. So making those type of changes, I think that's one of the most relatable changes that the average Burlingtonian can relate to. We have with our meetings added educational components. We talk about things that affect the average Burlingtonian. We talk about things that affect police officers because the average Burlingtonian really doesn't understand the things that our officers have to deal with on a daily basis. So we had an excellent speaker on officer wellness. We had an excellent speaker that talked about how certain use of force incidents that have gone viral. What are the back stories? What caused this? Was there an officer on the road that shouldn't have been and because of certain reasons why he shouldn't have been? Not because they were a bad officer, but because they had already been through something traumatic and had to continue with their shift when maybe really they should have been given a break. So there's a lot of things that go on, but unfortunately there are also issues of a lack of equity in policing and that is something that unfortunately we have seen in our area as well. So talking about racial disparities, talking about the best way to address racial disparities, hopefully having a change in the way we address certain communities because despite the fact that we are in one of the white estates in the country, Burlington is very diverse. You can go into certain areas of Burlington and you could be walking around in Brooklyn and that's because we have a number of new Americans that live here. Our schools are going to change our community in just maybe the next 10 years. We're looking school-wide as of the fall of 2021, roughly 38 percent of the children are a part of the global majority. We have some schools that are well over 50 percent, some are in 40 and some are in the lower 30s. That's way more than a lot of people realize and these children are growing up, they're working in our community, so there's more interactions and as we can see with issues at sporting games and the like that their presence is not always welcome and that does spill over into other aspects of our society including policing. So we discuss that as well and we do look at use of force incidents and we do our best to say what can we do better, right? What can we do better? Because sometimes it's not about punishment, sometimes it's not about firing someone, sometimes it's about what we can do better, what training needs to be revisited. Training should not be considered a one and done, especially around de-escalation. You know, where all types of people work in different businesses where you have rules and standards and procedures you should follow and then if you don't how is that addressed, right? And it doesn't mean that someone has to be fired but it does mean sometimes that you have to take a look and say how do we prevent this from happening again, how do we have honest conversation about that and how do we know that that's what the leadership in the department is doing and that's sometimes where I feel we butt heads at least from my personal opinion. Who sits on the Burlington Police Commission and how is that body kind of composed? Certainly, so for any commissions generally you can go to the city's website and you can look to see what positions are open. Most of the commission seats are two and three years depending on the commission and you fill out an application for what commission you're interested in and you give a little bit of information about yourself and it's reviewed by a committee on the city council and then voted on by the whole city council and you can go and you can speak on your behalf to say this is why I have something to offer to this committee in this process. So what you have are private citizens who've stepped up to serve and we have different backgrounds. I work in a field called consumer directed benefits. I help people with managing health reimbursement accounts, health savings accounts, things like that. We have Stephanie Segrino who is a college professor and an internationally renowned economist. So she's a fantastic resource with regards to looking at data. We have a commissioner Comerford who has a background in social work. We had our former chairman who just had twins. Congratulations. So with his time commitment being drastically reduced, he unfortunately had to resign but he is an individual who worked in a downtown bar. He works in downtown bars so he gets to see these things right up front. You know myself as a citizen, I've also DJ around town and I've DJ number shows. I've gone to a number show so I see what's happening downtown as well and we have another commissioner who works with people who have autism and the like and so he has this life experience. So what's great about this commission is we have these variety of life experiences that we can bring to the table to represent a variety of people in our community and advocate for them. Right okay and so this is it's a group that is appointed based on applications that are submitted and then who actually approves those applications and puts and so that it's the City Council. So that sounds a little bit different from what's being proposed through this initiative. Maybe we can get into it a little bit. So this initiative aims to establish a community control of police board which is appointed by nonprofit organizations around Burlington who are involved in racial justice work and also involve the A City Councilor and the mayor but can you talk a little bit about just how this board would be different from the Burlington Police Commission that you sit on currently. So what's interesting is that the the board would be independent and one of the reasons that the makeup that's being indicated in the ballot item is to really take a step to ensure voices that have quite frankly sometimes been previously blocked from being able to have a position express concerns around policing in our area and policing equity amongst the various groups that they would be representing. So it's a way to say we need to ensure that these voices are being heard. Right okay and my understanding also is that you were originally opposed to this charter change. I was. And you've since come around to supporting it. I was. I have attended meetings participated in conversations because I wanted to know what was going on. I wanted to know what people were talking about on the commission itself. We just kind of held our heads down and we just went on with the work. We're like we are going to continue with the work because there was this back and forth about the original charter change discussions that happened in fall of 2020 2021. But we were just like we just we don't know where all that's going to land. So as a commission we're just going to keep doing the work. And I felt that the commission could be that body that changes in the commission. Additional tools additional resources like the commission we have our own lawyer now. It's huge. It's huge because the city attorney's office doesn't really represent the commission and doesn't represent the city of the people of Burlington represents the city of Burlington. You know the administrative part. But that's like a different thing from actually representing community members who might not have had a good interaction with an officer. So that was a concern. But we have that tool now and we've had a lot of education including having an understanding of the directives and the policies. So I was feeling that yeah we can do this and I was like OK I'm going to have this conversation. I'm going to listen to what everyone's concerns are. I share these concerns. But hey just so you know what the police commission's up to. You know there's certain things I can't talk about that happen in executive sessions. But I could talk about the things that were discussing publicly. I incur I did a lot of outreach for the commission because I felt it was important for people to have an understanding of what the commission was working on what the commission was doing. And I went to these meetings and I talked about it. I was like hey we got a lawyer now. People are like oh that's major that's big. That's one of the big things that people felt an oversight body needed and a body that would be looking at accountability needed. But it became increasingly clear to me that the police commission wasn't getting the support that it needed. And then in fact more recently we've had the mayor and the police chief actively attack the police commission in a way that I personally feel is not appropriate. Like they have the police chief said in an open meeting that one of the reasons we didn't have lateral transfers. A lateral transfer is an officer that maybe has worked in another city or another state wants to change. Do we have an opportunity to bring them here to Burlington. They don't have to go through the full academy because they've already been through academy. They just have to go through some initial training about the city of Burlington and policing in Burlington. So lateral transfer you can get on the road a lot faster than someone who's just out of the academy. But that it was the fault of the police commission that they did not have applications at the time from lateral transfers. This is really amazing to say that the additional salary the additional incentives were not enough to overcome the work of the commission. So you're saying that people don't want to be here because they don't want oversight and they don't want accountability. What is that really saying about the type of officers that we want to attract. It's very deeply concerning to me and then September 19th our co-chair was asked to present the annual report of the police commission and this is a public meeting city council meeting near the end of the meeting September 19th anyone can go and watch this. And the mayor just said that the commission was out of sync with what the people of Burlington wanted that the commission was interfering with public safety and he said a number of things that were false. Then he said he was going to write a written response to to correct the record which he never did we're in February 2023 and he never did that. To me it was just kind of like a shiny object. Oh here look now put your anger toward the police commission. And I just felt that was pretty astounding. We are private citizens we have stepped up to serve who's going to protect us from that. Right now there's the attitude keep your head down do the work. But I personally felt this was a little bit too much. I felt that it was really inappropriate for the administration and then the department head to attack the work of the commission then turn around and say the commission can be the oversight body because you don't like the ballot item. It's just ingenuous it's it's inconsistent and very worrisome to me which is why I changed my mind because you literally are pushing the commission aside and blaming the commission so you don't have that belief that the commission can do this work. And that's why my my personal opinion has has changed and why I support it because if anything it's it's going to push the conversation forward which has been allowed to lapse in a vacuum of leadership. So what do you expect might be might be different from a typical Burlington resident experience. If this initiative is passed and this board is established what do you expect that folks might might see as different about their Burlington experience. I would like to hope that an independent board would reduce some of the political flexing right like it's truly independent and it can't be affected by some of these some of these falsehoods and it could be certain things can never be fully public because you can't talk about certain disciplinary things but there could be a better faith in the process and maybe people can be informed on what is the result of an investigation. So for example we can look at a use of force incident we or a complaint we can discuss it we can review the policies and the procedures if we make a determination whatever our determination is the actual complaint doesn't get to hear about that at this time it's really quite remarkable. But that's where we're at right that is that is a hurdle we haven't gotten past. I would hope that the independent board would be able to do that because there's something to say that if you can't even communicate that that information how are you there for someone that's had an injustice done against them you know if that is what occurred you know sometimes complaints are not valid you know sometimes we get complaints that are not even related to Burlington Vermont right and they just be like oh you got to let them know they got a file for Burlington I or wherever someone just did a search for Burlington filed a complaint didn't realize they were in the wrong state. And that happens absolutely and then sometimes people file complaints and unfortunately they don't give us enough information we don't have enough information and if we don't have enough information to proceed we can't and that can be very difficult because sometimes people stay anonymous for a reason they're afraid of being targeted that's a real fear and we have to respect that but sometimes it does interfere with how much we can we can do for them. So you mentioned that the commission can make a determination based on an incident but where does so where does that determination go as it stands right now with the current power of the body of the commission. Well we can we can talk to the chief the chief makes the ultimate determination as it is now we can talk to the mayor if we feel strongly about something and the mayor does meet with the commission. What I what I don't like is that when they talk about the commission having access to information and body camp footage related to use of force and related to complaints and that we can we have these meetings with the mayor they kind of stop there. They're not always honest about the fact that sometimes we disagree. We disagree with a great deal of passion and we have a great deal of concern that things could have been handled differently especially in issues of de-escalation and especially issues around equity and policing. So they're very very hard conversations and then there's a lot of there's so much work that people don't see and that is you know when people go well you guys don't really seem to do anything you don't seem to really be able to change anything that breaks my heart. But I'm beholden to confidentiality rules and so I can only say that we are well and truly doing our best and we have made some changes and we're going to keep our heads down and keep pushing through and doing the work but hope that the city council comes around them the meeting that was this past Monday was very was it Monday was a 6th of March recommend people watch that meeting to discuss that resolution of resolution that predisposes that this valid item will fail. I don't think that's appropriate and then talks about how the city council after that will come up with ideas like you've had all this time to come up with ideas. So I thought that it was very it was and I spoke out at the public forum I was just like you're saying that people weren't there wasn't a community conversation about this and that's simply false it's false people have been talking about this for some time people were talking about this prior to 2020 right this isn't just about the summer 2020 we have outstanding cases use of force cases still against the city from incidents that happened in 2018. You know for someone whose whose life was forever changed and has a permanent brain injury and and we're still messing with that you know because we what's a fair amount right and of course the city can't talk about the negotiations or anything like that but I as a citizen can see something's wrong that has taken this long to and even just just the sessions his decisions very interesting reading very interesting but it's heavy right because it's a legal determination but the bottom line is aspects of this case can proceed because of the history of racial disparities and that's important for people to read because sessions is not a left-wing commie it's not an extreme progressive you know it because we've thrown around these these terms we've made everything political and all this talk about politics has taken away from talk about solutions and I I know our city councilors can do better I and and they're they're good people with good hearts but because some of this hasn't affected them or affected their families or their friends or people within their communities they don't understand what's happening and they don't fully understand the urgency so that's a concern as well and so you you also mentioned a minute ago that you know discipline isn't always gonna be the answer in response to certain complaints about the police department and I wonder what that means about the role of this board in and and the actions that this board might take what kind of actions do you envision the board could take that look less like traditional discipline and embody some other ways of responding to complaints about the police yeah so I don't know I think we can't say a exactly it's hard to know without specific talking about specific incidents so I can only say in general my hope is that the board would be more effective with accountability like right now there is literally a wall like because it an admission of the need for any type of improvement is seen in my opinion they find it to be either they feel weak they feel embarrassed they worry about liability you know even in the medical profession they have changed about how the way that they handle mistakes that are made you know and how they apologize to people because it's changed that whole issue of of lawsuits and accountability you know we have to start to look at things differently what we have now is not working for us it doesn't work you can keep slamming the door and you can just you know say to people that they don't have the proper experience you know people who are police understand policing and you can understand the difference between right and wrong and we when you think that we're at a point with Eric Gardner okay this can't keep happening you think we're at a point with Sandra Blant oh no this can't keep happening you think we're at a point with Omar Arbery and George Floyd oh no this can't keep happening because even though you had with Omar Arbery you had a former law enforcement officer and then you had cover-ups from the prosecution in that area and there's still some ramifications around that and why the case didn't initially proceed so you think you keep thinking oh it's gonna stop it's gonna stop people gonna understand and now we have Tyree Nichols right there has to be understanding that the status quo has to change and that it's not working and so one of the more controversial elements is that there not be representatives of law enforcement so I think what people need to understand is don't focus on what there isn't focus on what there is there's nothing that says that when you do an investigation you cannot as part of that investigation have witnesses with law enforcement experience and certainly have a lawyer you know we've we've had that experience in the police commission so I know it can work with an independent board but it sometimes you can't if you can't watch your own clothes then maybe somebody else got to come in and do it you know so um yeah that was a pretty simple analogy but it's the best I can come up with and it just says if this you know for me if this department has shown a good faith initiative toward improving accountability instead of attacking the commission that is trying to work on that and saying you're interfering with our public safety because officers are not going to want to come here because of oversight and accountability I'm like what do you want just a warm body I think what does that say how are you supporting our officers that are here what is a caliber officer you bringing in to work with them how are you going to support our new officers who are coming out right out of the academy how are you going to teach them if you haven't improved your process and if you haven't changed your view of things that are actually hurtful so it does affect all of the officers and and saying that you want accountability oversight does not say you don't care about the officers in fact you do care about the officers because sometimes when things get escalated you can end up putting yourself in danger right and we would never as a commission ask any officer to change a response if they need to protect themselves or protect another community member that's never what it's been about it's saying that when you had options because you weren't in danger and another community member wasn't in danger there could have been different choices that would make that better outcomes right so and and you touched a little bit on I know we only have a couple minutes left here but you touched a little bit on something that I've heard from folks in opposition to this ballot item this this initiative which is that the impact of this board might be present a challenge to recruitment and retention of officers right and I wonder if you can speak a little bit to that and and whether you expect that this board will yeah well who do we want to serve here what is that saying about who we want to is to serve and what we're willing to just turn our heads and ignore it's a deep conversation right and people are like to say it's funny because I'm like I'm here you wanted to have the hard conversation I'm right here and they're like oh no we were only kidding what does that say that officers won't come here because of accountability they got a very good contract and I'm not just talking about health benefits and salary which of course all workers are entitled to I would never question that but when we talk about how saving information about complaints and complaint history how long is that information saved it went from one year to two years whoop-de-doo still way below best practice so they and they're delighted with that contract so they have a lot of protections in that contract and I would have liked to have seen more for the community in that contract and the Berlin police officer's contract yeah yeah I would have any can any role in the development of that contract do you think I think you know when the CNA CNA was the the consultant that did the review of the police department came out with their recommendations part of the review of that was to say these are the items that are our direct would be directed the affected by the contract so they have to be part of the contract negotiation so all you can really do is say these are the things that need to be taken into consideration in order to promote community oversight and accountability as well as having a department that is doing best practice and not hanging on to the status quo because that's what's hurting us all it's hurting them it's hurting the community right okay well that about wraps it up here I think we're about out of time thank you thank you so much Milo for joining us and very much yeah thank you for tuning in to town meeting TVs ongoing coverage of local candidates and ballot items for this year's town meeting day you can find this forum and others at our website ch17.tv or on our town meeting TV YouTube channel and most importantly don't forget to vote on her before March 7th and keep in mind that your ballots may not be mailed you automatically this year so check in with your local clerk to request a ballot if needed and thanks so much for watching town meeting TV so long


The last lecture where it is discussed in extensive detail about the resolution refutation method resolution refutation method is also considered to be one of the important decision procedure methods with which one will be able to know whether a given well-formed formula is tautology or valid or when two or three groups of statements are consistent to each other are satisfiable to each other etc all these things one can come to know. So resolution refutation method is also like semantic tableaux method where we looked for a counter example so here what we will do is given some set of clauses which are usually in disjunctions so given these clauses so we will try to prove an empty clause in all so after resolving these clauses in all so one will come up with a empty clause then that proof is called as resolution refutation method so that means you have used the resolution method and then you are refuting it in the sense that you have come up with an empty clause that is the contradiction so in this lecture what we will be doing is we will be studying some more examples based on resolution refutation method and then second in the second part of this lecture we will be talking about comparative evaluation of various methods that we have learnt so far so far we have learnt truth table method to start with this is considered to be the most simplest method and then truth table method we have used indirect truth table method so one need not have to construct all the rows and all it is more or less like a constructive method so especially when the number of rows increases number of variables increases and the number of rows increases then truth table method may not be an effective kind of decision procedure method maybe partly a computer can compute these things in a better way then especially when the number of row number of prepositional variables increases to 4 or 5 more than 5 things will become unmanageable in all for us because for checking the validity you need to check all the rows in which your true premises in a false conclusion that establishes that a given argument is invalid so then we talked about semantic table method and then we try to solve one single problem with the help of all these methods one is truth table method the second is semantic table method and the third one is reducing it into CNF and DNF and the fourth method is the semantic sorry the resolution method and we also use some kind of syntactic methods so that is the natural deduction method where we used conditional proof and the lecture add absurdum kind of proof so what I will be doing in the second part of this lecture is that I will take up one example then I will I will try to solve that problem using all these methods and then when the time arises I will talk about the importance the merits and demerits of these particular kinds of decision procedures that are available to us to start with in continuation to the last lecture here let us take some examples some more examples so that we can understand this resolution refutation method in a better way basically we it is a decision procedure method with which you can establish whether or not a given well formula is satisfiable or unsatisfiable or one can even come to know whether or not a given well formula is a valid or in the same way when you are talking about an argument you will come to know whether argument is valid or invalid so let us consider one simple example where we are trying to find out the inconsistent clauses inconsistent clauses in the sense that all these clauses that is p1 p2 p3 in the first example and the second clause is p1 and not p3 the third clause is not p1 and not p2 whether all these clauses after applying the resolution principle whether it lead to an empty clause or not is the one which we try to look for if you come across an empty clause that is considered to be these clauses are considered to be inconsistent otherwise it is considered to be consistent so now we have these clauses p1 p2 p3 usually this is expressed in this particular kind of format p3 and the second clause is p1 or p3 not p3 usually we write it in this way it is a set which consists of all these clauses and all and the third one is not p1 and not p2 so basically what we are trying to do is is that so these are the clauses C1 C2 and C3 so now what we will be doing is we will be applying the principle of resolution to it and we will find out the resolvent of these clauses now ultimately if we can reduce this empty clause this contradiction then it is considered to be inconsistent all these clauses are considered to be inconsistent so now apply the resolution principle for the first two things like this and this because you have a literal p3 and you have a literal not p3 applying resolution on a literal p3 taking into consideration the other things as formulas p1 p2 p1 etc what you will get is this p1 p2 and this will go away not p3 will go away then you have another p1 so now after applying the resolution principle you have to ensure that there is no redundancy and all for example in this case p1 appears twice enough so this is as good as same as p1 and p2 so now what we got is p1 and p2 so now once again you apply the resolution on these two things for example apply resolution on these two p1 p2 and this one so now you will write it write down here now you have not p1 and not p2 so that is the third clause in all so now applying simultaneously for example so applying resolution principle on p1 that leads to p2 so now once again applying this particular kind of thing resolution principle on these two clauses c1 and so now what we have here you have c1 c2 c3 and this is c4 for example and then c5 now this is as it is c3 only this is c5 so now once again applying a resolution on this one you will get these two on the solution you will get p1 p2 will go away because you have p2 and you have not p2 so that will go away and then so what is left is p3 so now here in this case so once you have this particular kind of thing so now you have p1 here and you have p2 here and you have not p1 and not p2 so now applying resolution on both p1 and p2 simultaneously then you will get this particular kind of clause since you have a literal here and you have negation of this literal here and the same way not p2 here and p2 here so applying simultaneously the resolution principle on both the literals p1 and p2 you will left with only an empty clause so that means that given these three clauses are said to be inconsistent to each other because when it got resolved by using resolution principle it led to some kind of empty clause that is a contradiction so empty clause is always false that means there is no interpretation which makes this particular kind of formula true that means the formula is considered to be unsatisfying so now let us assume that another example where we are trying to check for the validity of a given argument so in the second example that you are seeing this slide so let us try to solve this particular kind of problem by using resolution repetition method so these are the clauses that we have a implies D the first one second one is not a or C or D not a or C or D and the third one is not C or not C or D and a not C or D and a and C and not D C and not D implies not E so these are the clauses C1 C2 C3 C4 etc actually these are not in the actual conjunctive normal form and all you should note that resolution repetition method applies only to those formulas which are in the conjunctive normal form suppose if the formula is not in the conjunctive normal form then we should ensure that we convert it into the appropriate conjunctive normal form so each and every formula that occurs in the preposition logic will have its own corresponding conjunctive normal form so converting any given formula into conjunctive normal form may not be that difficult so now this leads to a conclusion which is not D implies B so now in the resolution repetition method what you will do here is is that given these clauses C1 C2 C3 and C4 and then in addition to that you take the negation of this particular kind of formula so now let us write the converted into appropriate form and on so the first clause can be written in this way because a in place B is nothing but not A or B now the second clause can be written as say as it is it is already in the disjunctive form so we need not have to do much so now the third clause is not C or D so now we need to apply distributive law then it will become not C or D and not C or A so this is a third clause so now the fourth one can be written in this way so now this whole thing is taken as X and this as Y so now this is not of C and not D or not E so these are the clauses that we have C1 C2 C3 and C4 in this particular kind of format and the third one is is that so now what we are trying to do is is that you have listed out all the premises and all and now we take the negation of the conclusion so now negation of the conclusion is not D implies B so first of all not D implies B is same as not not D or B so now if you apply negation to this one so this will become not D and B because not D is D only negation of D is negation of D a negation of disjunction will become conjunction and the negation of B so this is the one which we have so now this can be written as the same as this so now this is the final clause and all not of D or B so now this particular kind of formula we further converted into an appropriate form then it will become same thing will become not C or not not D is D or not E so this formula is same as this one so so now what is that we are trying to do is is that we now we need to apply resolution principle on these clauses and then in addition to that if you take the negation of that one ultimately you need to generate this particular kind of thing the contradiction that is the empty clause if you can generate empty clause and that means you have result with using resolution refutation process you have showed that all these things X1 X2 C1 C2 C3 etc and the negation of this particular kind of formula is unsatisfiable so now what you need to do here is this so now you start applying the resolution refutation method on this particular kind of thing so so there are two ways to prove this particular kind of thing either you resolve this consequence sorry the terms C2 C3 etc now ultimately you will generate this particular kind of formula or you take the negation of the conclusion and show that it leads to contradiction so now so these two for example this will not go to anything not because you are not here now taking into consideration any one of these things so not C or D and not C or A so that means both the things are there so you do not have to write anything and all so in and you can skip this particular kind of thing because all these are premises only all the premises will be in the form of conjunction on C1 C2 C3 and ultimately it leads to some conclusion X so now so where we can apply this particular kind of thing so you have a here and you have not a here so now what you will do is not a or B and not C or E so now you have listed out C1 and C4 for example so now these two resolution you will get B resolution applying on this particular kind of literal A leads to B or B or not C these two you will get this one so now you apply resolution on these two things not C or D and B or not sorry not this one so where else we have literal and its negation is the one which you need to take into consideration so now B or so now this will become B or not C now here you have C here and you have not C here so now you write it like this not A or C or D so now these two applying resolution principle it is applying on C then the C will vanish so now what you have is B or not A or D because C vanish vanishes here because you have not C here and C here so applying resolution principle on the literal C you will generate this B or not A so one can apply resolution principle many times and all ultimately in the process you should be in a position to generate whenever you come across an empty clause you need to stop the proof procedure and then that is that will serve as a proof for this particular kind of dinner of the conclusion leads to contradiction so now so now observe these two things so here we have not D and anyhow not B so that is what we have so not of D or B means not D not B so now applying the for the first thing for the not D you will get your applying resolution principle on D you will get B or not so this is what you get now once again applying a resolution principle on not B which is there already then this B and not B goes away and then you will get not so now we need to see whether we will generate a from some other things like so now you have not C or A and then you have not A so this leads to a particular kind of thing so B or not C not A or C or D so now we need to apply on this thing so not A or C or D not C or D and then somehow we need to take these clauses in such a way that you generate this empty clause so now instead of for taking this into consideration now you take this B or not C and not B so these two you will generate not C so this is what you generated from not B B or not C so now apply this particular kind of thing now not A and not C or A these two and under resolution you will get not C not C or A is not serving our purpose so somehow we need to get this particular kind of D or A B or not A not B you will get not so get this one is which we are trying to look for not A or B not here C or D so not C or D C or A etc. Somehow we did not still generate this particular kind of contradiction you take into consideration this is not not D or B not D and not B and not of D or so this and for example in this case not C or D and then not D this will you will generate not C and this one not C and not A or C or D you will get these two on resolution you will get this particular kind of applying resolution on C you will get not A or D so ultimately what is happening here is that we have applied result resolution n number of times and all somehow we are not able to generate contradiction C and not D or E not of C and D so if you can generate contradiction out of these four clauses and all then your proved not D implies B negation of not D implies B leads to unsatisfiability and hence you are said to have shown that true premises and a false conclusion that is an invalid kind of argument and all so somehow this needs to be worked out in greater detail I will come back to this problem in a while from now so what we will be doing is we will take up one simple problem and then we try to see how this problem can be solved in three different ways you know that is using the different decision procedure methods that we have learnt here. So let us consider some one more example and with which we will come to know how to solve this particular kind of problem by using various kinds of method so the one which is explained on the board in the first problem so ultimately what one needs to solve here is there so you apply resolution on in N number of steps and all and then resolve those things and ultimately so that has to be contradictory with this particular kind of thing so then you are said to have achieved your particular kind of task. So here what we have done simply is that we started applying resolution principle on different kinds of conjuncts and all ultimately we generated some kind of formulas so somehow we are not able to get to our conclusion that is the empty clause suppose if you do not get this particular kind of empty clause after applying the resolution exhaustively apply this resolution on all these steps and all then the argument is considered to be invalid. So now let us consider another example so we will see how we can apply this resolution principle in solving this particular kind of problem not a or b yeah this is what is creating problem here so I made a mistake here so that is the reason why I am looking for the solution here actually this is not of a implies B. So now this will become a or not not a means a or B so now as you can clearly see here so now we need to apply again and all so this problem changes in all so if it is simply a implies B and not a or C or D then there is no way in which you can generate a contradiction here that means the argument is going to be invalid that means not D implies B does not follow from this one so the actual problem which I could have taken for proving the validity of this given argument is in this sense so this negation is missing here if you take the negation sign here then by applying resolution principle then maybe one can come up with a kind of repetition so let us try to see this try to solve the same kind of problem by taking into consideration this negation sign and then we try to solve the same problem with the help of other methods so actual problem is this one negation of not not a implies B and not a or C and then not C or E and F not C or E and F this problem is different in all so forget about this thing so now let us come back to a different kind of problem this this problem will try to solve it by using different kind of methods so let us consider a simple example so this problem is the one which we have already seen so this is like this here is a puzzle in which there was a robbery in which lots of goods was stolen and the robbers left in a truck and it is known that nobody else could have been in all other than ABC that means it is simply represented as A or B or C and C never commits a claim without his participation that means C implies A and B does not know how to write that means B requires the company of A and C so this is represented as B implies B and A or B and C so now we need to find out whether A is innocent or guilty now this problem we try to solve it by using various kinds of methods first we will start with the simple resolution refutation method so in that method what we will be doing is we will be listing out all the all the conjunctions in all and we will start applying the resolution refutation method on this particular kind of thing so then if we can generate an empty clause from these things and that means we are said to have achieved our particular kind of thing so what is that we are trying to do here in this example is like this so here are these conjunctions all A R B R C so now what I will be doing here is that I will be trying to solve this problem by using one of the some of the methods that we have already discussed so far so the first C 1 clause is like this and second clause is C and A sorry C R A and the third one is B implies B and A R B and C so now this is already in the disjunctive form this is also in a this consists of disjunctions and now we need to convert this thing into appropriately into corresponding disjunctive form so now this whole thing is taken as X and this is why so now this will become not be R the whole thing B and A R B and C so now you need to apply associative law here so now this will become not B R B and A that is the first one and the second one is not B R is R not B R B and C so now these are the things which we have and then we can further expand it in this way using distributive law here so now this will become not B R B and not B R A so this is the first one if you apply distributive law this is the thing now R now the other one that is not B R B not B so this is not B R B and and not B R C so this is the one which we have so so what are the clauses now for us so these are the clauses that we have first one is A R B R C and not C R A and the whole thing so now in this case not B R B is obviously is going to be true only so you need not have to worry much about it is it is written as top always true and all so now whatever is left here is these things not B R A R again here not B R B is always true and all so we need not have to worry much about it so and then not me or C so that means not B R A and then the other clause is not B R C so now one can do it in various ways and all applying resolution principle on this one whether you will get a as an outcome or not that is a problem that is a question that we are trying to answer here so each resolvent is considered to be a logical consequence of the above two clauses so now so these are the clauses that we have C1 C2 and C3 so now the conclusion here for us is that now we are trying to find out whether or not a is guilty so assuming that a is guilty suppose if you take into consideration that not a whether that is inconsistent with this thing or not is on which we are trying to see so now A R B R C and this one so now we need to apply the resolution principle on this one so now these two applying resolution on little C you will get not B A R not B so because not C will go away so what is left is A R not B so you have to add those two things it will become a R not B so now applying resolution on these two things you will get applying resolution on the literal B you will get A R C R A so now in order to avoid redundancy here so you will simply write a occurs twice here so you will just simply write A R C so now this is what has come as an outcome of these resolutions so now you apply resolution on these things not C R A applying resolution on the clauses A R C and the clause that are that is there here not C R A so now the C and not C will vanish then you will get A R A so now this A R A is in order to avoid redundancy not we simply write A so what is that we got we listed out all this the information that is there here is the first clause AR B RC and not C R A and then the third clause is this one so we simplified this thing into this particular kind of format by using distribution and associative law and here is what we got so we got it because of this particular kind of thing not B or B is always true so you not have to worry much about it so what is left here is not B R A and not B RC that is what we have written here is the two clauses and applying resolution on C 2 and C 4 that means this is a logical consequence of these two clauses C 2 and C 4 we got AR not B and again applying C 1 and let us say this is C 5 and all resolution on C 1 and C 5 we got AR not AR C and we already have this particular kind of thing not C R A so that is what is already there and now again once again you apply resolution principle on this particular kind of thing concerned with the literal C whenever you have a literal C and negation is there it cancels annihilates then what is left here is AR A so AR A in order to avoid redundancy we got AR. So A is the one which we got it as an outcome of all these propositions that means A is in the original interpretation A means A is guilty if it is not here if you somehow you generated not A as a result of applying the resolution here then not A means A is innocent so now the same particular kind of thing which can be this can be solved by using the semantic tablux method as well we can show that whether or not is a guilty or not so now in the semantic tablux method what you need to do is this thing so these are the three propositions that we have so now we are trying to say that A is assuming that A is guilty so now we are assuming that suppose let us say A is the conclusion from this one and there are two ways to solve this particular kind of problem using the semantic tablux method semantic tablux method always look we look for the counter example that means if you assume that A is guilty in the beginning then what you need to do is you have to consider not A and then you constructed semantic tablux tree and then you need to generate a contradiction. So now you list out all the premises not CRA and B implies B and A are B and C so I am comparatively evaluating checking this particular kind of problem with various methods so that you will come to know the merits of these methods so now right now I am trying to solve the same problem by using semantic tablux method so now you list out all the premises in all so now the problem tells us that these are satisfiable that means all these statements are consistent to each other at least under some interpretation this formula is going to be true x1 x2 x3 so now you expand use treat rules and all to expand this particular kind of thing so now so you apply this one x implies y then it will become not x and y so this will become not B and this is a B and A are B and C so now so this is over now this can be further simplified into this thing so either it is B and A or it should be B and C now this we checked it and all so now we need to look into this particular kind of thing so now wherever the open branch is there you need to write this particular kind of information so since this is a branch it will be like this not C or A and here also you write the same information and every branch which is open you need to write this particular piece of information so now each time you finish with checking with this formula you need to see whether a literal and negation exist in a branch so this is considered to be one branch is considered to be one branch like this so now in this case we do not have we do not still have a literal and negation all the branches are open so now apply rule for this particular kind of thing a RBRC so then this particular kind of information needs to be written on every branch and on like B and C so this information a RBRC we have written it under whatever branch which is open so now so this is a RBRC a B or C B and C like this B and C so now we need to inspect all these branches and all wherever a literal and negation occurs the branch closes so now this brand goes like this a0 C0 B so that branch is open so now you have B here and not be at this branch closes here and C and not see this closes here itself and now this branch is open now you have B here and not be here this branch closes and this is also open so now you have a0 C and a B and there is no C here that means this branch is also open and this is also open but you have here you have C and not seen this closes it is a big branch in all so sometimes some resolution refutation method might be better than the semantic tableaux method because the number of branches are more here so in the resolution refutation method we have seen in the last slide that that will simplify our task you know so now here this is also open these also open and all the open branches suggest us that that makes this formula true and all that means if you observe this particular kind of open branch this says that under the interpretation in which a is true C is false sorry this branch closes here itself so need not have to worry about it because your BC here and then not see here this closes here itself so you need not have to worry much about whatever follows so now in this case all the branches are open so now open branches tells us the answer and all that satisfies this particular kind of formula so now any open branch which you take and take into consideration the first one is like this AC and not be so that is the first thing and the other open branch you will find it here a not be and we do not know whether about C in this particular kind of branch so this is the first one second one and third one and the third one is a not see and be also another kind of solution and then the other one is AB so this is the one which we have and other things are AB again the same thing which you need not have to write again another thing which satisfies this formula is AC and B and the other branches are like this ABC and BC we do not know about a here so now the last one is this thing ABC which is already we have listed so all these things are considered to be the interpretations which are going to satisfy this particular kind of formula that means when A is true C is false B is false that makes these three sentences true and in the same way when A is true B is false that also satisfies this particular kind of formula so now in all these cases you will observe that you have turned out it turned out to be the case that we got only AM so that means that usually A is considered to be guilty so our interpretation is that when I write simply a that means a is guilty when I write simply not a that means a is considered to be innocent so now the same kind of thing can be solved by using truth table method in the but in the truth table method the problem is that you have three variables that means number of entries would be eight eight rows will be will occur in the truth table so now in the truth table what you need to look for is a row in which all these statements are considered to be true that means conjunction of C1 C2 C3 whenever that is true and all so that row corresponds to our particular kind of answer the same thing which you might get it so a particular kind of example it can be done in n number of ways and all so so there in the natural deduction what you will do here is that from A or B or C and not CRA and all these things so what essentially you do here is that you list out all the premises in all so now we need to assume something in all here suppose if you start with a is guilty in all so that is the original conclusion so you need to assume something other then you take the negation of this thing into consideration and then see whether that leads to contradiction or not so for example in this case you list out all these things and all A or B or C is CRA etc and all so what essentially one needs to do is by taking all these premises and all ultimately you should be able in a position to deduce a in that case a follows from these things with using resolution refutation method we showed that a will come as a logical consequence by applying the resolution principle so in the natural deduction method what you will be doing is you will be using the principles of logic like modus ponens modus tollens etc and all and then you will generate something like a and all from these things so let us see whether we can deduce a from this particular kind of premises so now for so you have a or B or not see and you have not see are a so from these two things you will get of course A or B or C and not C or A so from this you will get a or B or B or A so in order to avoid redundancy you will write it only once and all so this will be a or B simply A or B so this rule is which we have discussed earlier this rule is called as cut rule so that says that alpha or gamma not alpha or beta suppose if you have a formula like this then so this will become gamma or beta this is called as cut rule which is also the rule responsible for the resolution principle the same rule which we apply here then you will get a or B so 1 and 2 this is a kind of modus ponens rule it is a special kind of rule you can use any rule which preserves the truth that you can use here so now so now this means something is A or B is true means definitely some one of these things should be true and so assuming that B is true here irrespective of whether A is false or A is true let us assume the B is true and all so now these two three and five modus ponens you will get B and A or B or C so how did you get this one three and five modus ponens you get this so now some of we have to reduce A as an outcome of this particular kind of so now from this since this is true and all B and A and B are C is already true so that means even B and A is also true because of this particular kind of thing X and X or Y is going to be true when both X and Y are true or even in the case in which one of the disjunct is false also then that also it leads to this thing so now since B and A is the case so now from this you can eliminate this conjunction, conjunction elimination rule which we use and then from this you will get this one conjunction elimination rule you will get a that means we have reduced A from these three premises you know using a kind of proof method which is called as natural deduction method so now you have to note that in this particular kind of method each step is considered to be the assumptions are obviously considered to be true and then if that has to be true this also has to be true each step is considered to be true and hence the final last step of your proof which is considered to be a theorem so that also turned out to be true so this is another way of showing that in this particular kind of problem A is said to be guilty in all in this particular kind of way so there is another way of doing this particular kind of thing within the natural deduction method so now what you do here is this particular kind of thing so now assuming that let us assume that A is guilty in all so now for the sake of argument you take into consideration not A that means you are assuming that A is not guilty so now we are trying to come up with some kind of contradiction so now so on the fourth step since not C or A and you have A here so this option is ruled out what you get is not see so now in the second principle so how did you get this one not not a is denial of conclusion so now you got from 2 to and 4 you got this not see so now since not a and not see are true you have not a and not see is also going to be true so now seven step not a and not see so now these two so from this particular kind of thing not see are a is already true that means a is also considered to be true and from this particular kind of thing we can take into consideration assumption that a is also true so now you have you have come across a situation where you are not a is true and a is also true so that means this leads to a contradiction that means the negation of this particular kind of formula a assuming that a is considered to be not guilty needs to this particular kind of contradiction so in this lecture what we have done is simply this that we started with some examples of resolution refutation method in that method what we essentially show is if I want to show that a given argument is valid then what you need to do is given these clauses there are the premises you add the conclusion to it the denial of the conclusion and then you will be deriving an empty clause if you can derive empty clause from that one that means denial of this particular kind of formula the denial of the conclusion is unsatisfiable that means the original conclusion holds so that is one way of showing that given argument is valid in case using resolution refutation method so then in the second part what we have seen is we have taken up one simple problem that exists in the prepositional logic and then we showed with various methods the methods that we have with which we have shown are semantic tableaux method and we also shown the same thing by using a syntactic method that is a natural deduction method with which we showed that in fact a is considered to be guilty that is what we have deduced from a given set of premises that is a natural deduction method the same kind of thing which we did not show in this class is that we can show the same thing with the help of truth table method that means you list out all the premises and then you assume that not here and then you will come across a row in the truth table in which your true premises and a false conclusion so in that case you can show that this argument is invalid that means not a leads to contradiction that means a has to be true so in this sense one can solve the same problem by using any one of these decision procedure methods it is all up to our convenience which method to employ so in some cases natural deduction method might be simpler or in other case semantic tableaux method may be better or in some simple cases to begin with truth table method face better than other methods are in some other cases resolution refutation method especially when you have conjunctive normal forms then you can straight away apply the resolution principle and simply get your answer because each resolvent is considered to be a logical consequence of the conjunctions that you are taking into consideration that conjunction is nothing but each conjunction will have its own corresponding disjunctions so that is what is in a conjunctive normal form so in the next class what we will be doing is that we will be taking up the axiomatic propositional calculus in that what you will be doing here is that we will be taking into consideration the primitive axioms and then we will be using as many little as many minimal kind of principles and all like only modus ponens is the one which we use and we use transformation rules and then we will reduce all the valid formulas within your logical system so in the next class we will be taking up the axiomatic propositional calculus there we will study two axiomatic systems one is due to Russell and Whitehead that is in the Pinkipia Mathematica and the second one is due to Hilbert and Ackerman Hilbert Ackerman axiomatic system.


Welcome to Digital Asset News or Dan for short. My name is Rob. And today I want to talk to you about is the upcoming deadline for taxes. Now, there's been an extension here in the U.S. October 17th is the last day to file your taxes, which is six days away.  You don't really like to pour over all those different spreadsheets. And the reason I also bring it up is because the IRS is really cracking down on us. They've added 87,000 new agents. And this was just in August 11, 2022. And the reason they did that was because of the Inflation Reduction Act, which passed the Senate on Sunday and was also passed by the House later. It raises taxes and will give the IRS billions to go into the Wall Street Journal called Beast Mode. The bill will dole out about $80 billion to the IRS for increased enforcement, operational improvements, customer service and systems modernization. That is six times the current IRS budget of $12.6 billion. So look, I personally have been audited by the IRS. Do not go through that. It would behoove you to file your taxes.  I just make it simple. What I've done the last two years is I've used coin ledger. Very simple. From the time that I integrated all my exchanges, all my wallets, all the NFTs and all the DeFi projects and all that stuff. And I put it in. It took me 30 minutes. 30 minutes to get a spreadsheet that I shipped over to my CPA. She got it done. Bing bang boom. And I am out of here. So I've already done a video about this, which is pretty comprehensive. There's a link in the description. It looks just like this. And you can watch the video. It goes over a lot of things. What I want to do is just do a down and dirty real quick video about what coin ledger is and how it works. So quite simply, you're going to import your transactions. And what's pretty cool about this is that it's every different wallet, DeFi or exchange you can think of. It's all right there.  And this is like all the ones they have. There's a lot of things I've never even heard of in my life here. Double X, Coinal, was your ad for that one. But again, everything you think of is pretty much right there. And on top of that, once you're done with there, you're going to preview your report. And what I thought about was cool is this. It'll show you your capital gains, short term and long term, your total, cost basis, all that stuff. And what I thought was cool about this was that it is absolutely for free. So you can view your gains and losses before you print out your report. So before you pay for a tax report, you'll have the opportunity to view your cap gains and income for free. I like free. I think you might too.  And the question you might have is, well, how much does that cost? Well, quite simply, it's very simple. If you have 20 or so transactions, you probably don't need coin ledger. You don't need it. It's very simple to do taxes yourself. Now, you might want to do it for cost basis analysis. That's fine, which they offer. But for 100 transactions, it's about 50 bucks, 1,500 transaction, 99 high volume. This one that I use is $200 and unlimited is $300. You get all of it done. Very easy, very smooth. So I've done two years, worked out like a charm. And then also, what I like about this is that you can file yourself sent into your account or import to your filing software, again, TurboTax or tax app, whatever you want to do. And then finally, I will say this, even though we're talking about the US, this is all this is good for international. If you go to learn CryptoTax 101, USA, Australia, Canada, UK, India, Ireland, Germany, New Zealand, whichever one works for you or wherever you live, they've got a solution for you. And then if we take a look on top of that, what I really like about this is that they've got this to track the cost basis and historical prices. You can automatically track the cost base of your assets. So am I in profit? Am I in loss as they move from one wall to another? And you can kind of take a look at that. And that also is available for free. So lastly, I will just say this, it's not a fly by night company. I mean, they have 300,000 users. I wanted them for two years straight. They've processed 70 billion and 50 million has saved through tax loss harvesting, which if you're familiar with that, is a pretty big perk. And that's it. So look, I just want to do this really quick just to show you what's going on and the options that are available to you. If this is something that could you could use as a link in the description looks just like this, and you can sign off and pull your reports. But that's it for today. So if you like today's video, do me a favor and give it a thumbs up. That would be great. Also, consider subscribing while things talk about our time sensitive. But that's it for today. So thanks so much for stopping by. I appreciate it. And I'll see you on the next one.