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Re: [aima-talk] Quasilogical Form & "type"

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  • Peter Norvig
    Thanks for your questions. The quasi-logical form is all about semantics in logical form, so sentence means a sentence in logic (and is unrelated to the
    Message 1 of 2 , Jan 10, 2002
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      in logical form, so "sentence" means a sentence in logic (and is unrelated
      to the grammatical notion of sentence in language), like
      Smelly(cheese). An object is a logical object, like cheese. (It is
      unrelated to the idea of object-vs-subject of a verb.) Smelly is a logical
      predicate. The logical form for the adjective "smelly" is lambda x
      Smelly(x), and the type is object -> sentence, which means if you apply it
      to an object, such as cheese, you get back a logical sentence: (lambda x
      Smelly(x))(cheese) is Smelly(cheese).

      You ask about "I sleep". The trick is that the semantic form for each
      sense of each verb has the right number of missing arguments. For "sleep",
      there would be only one missing argument: lambda x Sleep(x). Then the rule
      S(rel(obj)) -> NP(obj) VP(rel)
      for the sentence "I sleep" gets parsed as
      S(Sleep(Speaker)) -> NP(Speaker) VP(lambda x Sleep(x))
      so Sleep is not an object, it is a predicate. Speaker is an object, and
      Sleep(Speaker) is a sentence.

      Does that help?


      At 06:38 PM 1/10/2002 +0000, sinuously wrote:
      > Okay, I confess I have skipped around in the book. After all it
      >borrowed from a friend, and I only meant to read about language
      >parsing, and then one thing lead to another - but if I've missed
      >something the index hasn't helped me sort out where to find the
      >missing pieces. So far I've read chapters 6, 7, part of 8, and 22 up
      >to this section. But, to the point:
      > I cannot figure what is meant by the "Type" column in table 22.17
      >on page 678 (20th printing). The note says that the arrow notation
      >specifies a function that takes an argument of type "t" and returns
      >type "r". But for two places, where the notation appears it takes
      >object(s) and returns a sentence. In fact they all return sentences.
      > So in what sense do they return sentences, or more broadly in what
      >sense are these "types" defined? Grammatically? If so then an
      >adjective would take an object and convert it into a noun phrase
      >'lambda x Smelly(x) (cheese)' would take a noun symantically
      >representing cheese and return a noun phrase symantically
      >cheese that smells. This doesn't fit the table, so I turn to the
      >notion that it is merely taking a predicate object and returning an
      >atomic sentence; presumably returning the proposition that some
      >object, like a cheese that might be specified, has strong odor.
      > The relationship which makes it a sentence would have to be an
      >implicit one between an unstated strong odor object and a cheese
      >object, e.g. has(strongOdor, cheese), or HasStrongOdor(cheese).
      >I guess is the same as Smelly(cheese), which proposes a unique
      >relationship between an intrinsic smell and a specified cheese. This
      >actually makes more sense, especially as other argument types or
      >constants are 'object', 'event', and 'quantifier', constructions
      >extended from predicate logic (though 'number' seems previously
      >unintroduced ).
      > But if that is what 'sentence' refers to, what is the relationship
      >implied in the sentence "I sleep", which has a subjective noun but no
      >objective one? I sleep with me? I have sleep? Can sleep even be an
      >object, poetry notwithstanding? It's all rather vague, and
      >because I don't know what I can ignore there is a lack of utility,
      >which bugs me, so I can't help but think that I haven't gotten the
      >gist of this.
      > All in all the domain and range of this 'function' mapping is not
      >well explained, unless I am to take the sections immediately leading
      >up to it as explanation (it which case they haven't been focused
      >enough). Which is a shame because I suspect the Type column is there
      >to *help* focus the concepts, not to introduce new unknowns.
      > So please excuse any implicit criticisms, as I'm sure they are
      >of my own ignorance, and please tell, someone, what does this column
      >In hopes of Illumination,
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