special marker indicate data value exist database introduced creator database model serves fulfill requirement true database management systems support representation missing information information introduced use greek symbol represent database theory reserved identify special marker confused value value indicates lack value lack value thing value zero way lack answer thing answer example consider question books juan answer zero know owns know owns doesn database table column reporting answer start value marked updated value zero juan owns books state unknown value usage different programming languages means assigned particular instance history mentioned method representing missing data model paper paper commonly cited relation adopted paper introduced proposals paper remained obscure section paper details propagation operations comparisons employing valued logic comparing details treatment set operations issue controversial today database theory circles original proposal referred tables later reinforced requirement support indicate missing data article published magazine standard basically adopted proposal implementation prototype system recognized alongside duplicate rows controversial features defended design pragmatic arguments expensive form system support missing information saving programmer application level checks problem time providing database designer option use desires example order avoid known discussed section article argued providing missing value functionality practical experience led language features rely like certain grouping outer joins finally argued practice end quick way patch existing needs evolve original intent missing information example database quickly needs support electric cars having miles column indicated book model database management version single mandated standard inadequate replaced separate type markers indicate reason data missing book type markers referred values values representing missing applicable missing respectively recommendation required logic system expanded accommodate valued logic system additional complexity idea multiple different definitions gained widespread acceptance database practitioners domain remains active field research numerous papers published challenges focus controversy source debate associated valued logic special requirements use joins special handling required aggregate functions grouping operators computer science professor der summarized issues inconsistencies standard mean possible intuitive logical treatment proposals resolving issues complexity alternatives prevented widespread adoption propagation operations data value marker absent value mathematical operators gives unknown result represented following example results lead results instance attempt divide zero platforms return instead throwing expected data exception division zero behavior defined standard vendors treat operation similarly instance platforms return result following string string operations common result following example demonstrates result returned string operator true database example string considered thing fish chips results fish chips comparisons valued logic member data domain considered value marker indicating absence value comparisons result true false logical result unknown logical result expression compares value unknown certain operations return values absent value relevant outcome operation consider following example case fact value left irrelevant outcome operation true regardless value left logical results provide specialized valued logic rules governing valued logic shown tables represent logical states truth tables uses correspond common fragment valued logic differ definition defines operation effect unknown clauses valued logic encountered data manipulation language comparison statements clause causes statement act rows true rows false unknown acted insert update statements discarded select interpreting unknown false logical result common error encountered dealing following simple example demonstrates example returns zero rows comparison column returns unknown rows unknown result causes select statement row practice tools retrieve rows comparison specific specific comparison basic comparison operators return unknown comparing standard provides special specific comparison use test data standard contains extension truth value tests introduces additional logical operators fact count following truth tables extension presence discussed later article despite similarities introduce valued language extension actually present introduced standard extension implemented systems implementing addition unknown operators valued logic makes valued logic complete meaning logical operators express combination valued logical function systems don support extension possible emulate unknown going argument expression unknown test arguments specific functions law excluded fourth clauses valued logic law excluded middle longer true precisely valued logic unknown precisely unknown true direct comparisons result unknown logical value following equivalent column contains case second return rows return classical valued logic law excluded middle allow clause fact elimination attempting apply law excluded middle effectively false second actually equivalent correctly statement requires return rows view observe clause similar law excluded middle written assuming unknown operator present unknown true called law excluded fourth expressions obvious false dilemma occurs example produces rows translates version equality argument set unknown unknown cast example needed like reject type checking error systems plain select works missing case course effect unknown joins joins evaluate comparison rules clauses care taken columns join criteria particular table containing equal natural self join meaning formula true relation self join exclude rows having example behavior given section analyzing missing value function case expressions simulate equality join criteria join criteria following tests equality values treats equal case expressions provides expressions called simple case operates like switch statement called searched case standard operates like simple case expressions use implicit equality comparisons operate rules clause rules simple case expression check existence directly check simple case expression results unknown following expression unknown matter value column contains contains string returned hand searched case expression use like conditions following example shows use searched case expression properly check searched case expression string result returned rows dialect provides built function instead simple case expressions considers equal finally return match found default clause statements procedural extensions persistent defines procedural extensions statement major vendors historically included procedural extensions procedural extensions comparisons operate comparison rules similar statements following code fragment standard format demonstrates use statement statement performs actions comparisons evaluate true statements evaluate false unknown statement passes control clause finally clause result code message result unknown comparisons evaluate unknown analysis missing value groundbreaking work provided framework evaluate intended proposals implement missing value section roughly follows chapter alice textbook similar presentation appears review der selections projections weak representation representing missing information tables actually intended represent set relations possible parameters case tables means replacement concrete value example construct table said strong representation system missing information answer construct obtain answer corresponding relations represents seen models construct precisely formula formula pure relations formula lifting construct intended represent missing information strong representation property table construct formula lifts answers construct formula hold taking number tables arguments restriction table discussion clearly tables strong property selections projections considered language example answers include possibility relation like exist tables represent result possibly rows device theoretical interest called table table represent answer condition column interpreted row doesn exist condition false turns condition column table arbitrary logic problem table represents concrete relation complete complexity little practical worth weaker notion representation desirable introduced notion weak representation essentially allows lifted construct return representation sure information valid possible world models construct construct weak representation system formula right hand equation sure information information certainly extracted database regardless values replace database example considered easy intersection possible models sure information selecting age actually instance returns rows relation generally shown tables weak representation system language restricted projections selections renaming columns soon add joins unions language weak property lost evidenced section joins unions considered weak representation let consider following table previous section concrete value choose age return column names model lifted run missing unions added language tables weak representation system missing information meaning don report sure information important note union discussed later section come play nature sub took guarantee sure information went run table natural joins example needed sure information slightly complicated consider table happens tables representing projections lose track fact columns actually copies originals table observation suggests relatively simple improvement tables works correctly example use meaning functions constant functions instead single symbol approach called tables naive tables expensive tables discussed complete solution incomplete information sense tables weak representation selection set difference example considered section negative selection clause age example tables report sure information check constraints foreign keys primary place valued logic intersects form check constraints check placed column operates slightly different set rules clause clause evaluate true row check evaluate false logic perspective designated values true unknown means check succeed result check true unknown following example table check prohibit values inserted column allow inserted result check evaluate unknown change designated values relative clause logic perspective law excluded middle check constraints meaning check succeeds furthermore assuming interpreted existing unknown values checks like allow replaced non value order column reject applied shown example equivalent check default check constraints foreign keys succeed fields keys example table allow rows author author table authors defined contains precisely fields allow value found authors table example authors contained john smith satisfy foreign key added extra options matches cases match partial added references declaration non match foreign key match smith finally match added smith match match outer joins outer joins including left outer joins right outer joins outer joins automatically produce missing values related tables left outer joins instance produced place rows missing table appearing right hand left outer join operator following simple example uses tables demonstrate production left outer join table employee contains employee numbers names second table contains related employee numbers phone numbers shown following sample performs left outer join tables result set generated demonstrates uses values missing right hand table shown aggregate functions defines aggregate functions aggregate calculations data count function aggregate functions perform elimination step included final result calculation note elimination equivalent replacing zero example following table average values different result average average known effect equivalent sum count equal grouping set operations defines markers unequal special definition required order group performing certain operations defines values equal distinct definition distinct allows group sort group clause perform grouping operations clauses use distinct treatment include following partition clause ranking functions like row intersect operator treat row comparison elimination purposes distinct select principle aren equal result unknown effectively violated specification union operator identify consequently set operations like union difference produce results representing sure information unlike operations involving explicit comparisons clause discussed proposal basically adopted arguing removal set operations happens lower level detail equality testing evaluation operations standard explicitly define default sort order instead systems data values clauses order list respectively vendors implement functionality vendors implement functionality specify different treatments effect index operation products index keys containing instance versions prior documentation tree index stating trees handle equality range data ordering particular consider tree index column involved comparison operators equivalent combinations operators implemented tree index search note equivalent cases index excluded index enforced quoting documentation index declared unique multiple table rows equal values allowed considered equal unique index reject cases columns equal rows consistent defined behavior comparisons method involves handling distinct accordance defined behavior example documentation states following purposes compare equal unique index unique created keys row select columns defined columns unique index unique chosen strategies consistent defined behavior explicitly defined standard strategies left entirely vendors design implement handling functions defines functions explicitly handle functions searched case expressions function accepts parameters equal second returns value returned following case expression function accepts list parameters returning value list defined following case expression implement specific functions similar systems implement function similar functions similar functions functions function accepts parameters returns non parameters expression converted equivalent expression turns use case function replace expression value like salary says salary replace value notable exception parameters reaches non parameters important reasons non function expensive invalid create unexpected effects data unknown literal meaning designated character specific data type mandatory desirable explicitly convert specific data type instance functions supported able automatically resolve correct function knowing data types parameters including passed conversion literal specific type possible cast introduced example represents absent value type actual unknown distinct varies example following successfully environments unify unknown fails similarly regard minor exception regards true false different ordinary additionally unknown test value logical outcome unknown merely sugar data type standard introduced data type optional non core feature coded restricted works like type languages despite hold truth values true false unknown defined according standard standard asserts unknown mean exactly thing type subject criticism particularly mandated behavior unknown literal equal identification discussed implementation represent unknown results including unknown implement unknown literal implement unknown operator feature major vendors support type defined procedural supports assigned value considered unknown controversy common mistakes misunderstanding works cause great number errors code standard statements specific supported real world database management systems mistakes usually result confusion zero string string value length zero represented defined standard different string numerical value indicates absence value string numerical zero represent actual values classic error attempting use equality operator find execute following correct error message returns rows regardless exist table related subtle example clause statement compare column value constant incorrectly assumed missing value equal constant field contains fact expressions return unknown example similarly confused strings consider length function returns number characters string passed function function returns lead unexpected results users value logic example complicated fact database interface programs database like reported string strings incorrectly stored criticisms implementation subject criticism debate calls change model database management version suggested implementation flawed replaced distinct type markers markers proposed stand missing applicable missing known values values respectively recommendation accepted required implementation valued logic suggested adding additional type markers recommendation indicate reasons data value missing increasing complexity logic system times proposals forth implement multiple user defined markers complexity handling logic systems required support multiple markers proposals gained widespread acceptance authors manifesto suggested implementation inherently flawed eliminated altogether pointing inconsistencies flaws implementation particularly aggregate functions proof entire concept flawed removed model like author stated belief function calculation treat missing values governed model closed world assumption point conflict concerning violate closed world assumption model introducing open world assumption closed world assumption states stated database explicitly true false view assumes knowledge world stored database complete operate open world assumption items stored database considered unknown making database stored knowledge world incomplete
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