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Vivid Knowledge and Tractable Reasoning

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Vivid Knowledge and Tractable Reasoning Vivid Knowledge and Tractable Reasoning Preliminary Rep ort David W Etherington Alex Borgida Ronald J Brachman ATT Bell Lab oratories Department of Computer Science Henry Kautz Mountain Avenue Rutgers University ATT Bell Lab oratories Murray Hill NJ New Brunswick NJ Murray Hill NJ Abstract intractability of such systems have generally fallen under two headings limited languages eg PatelSchneider Mundane everyday reasoning is fast Given Borgida et al and limited inference eg the inherent complexity of sound and com Frisch PatelSchneider In the former what plete reasoning with representations expressive can b e expressed in the knowledge base KB is restricted enough to capture what p eople seem to know sometimes severely to guarantee that queries can b e commonsense reasoning must require shortcuts answered in more or less reasonable time In the lat and assumptions Some means of simplifying ter restrictions like avoiding chaining or fourvalued in the retrieval of the inferential consequences of terpretations yield limited conclusions alb eit from rela a set of facts is obviously required Instead of tively expressive KBs lo oking as others have at limited inference or We conjecture that a key to ecient problemsolving syntactic restrictions on the representation we lies in a notion of commonsense reasoning the kind of explore the use of vivid forms for knowledge reasoning that p eople engage in all the time without re in which determining the truth of a sentence is course to pap er and p encil reasoning by cases back 1 on the order of a database retrieval tracking or particularly deep thought Commonsense reasoning is fast if it were a problemsolvers normal In order to base a reasoning system on mo de of reasoning then the problemsolver would b e vivid knowledge we consider ways to construct fast Paradoxically studies of commonsense reasoning a vivid KBa complete database of ground in AI eg nonmonotonic logics have frequently led to atomic factsgiven facts that may b e pre mechanisms that are even less tractable than logical de sented in a more expressive language that al duction lows incompleteness eg rstorder logic Be This pap er describ es an attempt to bridge the gulf b e sides oering an architecture for examining tween principled theories of inference and practical infer these problems our results show that some forms of incomplete knowledge can still b e han ence systems We discuss some comp onents that might combine to supp ort fast reasoning and a uniform ar dled eciently if we extend a vivid KB in a chitecture that incorp orates them Obviously common natural way Most interesting is the way that sense reasoning is inherently approximate and fallible this approach trades accuracy for sp eed Our architecture lets us move towards commonsense p er formance and yet still say something substantive ab out Intro duction the systems relationship to ideal comp etence People p erform quickly and comp etently in most ev eryday situationsdespite an overwhelming barrage of Vivid Reasoning information that nonetheless do es not unambiguously What would b e a go o d basis on which to build a characterize the state of the world In contrast com fast reasoner Given the massive amounts of infor puter problemsolversesp ecially those with clear for mation agents are faced with we cannot even inter mal foundationsare extremely slow in most circum pret fast as p olynomialtimewe really need p er stances even when presented with little information formance sublinear in the total size of the KB for simple Consider a problemsolver that relies on a knowledge queries The natural candidate from Computer Science representation KR system to answer queries ab out is something like a relational database where query what follows from a knowledge base Although there are many factors that contribute to the overall p erformance 1 We call reasoning that do es not t this description puzzle of the problemsolver clearly the eciency of the KR mode reasoning after logic puzzles of the form The man who owns the camel lives next to the orangejuice drinker system is imp ortant Recent attempts to deal with the answeringreasoning is merely lo okup for the kinds of plicitly represent disjunction negation or any form of simple questions that we exp ect to b e frequently asked incompleteness This makes it imp ortant to determine of the KB the relationship b etween the answers that a complete Analyses such as Levesques and Reiters theoremprover would return when queried given the suggest that a crucial factor in the eciency of databases KB and the answers that would b e retrieved from the 0 is the assumption that the database has a complete and vivid knowledge in the VKBie b etween and in accurate view of the world Generalizing from this we the gure This relationship can b e thought of as the de conjecture that the prop er basis for commonsense rea gree of soundness and completeness of the VKB Vivid 0 soning is some vivid representation of knowledgeone reasoning will not b e very useful if is to o small a sub that b ears a strong and direct resemblance to the world set of or b ears no understandable relationship to it represents A vivid representation has symb ols that stand in a onetoone corresp ondence to ob jects of inter est in the world with connections b etween those symb ols corresp onding to relationships of concern For example Levesque a KB containing the sentences Dan drank ounces of gin and Jack drank ounces of gin would b e vivid with resp ect to the amount Jack and Dan drank individually while one containing Jack and Dan together p olished o ounces of gin and Dan had one more ounce drink than Jack would not de spite the fact that the same information follows from b oth KBs The notion of vivid representations is app ealing for reasons b eyond supp orting reasoning as databasestyle Figure Simple view of a vivid knowledge base lo okup it corresp onds well to the kind of information expressed in pictures thus it is reasonable to think Because not all reasoning ts our commonsense rea that much of the information we gain ie p ercep soning paradigm we prop ose a hybrid system that re tually o ccurs naturally in vivid form Also various tains the original information to supplement as nec psychologicallyoriented explanations of cognition sug essary the vivid form We attempt to answer queries gest that p eople often seem to reason directly from men by simple retrieval directly from the vivid KB If that tal mo dels JohnsonLaird rather than by syntac provides inadequate answers general or sp ecialpurp ose tic manipulation of sentential constructs reasoning with the original KB may b e tried p erhaps Of course not all information we obtain ab out the dep ending on the imp ortance of the query Ultimately world is in vivid form linguistic communication for ex one measure of success will b e the prop ortion of reason ample may yield disjunctive or otherwise incomplete or ing that can b e delegated to the VKB general input eg Jo e do esnt have his PhD yet or Everyone in the department has an advanced de gree Fortunately much of this information can b e co erced into a vivid form in a principled way System Architecture What is needed is an appropriate architecture that would allow an AI system to fall back on more general reason ing eg rstorder logic when necessary but would dep end primarily on ecient vivid reasoning The ap proach of standard hybrid reasoners which delegate questions to submo dules that can handle them eciently will not suce We need a much more active approach in which incoming information is pro cessed to augment and maintain a vivid view of the world We have b een investigating an architecture that exemplies this view Figure A more general architecture see Fig rstorder facts are vivied into a knowl 2 edge base of a sp ecial form the VKB This vivica A generalization of the architecture of Fig and a tion may lose information since the VKB cannot ex more realistic view is illustrated in Fig Notice rst 2 We distingui sh b elow b etween the KBthe knowledge given to the systemand the VKBthe systems vivid rep resentation of that knowledge the inuence of a variety of comp onents on the vivica by database techniques eg memb ership in dened re tion of the original facts Universal rules aect vivica lations need not b e computed tion simply and directly see b elow However where the Disjunctive and negative information do not t read available knowledge is incomplete we can often do b etter ily into the database worldview and are ma jor contrib than simply leaving the information in nonvivid form It utors to the complexity of logical reasoning We address may b e p ossible for example to eliminate the ambiguity disjunction and negation piecemeal distinguishing sev of the given disjunction in favour of denite factsfacts eral dierent forms and treating each dierently Ab ove not strictly equivalent but sucient for the purp oses all we strive to avoid reasoning by cases We hyp othe 3 of the system For example defaults or preferences size that commonsense reasoning achieves its eciency can b e used to capture the contribution of previous ex in part by not resorting to case analysis and we treat p erience Gricean communication conventions Grice problems that absolutely require reasoning by cases as 4 and linguistic context eects in forming mental puzzlemo de problems mo dels In other cases abstraction provides a p owerful Perhaps the b est way to discuss the various versions to ol In some circumstances it may even suce to make of vivication is to
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