cs440-lec18-19-FOL - First Order Logic First Order Logic...

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Unformatted text preview: First Order Logic First Order Logic Russell and Norvig: Chapters 8 and 9 CMSC421 Fall 2005 Propositional logic is a weak language Hard to identify individuals. E.g., Mary, 3 Cant directly talk about properties of individuals or relations between individuals. E.g. Bill is tall Generalizations, patterns, regularities cant easily be represented. E.g., all triangles have 3 sides First-Order Logic (abbreviated FOL or FOPC) is expressive enough to concisely represent this kind of situation. FOL adds relations, variables, and quantifiers, e.g., Every elephant is gray: 2200 x (elephant(x) gray(x)) There is a white alligator: 5 x (alligator(X) ^ white(X)) Example Consider the problem of representing the following information: Every person is mortal. Confucius is a person. Confucius is mortal. How can these sentences be represented so that we can infer the third sentence from the first two? Example cont. In PL we have to create propositional symbols to stand for all or part of each sentence. For example, we might do: P = person; Q = mortal; R = Confucius so the above 3 sentences are represented as: P => Q; R => P; R => Q Although the third sentence is entailed by the first two, we needed an explicit symbol, R, to represent an individual, Confucius, who is a member of the classes person and mortal. To represent other individuals we must introduce separate symbols for each one, with means for representing the fact that all individuals who are people are also "mortal. Problems with the propositional Wumpus hunter Lack of variables prevents stating more general rules. E.g., we need a set of similar rules for each cell Change of the KB over time is difficult to represent Standard technique is to index facts with the time when theyre true This means we have a separate KB for every time point. First-order logic First-order logic (FOL) models the world in terms of Objects, which are things with individual identities Properties of objects that distinguish them from other objects Relations that hold among sets of objects Functions, which are a subset of relations where there is only one value for any given input Examples: Objects: Students, lectures, companies, cars ... Relations: Brother-of, bigger-than, outside, part-of, has- color, occurs-after, owns, visits, precedes, ... Properties: blue, oval, even, large, ... Functions: father-of, best-friend, second-half, one-more-than ... A BNF for FOL S := <Sentence> ;...
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This note was uploaded on 05/04/2008 for the course CS 440 taught by Professor Eyalamir during the Spring '08 term at University of Illinois at Urbana–Champaign.

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cs440-lec18-19-FOL - First Order Logic First Order Logic...

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