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REPRESENTAÇÃO DO CONHECIMENTO Terças – 13 hs – sala 512 RDC

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Definition: The study of propositions and their use in argumentation. Major task: establish a systematic way of deducing the logical consequences of a set of sentences. EnciclopÆdia Britannica. Logic

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Lógica Matemática Leibniz Reduce reasoning to mathematical computation Corpo = substância material = 2x3=6 Humano = 2x3x7x13x19= 10.374 Divide por 6 =>Humano é corpo Não divide por 66(mineral) => Humano não é mineral

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T-Box & A-Box Brachman et al. T-box – term definition A-box – assertion definition lattices

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Álgebra Booleana 0 – false 1 – truth Conjunction X – and Disjunction + - or Negation – not

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Truth Tables

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Portas Lógicas

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Frege’s Begriffsschrift

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Peirce Σ – repeated or (logical sum) Π – repeated and (logical product)

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Peano

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Propositional Logic Every trailer truck has 18 wheels.

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Propositional Logic Every trailer truck has 18 wheels. => p

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Syllogism Predicate and Subject

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Predicate Logic Universal with implication Existential with conjuction

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Logic and Ontology Harder to read Distracting detail from the variables – used to link parts of the formula Logic is simple – half a dozen symbols. Level of detail depends on the predicates that do not belong to logic. They represent an ontology of relevant things in the domain. Choices represent ontological commitments. Predicates in an ontology Domain dependent Domain independent

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Varieties of Logic Syntax Subsets description logics Proof theory Model theory Ontology Uninterpreted logic: bunch of symbols, quatifiers, operators Set theory for Math Metalanguage

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Typed Logic Notational engineering Avoids extra implications that accompany the universal quantifier

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Lambda Calculus Church notation for defining functions and a method for converting any given definition into other equivalent definitions

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Conceptual Graphs System of logic Based on Existential graphs by Peirce Semantic Networks A cat is on the Mat Every cat is on a mat

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KIF Knowledge Interchange Format Version of typed predicate logic – Genesereth, Fikes et al.

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KIF Knowledge Interchange Format Version of typed predicate logic – Genesereth, Fikes et al. A cat is on the Mat Every cat is on a mat

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Logic Vocabulary Domain independent logical symbols Constants: individuals, properties, relations Variables Punctuation Syntax Semantics Rules of inference

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