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REPRESENTAÇÃO DO CONHECIMENTO

REPRESENTAÇÃO DO CONHECIMENTO. Terças – 13 hs – sala 512 RDC. Logic. 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. Lógica Matemática. Leibniz

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REPRESENTAÇÃO DO CONHECIMENTO

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  1. REPRESENTAÇÃO DO CONHECIMENTO Terças – 13 hs – sala 512 RDC

  2. Logic 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.

  3. 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

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

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

  6. Truth Tables

  7. Portas Lógicas

  8. Frege’s Begriffsschrift

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

  10. Peano

  11. Propositional Logic • Every trailer truck has 18 wheels.

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

  13. Syllogism • Predicate and Subject

  14. Predicate Logic • Universal with implication • Existential with conjuction

  15. 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

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

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

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

  19. 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

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

  21. 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

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

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