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Introduction to Logic and Knowledge Representation

Explore the fundamentals of logic and knowledge representation, covering topics like propositional logic, truth tables, different types of logics, ontology, Lambda Calculus, Conceptual Graphs, and more in this informative session.

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Introduction to Logic and Knowledge Representation

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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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