REPRESENTAÇÃO DO CONHECIMENTO Terças – 13 hs – sala 512 RDC

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

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

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

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

Truth Tables

Portas Lógicas

Frege’s Begriffsschrift

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

Peano

Propositional Logic  Every trailer truck has 18 wheels.

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

Syllogism  Predicate and Subject

Predicate Logic  Universal with implication  Existential with conjuction

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

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

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

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

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

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

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

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