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= 10.374

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 convertingany 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