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om C nh Vi en Zo ne Structured Knowledge Si Chapter om Logic Notations Si nh Vi en Zo ne C Does logic represent well knowledge in structures? om Logic Notations assert P P not P Zo ne C Frege’s Begriffsschrift (concept writing) - 1879: if P then Q nh Vi en P x P(x) Si for every x, P(x) Q P om Logic Notations Zo x nh Vi en “Every ball is red” x red(x) ball(x) red(x) ball(x) Si “Some ball is red” ne C Frege’s Begriffsschrift (concept writing) - 1879: Zo Universal quantifier: xPx ne C Algebraic notation - Peirce, 1883: om Logic Notations Si nh Vi en Existential quantifier: xPx ne C Algebraic notation - Peirce, 1883: om Logic Notations Zo “Every ball is red”: x(ballx —< redx) Si nh Vi en “Some ball is red”: x(ballx • redx) om Logic Notations ne C Peano’s and later notation: Zo “Every ball is red”: (x)(ball(x) red(x)) Si nh Vi en “Some ball is red”: (x)(ball(x) red(x)) .C Existential graphs - Peirce, 1897: om Logic Notations Zo ne Existential quantifier: a link structure of bars, called line of identity, represents nh Vi en Conjunction: the juxtaposition of two graphs represents Si Negation: an oval enclosure represents ~ om Logic Notations owns donkey beats Si nh Vi en farmer Zo ne C “If a farmer owns a donkey, then he beats it”: om Logic Notations C EG’s rules of inferences: ne Erasure: in a positive context, any graph may be erased Zo Insertion: in a negative context, any graph may be inserted nh Vi en Iteration: a copy of a graph may be written in the same context or any nested context Si Deiteration: any graph may be erased if a copy of its occurs in the same context or a containing context Double negation: two negations with nothing between them may be erased or inserted 10 om Conceptual Graphs ne C • Sowa, J.F 1984 Conceptual Structures: Information Processing in Mind and Machine Si nh Vi en Zo • CG = a combination of Perice’s EGs and semantic networks 28 om Conceptual Graphs C • 1968: term paper to Marvin Minsky at Harvard Zo ne • 1970's: seriously working on CGs nh Vi en • 1976: first paper on CGs • 1981-1982: meeting with Norman Foo, finding Peirce’s EGs Si • 1984: the book coming out • CG homepage: http://conceptualgraphs.org/ 29 relation ne concept Zo concept type (class) C om Simple Conceptual Graphs nh Vi en CAT: tuna Si individual referent On relation type MAT: * generic referent 30 om Ontology C • Ontology: the study of "being" or existence Zo ne • An ontology = "A catalog of types of things that are assumed to exist in a domain of interest" (Sowa, 2000) Si nh Vi en • An ontology = "The arrangement of kinds of things into types and categories with a well-defined structure" (Passin 2004) 31 top-level categories domain-specific Si nh Vi en Zo ne C om Ontology 32 om Ontology C Being Aristotle's categories Substance ne Accident Property Inherence Directedness Quantity Si Quality nh Vi en Zo Relation Movement Activity Containment Intermediacy Passivity Having Spatial Temporal Situated 33 om Ontology Geographical-Feature ne C Geographical categories Dam Terrain nh Vi en Block Point Zo Area Town Country Bridge Si Wetland Mountain Airstrip Heliport Line On-Land On-Water Road Border River Railroad Power-Line 34 Si nh Vi en Relation Zo ne C om Ontology 35 ANIMAL FOOD Si nh Vi en Eat Zo ne C om Ontology PERSON: john Eat CAKE: * 36 ne Has-Relative PERSON: * nh Vi en Zo PERSON: john C om CG Projection Has-Wife WOMAN: mary Si PERSON: john 37 Neg On MAT: * On MAT: * nh Vi en Zo CAT: tuna ne C om Nested Conceptual Graphs Si CAT: tuna It is not true that cat Tuna is on a mat 38 C om Nested Conceptual Graphs Zo CAT: * On MAT: * nh Vi en CAT: * ne Si coreference link Every cat is on a mat 39 .C om Nested Conceptual Graphs nh Vi en PERSON: julian Si Poss Zo ne Fly-To PLANET: mars Past Julian could not fly to Mars 40 .C om Nested Conceptual Graphs PERSON: julian Si nh Vi en Poss Zo ne Fly-To PLANET: mars Past Tom believes that Mary wants to marry a sailor 41 om Exercises ne C • Reading: nh Vi en Zo Sowa, J.F 2000 Knowledge Representation: Logical, Philosophical, and Computational Foundations (Section 1.1: history of logic) Si Way, E.C 1994 Conceptual Graphs – Past, Present, and Future Procs of ICCS'94 42 ... Frames Zo ne C • A vague paradigm - to organize knowledge in highlevel structures nh Vi en • “A Framework for Representing Knowledge - Minsky, 1974 Si • Knowledge is encoded in packets, called frames... quantifier: xPx ne C Algebraic notation - Peirce, 18 83: om Logic Notations Si nh Vi en Existential quantifier: xPx ne C Algebraic notation - Peirce, 18 83: om Logic Notations Zo “Every ball is red”:... containing context Double negation: two negations with nothing between them may be erased or inserted 13 om Existential Graphs C Prove: ((p r) (q s)) ((p q) (r s)) nh Vi en Iteration: a copy
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