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