HAPPY VALENTINE'S DAY 14 Feb 2011 JAIST 1
BK TP.HCM Conceptual Graphs and Fuzzy Logic JAIST, 14 Feb 2011 Tru H. Cao Ho Chi Minh City University of Technology and John von Neumann Institute
Outline Conceptual graphs and fuzzy logic Fuzzy conceptual graph programs Quantified conceptual graphs Query conceptual graphs Conclusion 3
Conceptual graphs Sowa, John F. (1984) Conceptual Structures: Information Processing in Mind and Machine, Addison- Wesley, Reading, MA. CG = semantic networks + Peirce s existential graphs 4
Conceptual graphs 1968: term paper to Marvin Minsky at Harvard 1970's: seriously working on CGs 1976: first paper on CGs Conceptual graphs for a database interface, IBM Journal of Research & Development, 20 (4). 1981-1982: meeting with Norman Foo and encountering Charles Peirce's existential graphs (1897) 1984: the book coming out 5
Simple conceptual graphs concept type (class) concept relation relation type 1 2 CAT: tuna On MAT: * individual referent generic referent The cat Tuna is on a mat. 6
Negated conceptual graphs Neg PROPOSITION: CAT: tuna On MAT: * CAT: tuna On MAT: * 7
Conceptual graphs as a logic A full-fledged first-order typed logic Conceptual graph programming Smooth mapping to and from natural language 8
Fuzzy sets Zadeh, Lofti A. (1965) Fuzzy Sets, Information and Control, 8 (3). 9
Fuzzy sets Vagueness: "Words like smart, tall, and fat are vague since in most contexts of use there is no bright line separating them from not smart, not tall, and not fat respectively " The Oxford Companion to Philosophy (1995) 10
Fuzzy sets Imprecision vs. Uncertainty: The bottle is about half-full. vs. It is likely to the degree of 0.5 that the bottle is full. 11
Fuzzy sets Membership function: µ young : U [0, 1] 1 0.5 young 0 20 30 40 Age 12
Fuzzy sets Membership function: Preference distribution Possibility distribution Family of probability distribution 13
Multi-valued logic Truth values are in [0, 1] Lukasiewicz: a = 1 a a b = min(a, b) a b = max(a, b) a b = min(1, 1 a + b) 14
Fuzzy logic if x is A then y is B x is A* ------------------------ y is B* 15
Fuzzy logic if height is tall then shoe-size is large height is rather tall ---------------------------------------------- shoe-size is? 16
Fuzzy logic if x is A then y is B x is A* ------------------------ y is B* Viewing a fuzzy rule as a fuzzy relation: R(u, v) A(u) B(v) A*(u) -------------------------- B*(v) 17
Fuzzy logic if x is A then y is B x is A* ------------------------ y is B* Measuring the similarity of A and A*: if x is A then y is B x is A* ------------------------- B*(v) = B + (A/A*) 18
CG and FL Both have the common target of natural language CG provides a syntactic structure for smooth mapping to and from natural language Sowa, John F. (1997) Matching logical structure to linguistic structure. In Studies in the logic of Charles Sanders Peirce. Indiana University Press. FL provides a semantic processor for approximate reasoning with vagueness in natural language Zadeh, Lofti A. (1996) Fuzzy logic = Computing with words. IEEE Transactions on Fuzzy Systems. 19
Fuzzy conceptual graphs Morton, S.K. (1987) Conceptual graphs and fuzziness in artificial intelligence. PhD Thesis, University of Bristol. Manzano, M.B. (1991) Knowledge representation using fuzzy conceptual graphs. Master s Thesis, Asian Institute of Technology. Cao, T.H. (1999) Foundations of order-sorted fuzzy set logic programming in predicate logic and conceptual graphs. PhD Thesis, University of Queensland. 20
Fuzzy conceptual graphs It is very true that John is an American man who is young, and it is more or less true that he likes a car whose color is blue. 21
FCG programs 22
FCG programs Piece resolution (Salvat, E. 1997): 23
FCG programs Annotated fuzzy logic programs (Cao, T.H. 1998): 24
Quantified conceptual graphs Mapping linguistic structure to logical structure: "Every student likes every course" STUDENT: Like COURSE: 25
Quantified conceptual graphs Mapping linguistic structure to logical structure: "Most Swedes are tall" most = Pr(tall(x) Swede(x)) 26
Reasoning with relative quantifiers Generalization: "Most people who are tall are not fat" "Most people who are tall are not very fat" 27
Reasoning with relative quantifiers Specialization: "About 9% people who are tall are fat" "At most about 9% people who are tall are very fat" 28
Reasoning with relative quantifiers With universal quantifier: "All people who are tall are not fat" "All males who are very tall are not fat" 29
Reasoning with absolute quantifiers Generalization: "Few people who are tall are fat" "At least few people who are fairly tall are fairly fat" 30
Reasoning with absolute quantifiers Specialization: "Few people who are tall are fat" "At most few people who are very tall are very fat" 31
Jeffrey's rule (1965) The conditional probability on a property of a specific object of a class is equal to that of the whole class. "Most birds can fly" "The probability that Tweet can fly given that it is a bird is most" 32
Jeffrey's rule (1965) The conditional probability on a property of a specific object of a class is equal to that of the whole class. "Most people who are tall are not fat" "The probability that John is not fat is p" 33
Jeffrey's rule (1965) p = (at least (most.ε π )) (at most (most.ε π + (1 - ε π ))) Probabilistic FCG projection: ε π = Pr(tall fairly tall) 34
Query conceptual graphs Connective query: "What international leaders sent or gave congratulations?" 35
Query conceptual graphs Superlative query: "What s the tallest building in New York City?" 36
Query conceptual graphs Counting query: "How many languages has Harry Potter and the Goblet of Fire been translated to?" 37
Query conceptual graphs A syntax-free approach for understanding natural language queries: 38
Query conceptual graphs 39
Query conceptual graphs Experiment on TREC 2002 dataset: 40
Query conceptual graphs Experiment on TREC 2007 dataset: 41
VN-KIM system Plug-ins S-Search S-Editor VN-KIM Front-End Applications Interface A KB of over 200,000 popular entities in Vietnamese news Semantic LUCENE VN-KIM IE Fuzzy SESAME Semantic Web Document Repository Semantic Annotation Ontology and Knowledge Base 42
VN-KIM entity recognition 43
VN-KIM search 44
VN-KIM search 45
Conclusion Artificial intelligence needs a knowledge representation language that approaches natural language 46
Conclusion "Form without content is empty. Content without form is so indeterminate that it cannot be grasped as an object of knowledge." John Hibben, Hegel s Logic: An Essay in Interpretation CG+FL is just an attempt. 47
Thanks for your attention