Logic programming in tensor spaces

This paper introduces a novel approach to computing logic programming semantics. First, a propositional Herbrand base is represented in a vector space and if-then rules in a program are encoded in a matrix. Then the least fixpoint of a definite logic program is computed by matrix-vector products wit...

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Veröffentlicht in:Annals of mathematics and artificial intelligence Jg. 89; H. 12; S. 1133 - 1153
Hauptverfasser: Sakama, Chiaki, Inoue, Katsumi, Sato, Taisuke
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2021
Springer
Springer Nature B.V
Schlagworte:
Algebra
Artificial Intelligence
Boolean
Cognition & reasoning
Complex Systems
Computation
Computer Science
Integer programming
Knowledge bases (artificial intelligence)
Linear algebra
Logic programming
Logic programs
Mathematical analysis
Mathematics
Matrices (mathematics)
Matrix algebra
Optimization techniques
Semantics
Tensors
Vector spaces
Vectors (mathematics)
Tensor space
68N17
68W30
Linear algebra
Logic program
15A69
Knowledge representation and reasoning
68T30
ISSN:1012-2443, 1573-7470
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Zusammenfassung:This paper introduces a novel approach to computing logic programming semantics. First, a propositional Herbrand base is represented in a vector space and if-then rules in a program are encoded in a matrix. Then the least fixpoint of a definite logic program is computed by matrix-vector products with a non-linear operation. Second, disjunctive logic programs are represented in third-order tensors and their minimal models are computed by algebraic manipulation of tensors. Third, normal logic programs are represented by matrices and third-order tensors, and their stable models are computed. The result of this paper exploits a new connection between linear algebraic computation and symbolic computation, which has the potential to realize logical inference in huge scale of knowledge bases.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-021-09767-x