Semantic Programming and Polynomially Computable Representations

In the present article, we consider the question on existence of polynomially computable representations for basic syntactic constructions of the first-order logic and for objects of semantic programming (such as -programs and -formulas). We prove that the sets of linear or tree-like derivations in...

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Veröffentlicht in:Siberian advances in mathematics Jg. 33; H. 1; S. 66 - 85
1. Verfasser: Nechesov, A. V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.02.2023
Springer Nature B.V
Schlagworte:
Algorithms
Calculus
Language
Mathematics
Mathematics and Statistics
Polynomials
Predicate calculus
Programming languages
Representations
Semantics
semantic programming
Gandy theorem
smart contracts
proof verification
GNF-systems
iterative terms
polynomial computability
PAG-theorem
artificial intelligence
proof theory
ISSN:1055-1344, 1934-8126
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Zusammenfassung:In the present article, we consider the question on existence of polynomially computable representations for basic syntactic constructions of the first-order logic and for objects of semantic programming (such as -programs and -formulas). We prove that the sets of linear or tree-like derivations in the first-order predicate calculus admits a polynomially computable representation. We also obtain a series of assertions that allow us to prove polynomial computability in a more efficient way. Among them, we mention the generalized PAG-theorem with polynomially computable initial data and an assertion on -iterative terms with weakened estimates. Our results may be useful for construction of logical programming languages, in smart contracts, as well as for developing fast algorithms for automatic proof verification.
Bibliographie:ObjectType-Article-1
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ISSN:1055-1344
1934-8126
DOI:10.1134/S1055134423010066