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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Bibliographic Details
Published in:Siberian advances in mathematics Vol. 33; no. 1; pp. 66 - 85
Main Author: Nechesov, A. V.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.02.2023
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1055-1344
1934-8126
DOI:10.1134/S1055134423010066