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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Vydáno v:	Siberian advances in mathematics Ročník 33; číslo 1; s. 66 - 85
Hlavní autor:	Nechesov, A. V.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Moscow Pleiades Publishing 01.02.2023 Springer Nature B.V
Témata:	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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Abstract	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.
AbstractList	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. 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.
Author	Nechesov, A. V.
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References	CR4 Goncharov, Ospichev, Ponomaryov, Sviridenko (CR9) 2020; 17 Alaev, Selivanov (CR2) 2018; 98 CR8 CR7 Ershov (CR3) 1996 Goncharov (CR6) 2017; 58 Goncharov, Sviridenko (CR11) 2018; 59 Alaev (CR1) 2017; 55 Ershov, Palyutin (CR5) 1987 Nechesov (CR13) 2022; 32 Goncharov, Sviridenko (CR10) 1989; 142 Ospichev, Ponomaryov (CR14) 2018; 15 Goncharov, Sviridenko (CR12) 2019; 99 S.S. Goncharov (5063_CR11) 2018; 59 A.V. Nechesov (5063_CR13) 2022; 32 5063_CR7 5063_CR8 S.S. Goncharov (5063_CR9) 2020; 17 S.S. Goncharov (5063_CR10) 1989; 142 P.E. Alaev (5063_CR1) 2017; 55 S.S. Goncharov (5063_CR6) 2017; 58 Yu.L. Ershov (5063_CR3) 1996 S.S. Goncharov (5063_CR12) 2019; 99 5063_CR4 S.S. Ospichev (5063_CR14) 2018; 15 Yu.L. Ershov (5063_CR5) 1987 P.E. Alaev (5063_CR2) 2018; 98
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SubjectTerms	Algorithms Calculus Language Mathematics Mathematics and Statistics Polynomials Predicate calculus Programming languages Representations Semantics
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