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2020 Provenance analysis for logic and games
Erich Grädel, Val Tannen
Mosc. J. Comb. Number Theory 9(3): 203-228 (2020). DOI: 10.2140/moscow.2020.9.203

Abstract

A model-checking computation checks whether a given logical sentence is true in a given finite structure. Provenance analysis abstracts from such a computation mathematical information on how the result depends on the atomic data that describe the structure. In database theory, provenance analysis by interpretations in commutative semirings has been rather successful for positive query languages (such as unions of conjunctive queries, positive relational algebra, and Datalog). However, it did not really offer an adequate treatment of negation or missing information. Here we propose a new approach for the provenance analysis of logics with negation, such as first-order logic and fixed-point logics. It is closely related to a provenance analysis of the associated model-checking games, and based on new semirings of dual-indeterminate polynomials or dual-indeterminate formal power series. These are obtained by taking quotients of traditional provenance semirings by congruences that are generated by products of positive and negative provenance tokens. Beyond the use for model-checking problems in logics, provenance analysis of games is of independent interest. Provenance values in games provide detailed information about the number and properties of the strategies of the players, far beyond the question whether or not a player has a winning strategy from a given position.

Citation

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Erich Grädel. Val Tannen. "Provenance analysis for logic and games." Mosc. J. Comb. Number Theory 9 (3) 203 - 228, 2020. https://doi.org/10.2140/moscow.2020.9.203

Information

Received: 2 August 2019; Accepted: 21 February 2020; Published: 2020
First available in Project Euclid: 22 October 2020

zbMATH: 07272347
MathSciNet: MR4164867
Digital Object Identifier: 10.2140/moscow.2020.9.203

Subjects:
Primary: 03B70, 03C13, 05C57, 68Q19, 91A43

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.9 • No. 3 • 2020
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