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A general framework for computing maximal contractions

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Abstract

This paper investigates the problem of computing all maximal contractions of a given formula set Γ with respect to a consistent set Δ of atomic formulas and negations of atomic formulas. We first give a constructive definition of minimal inconsistent subsets and propose an algorithmic framework for computing all minimal inconsistent subsets of any given formula set. Then we present an algorithm to compute all maximal contractions fromminimal inconsistent subsets. Based on the algorithmic framework and the algorithm, we propose a general framework for computing all maximal contractions. The computability of the minimal inconsistent subset and maximal contraction problems are discussed. Finally, we demonstrate the ability of this framework by applying it to the first-order language without variables and design an algorithmfor the computation of all maximal contractions.

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Authors and Affiliations

  1. State Key Laboratory of Software Development Environment, School of Computer Science and Engineering, Beihang University, Beijing, 100191, China

    Jie Luo

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  1. Jie Luo
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Correspondence to Jie Luo.

Additional information

Jie Luo received his PhD degree in computer science from Beihang University, Beijing, China, in 2012. His research interests include mathematical logic, formal methods, automated reasoning, and software testing.

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Luo, J. A general framework for computing maximal contractions. Front. Comput. Sci. 7, 83–94 (2013). https://doi.org/10.1007/s11704-012-2044-8

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  • DOI: https://doi.org/10.1007/s11704-012-2044-8

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