8 research outputs found

    Evidence for Fixpoint Logic

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    For many modal logics, dedicated model checkers offer diagnostics (e.g., counterexamples) that help the user understand the result provided by the solver. Fixpoint logic offers a unifying framework in which such problems can be expressed and solved, but a drawback of this framework is that it lacks comprehensive diagnostics generation. We extend the framework with a notion of evidence, which can be specialized to obtain diagnostics for various model checking problems, behavioural equivalence and refinement checking problems. We demonstrate this by showing how our notion of evidence can be used to obtain diagnostics for the problem of deciding stuttering bisimilarity. Moreover, we show that our notion generalizes the existing notions of counterexample and witness for LTL and ACTL* model checking

    Completeness for Flat Modal Fixpoint Logics

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    This paper exhibits a general and uniform method to prove completeness for certain modal fixpoint logics. Given a set \Gamma of modal formulas of the form \gamma(x, p1, . . ., pn), where x occurs only positively in \gamma, the language L\sharp (\Gamma) is obtained by adding to the language of polymodal logic a connective \sharp\_\gamma for each \gamma \epsilon. The term \sharp\_\gamma (\varphi1, . . ., \varphin) is meant to be interpreted as the least fixed point of the functional interpretation of the term \gamma(x, \varphi 1, . . ., \varphi n). We consider the following problem: given \Gamma, construct an axiom system which is sound and complete with respect to the concrete interpretation of the language L\sharp (\Gamma) on Kripke frames. We prove two results that solve this problem. First, let K\sharp (\Gamma) be the logic obtained from the basic polymodal K by adding a Kozen-Park style fixpoint axiom and a least fixpoint rule, for each fixpoint connective \sharp\_\gamma. Provided that each indexing formula \gamma satisfies the syntactic criterion of being untied in x, we prove this axiom system to be complete. Second, addressing the general case, we prove the soundness and completeness of an extension K+ (\Gamma) of K\_\sharp (\Gamma). This extension is obtained via an effective procedure that, given an indexing formula \gamma as input, returns a finite set of axioms and derivation rules for \sharp\_\gamma, of size bounded by the length of \gamma. Thus the axiom system K+ (\Gamma) is finite whenever \Gamma is finite

    Computer Science Logic 2018: CSL 2018, September 4-8, 2018, Birmingham, United Kingdom

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    Getting the point : obtaining and understanding fixpoints in model checking

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    Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

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    This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

    Automated Reasoning

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    This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

    Automated Deduction – CADE 28

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    This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
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