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Phase Semantics and Petri Net Interpretation for Resource-Sensitive Strong Negation

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Abstract

Wansing’s extended intuitionistic linear logic with strong negation, called WILL, is regarded as a resource-conscious refinment of Nelson’s constructive logics with strong negation. In this paper, (1) the completeness theorem with respect to phase semantics is proved for WILL using a method that simultaneously derives the cut-elimination theorem, (2) a simple correspondence between the class of Petri nets with inhibitor arcs and a fragment of WILL is obtained using a Kripke semantics, (3) a cut-free sequent calculus for WILL, called twist calculus, is presented, (4) a strongly normalizable typed λ-calculus is obtained for a fragment of WILL, and (5) new applications of WILL in medical diagnosis and electric circuit theory are proposed. Strong negation in WILL is found to be expressible as a resource-conscious refutability, and is shown to correspond to inhibitor arcs in Petri net theory.

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Authors and Affiliations

  1. Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan

    Norihiro Kamide

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  1. Norihiro Kamide
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Correspondence to Norihiro Kamide.

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Kamide, N. Phase Semantics and Petri Net Interpretation for Resource-Sensitive Strong Negation. JoLLI 15, 371–401 (2006). https://doi.org/10.1007/s10849-005-9000-z

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  • DOI: https://doi.org/10.1007/s10849-005-9000-z

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