Phase semantics and Petri net interpretation for resource-sensitive strong negation

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.
Keywords electric circuit  linear logic with strong negation  medical diagnosis  Petri net with inhibitor arc  phase semantics
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DOI 10.1007/s10849-005-9000-z
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References found in this work BETA
A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
Constructible Falsity and Inexact Predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Logics Without the Contraction Rule.Hiroakira Ono & Yuichi Komori - 1985 - Journal of Symbolic Logic 50 (1):169-201.

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Citations of this work BETA
Constructive Negation, Implication, and Co-Implication.Heinrich Wansing - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):341-364.
Towards a Theory of Resource: An Approach Based on Soft Exponentials.Norihiro Kamide - 2007 - Journal of Applied Non-Classical Logics 17 (1):63-89.

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