David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Logic, Language and Information 15 (4):371-401 (2006)
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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References found in this work BETA
Laurence Horn (1989). A Natural History of Negation. University of Chicago Press.
A. S. Troelstra (1991). Lectures on Linear Logic. Monograph Collection (Matt - Pseudo).
Hiroakira Ono & Yuichi Komori (1985). Logics Without the Contraction Rule. Journal of Symbolic Logic 50 (1):169-201.
Ahmad Almukdad & David Nelson (1984). Constructible Falsity and Inexact Predicates. Journal of Symbolic Logic 49 (1):231-233.
Citations of this work BETA
Heinrich Wansing (2008). Constructive Negation, Implication, and Co-Implication. Journal of Applied Non-Classical Logics 18 (2-3):341-364.
Norihiro Kamide (2007). Towards a Theory of Resource: An Approach Based on Soft Exponentials. Journal of Applied Non-Classical Logics 17 (1):63-89.
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