Classical Natural Deduction for S4 Modal Logic

This paper proposes a natural deduction system CNDS4 for classical S4 modal logic with necessity and possibility modalities. This new system is an extension of Parigot’s Classical Natural Deduction with dualcontext to formulate S4 modal logic. The modal λ μ -calculus is also introduced as a computat...

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Bibliographic Details
Published inNew generation computing Vol. 29; no. 1; pp. 61 - 86
Main Authors Kimura, Daisuke, Kakutani, Yoshihiko
Format Journal Article
LanguageEnglish
Published Heidelberg Verlag Omsha Tokio 01.01.2011
Subjects
Artificial Intelligence
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Software Engineering/Programming and Operating Systems
Lambda-Calculus
Staged Computation
Classical S4 Modal Logic
Functional Programming
Curry-Howard Isomorphism
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Summary:This paper proposes a natural deduction system CNDS4 for classical S4 modal logic with necessity and possibility modalities. This new system is an extension of Parigot’s Classical Natural Deduction with dualcontext to formulate S4 modal logic. The modal λ μ -calculus is also introduced as a computational extraction of CNDS4. It is an extension of both the λ μ -calculus and the modal λ-calculus. Subject reduction, confluency, and strong normalization of the modal λ μ -calculus are shown. Finally, the computational interpretation of the modal λ μ -calculus, especially the computational meaning of the modal possibility operator, is discussed.
ISSN:0288-3635
1882-7055
DOI:10.1007/s00354-010-0099-3