Classical Natural Deduction for S4 Modal Logic

• Published in: New generation computing Vol. 29; no. 1; pp. 61 - 86
• Main Authors: Kimura, Daisuke, Kakutani, Yoshihiko
• Format: Journal Article
• Language: English
• 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

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...