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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| Published in | New generation computing Vol. 29; no. 1; pp. 61 - 86 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Verlag Omsha Tokio
01.01.2011
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| Subjects | |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Kimura, Daisuke Kakutani, Yoshihiko |
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| Cites_doi | 10.1145/382780.382785 10.1016/S0304-3975(00)00053-0 10.1023/A:1005291931660 10.2307/1968867 10.1017/S0960129598002667 10.2178/jsl/1154698578 10.1017/S0960129501003322 10.1007/3-540-58216-9_27 10.1007/978-3-540-32033-3_15 10.1007/978-3-540-76637-7_27 10.1007/3-540-45793-3_34 10.1145/1140335.1140360 10.1109/LICS.1996.561317 10.1007/BFb0013061 10.1017/S096012950000311X 10.1145/357766.351262 10.1145/263699.263722 10.1145/96709.96714 10.1007/BFb0055098 10.1109/LICS.1993.287602 |
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| Copyright | Ohmsha and Springer Japan jointly hold copyright of the journal. 2011 |
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| Keywords | Lambda-Calculus Staged Computation Classical S4 Modal Logic Functional Programming Curry-Howard Isomorphism |
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| Title | Classical Natural Deduction for S4 Modal Logic |
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