The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
A judgmental reconstruction of modal logic
Open accessAbstract
We reconsider the foundations of modal logic, following Martin-Löf's methodology of distinguishing judgments from propositions. We give constructive meaning explanations for necessity and possibility, which yields a simple and uniform system of natural deduction for intuitionistic modal logic that does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic and find that the lax modality is already expressible using possibility and necessity. Through a computational interpretation of proofs in modal logic we further obtain a new formulation of Moggi's monadic metalanguage.
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Cites
Untersuchungen �ber das logische Schlie�en. I
Gentzen, G. (1935) · Mathematische Zeitschrift · doi:10.1007/bf01201353 · Cited by 2,024
Notions of computation and monads
Moggi, E. (1991) · Information and Computation · doi:10.1016/0890-5401(91)90052-4 · Cited by 1,688
Computational lambda-calculus and monads
Moggi, E. (2003) · [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science · doi:10.1109/lics.1989.39155 · Cited by 842
Constructive mathematics and computer programming
Martin-Lof, P. (1984) · Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences · doi:10.1098/rsta.1984.0073 · Cited by 499
Logic Programming in a Fragment of Intuitionistic Linear Logic
Hodas, J. S., & Miller, D. (1994) · Information and Computation · doi:10.1006/inco.1994.1036 · Cited by 388
A modal analysis of staged computation
Davies, R., & Pfenning, F. (2001) · Journal of the ACM · doi:10.1145/382780.382785 · Cited by 293
Self-citationSabry, A., & Wadler, P. L. (1997) · ACM Transactions on Programming Languages and Systems · doi:10.1145/267959.269968 · Cited by 125
Computational types from a logical perspective
BENTON, P. N., BIERMAN, G. M., & DE PAIVA, V. C. V. (1998) · Journal of Functional Programming · doi:10.1017/s0956796898002998 · Cited by 110
Using typed lambda calculus to implement formal systems on a machine
Avron, A., Honsell, F., Mason, I. A., & Pollack, R. (1992) · Journal of Automated Reasoning · doi:10.1007/bf00245294 · Cited by 103
An intuitionistic modal logic with applications to the formal verification of hardware
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Cited by
Quantitative program reasoning with graded modal types
Orchard, D., Liepelt, V.-B., & Eades III, H. (2019) · Proceedings of the ACM on Programming Languages · doi:10.1145/3341714 · Cited by 85
Coeffects: a calculus of context-dependent computation
Petricek, T., Orchard, D., & Mycroft, A. (2014) · Proceedings of the 19th ACM SIGPLAN international conference on Functional programming · doi:10.1145/2628136.2628160 · Cited by 74
Coeffects: Unified Static Analysis of Context-Dependence
Petricek, T., Orchard, D., & Mycroft, A. (2013) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-39212-2_35 · Cited by 48
Embedding a full linear Lambda calculus in Haskell
Polakow, J. (2015) · Proceedings of the 2015 ACM SIGPLAN Symposium on Haskell · doi:10.1145/2804302.2804309 · Cited by 17
Metadata
- Authors
- PFENNING, F., & DAVIES, R.
- Venue
- Mathematical Structures in Computer Science
- Publisher
- Cambridge University Press (CUP)
- Published
- 2001-07-25
- Volume
- 11
- Issue
- 4
- Pages
- 511-540
- ISSN
- 0960-1295 (ISSN-L)
- 1469-8072
- OpenAlex
- W1988824860
- Cited by
- 342
- References
- 10
- FWCI
- 15.77
- Type
- journal article
- Language
- en
- Open access
- green
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