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Abstract: This paper is about relating traditional Kripke-style semantics for intuitionistic modal logics to their corresponding categorical semantics. Both forms of semantics have important applications within computer science. One of our aims is to persuade traditional modal logicians that categorical semantics is easy, fun and useful; just like Kripke semantics. (Update)
Context of citations to this paper: More
...models of the previous section. Indeed there appears to be more than one way to approach the question. One approach is given by Alechina et al. 1997), who demonstrate a natural method of finding a CL Kripke model within a (categorical) CL model. 8 Conclusions We have shown that...
.... necessitation A true nec 2A true together with the following three axioms (see, for example, Vigan o, 1997; Kobayashi, 1997; Alechina et al. 1998)) 2(A oe B) oe(2A oe 2B) true 2A oe A true 2A oe 22A true A Judgmental Reconstruction of Modal Logic 11 The derivations...
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BibTeX entry: (Update)
Alechina, N., de Paiva, V.C.V., & Ritter, E (1997). Relating Categorical and Kripke Semantics for Intuitionistic Modal Logics. Unpublished report. School of Computer Science, University of Birmingham. http://citeseer.ist.psu.edu/alechina98relating.html More
@misc{ alechina97relating,
author = "N. Alechina and V. de Paiva and E. Ritter",
title = "Relating Categorical and Kripke Semantics for Intuitionistic Modal Logics",
text = "Alechina, N., de Paiva, V.C.V., & Ritter, E (1997). Relating Categorical
and Kripke Semantics for Intuitionistic Modal Logics. Unpublished report.
School of Computer Science, University of Birmingham.",
year = "1997",
url = "citeseer.ist.psu.edu/alechina98relating.html" }
Citations (may not include all citations):359 Introduction to Higher-Order Categorical Logic (context) - Lambek, Ph - 1985
143 A Modal Analysis of Staged Computation - Davies - 1996
87 Notions of Computation and Monads - Moggi - 1991
66 Primitive recursion for higher-order abstract syntax (context) - Despeyroux, Pfenning et al. - 1997
65 Modal logic and classical logic (context) - van - 1983
52 Intuitionistic necessity revisited - Bierman - 1996
51 Computational Types From a Logical Perspective - Benton, Bierman et al. - 1998
44 The Proof Theory and Semantics of Intuitionistic Modal Logic (context) - Simpson - 1994
35 Stone Spaces (context) - Johnstone - 1982
31 Metamathematics of modal logic (context) - Goldblatt - 1976
21 A framework for intuitionistic modal logic (context) - Plotkin - 1986
17 Natural Deduction: A Proof-Theoretic Study (context) - Prawitz - 1965
14 An incompleteness theorem in modal logic (context) - Thomason - 1974
11 the Relation between Intuitionistic and Classical Modal Logi.. - Wolter - 1996
10 Explicit Substitutions for Constructive Necessity (context) - Neil, de Paiva et al. - 1998
9 Grothendieck Topology as Geometric Modality (context) - Goldblatt - 1981
7 Intuitionistic Modal Logics - Wolter - 1995
5 Propositional Lax Logic - Fairtlough - 1997
4 Models for stronger normal intuitionistic modal logics (context) - Dosen - 1985
4 Monad as modality (context) - Kobayashi - 1997
4 Mathematics of Modality (context) - Goldblatt - 1993
3 Logical Foundations of Eval/Quote Mechanisms (context) - Goubault-Larrecq - 1996
2 An incomplete logic containing S4 (context) - Fine - 1974
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