G. M. Bierman and V. de Paiva. On an intuitionistic modal logic. Studia Logica, 65(3):383--416, 2000. Home/Search Document Details and Download
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A Model for Knowledge Representation in Distributed Systems - Brunet (2002) (Correct)
..... Much work exist on different models for intuitionistic modal logic. The classical approach is based on Kripke s possible worlds models, where both modal logic and intuitionistic logic have a natural translation. Such semantics are described in [13] Other approach include categorical ones [3, 4], computational ones [3, 11, 9] and others [8] 3.3 Relating IS4 KV and description models We now show that there is a close relation between the logic IS4 KV#,I and the description models of L(#, I) For this, we define two notions of truth and prove that they are equivalent. First, we ....
....in IS4 KV (that is those which verify IS4 KV #) The proof of this theorem is given more precisely in Appendix B. This theorem provides a simple and general class of model for the modal logic IS4 KV. While many classes of model exist, either based on Kripke structures [13] on categories [3, 4] or on adaptations of # calculus [9, 11] the present model originates from approximation techniques and its application to information flow formalisms [6] offering new possibilities in the logical study of complex systems and knowledge representation. 4 Conclusion In this paper, we have ....
G. M. Bierman and Valeria de Paiva. On an intuitionistic modal logic. Studia Logica, 65:383--416, 2000.
Extended Curry-Howard Correspondence for a Basic.. - Bellin, de Paiva, Ritter (2001) Self-citation (De paiva) (Correct)
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G. M. Bierman and V. de Paiva. On an Intuitionistic Modal Logic. Studia Logica, 65: 383-416, 2000.
Extended Curry-Howard Correspondence for a Basic.. - Bellin, de Paiva, Ritter (2001) Self-citation (De paiva) (Correct)
....logic and to appropriate classes of categories are widely known. In this note we pursue an analogous correspondence for a basic intuitionistic (or constructive) modal logic IKwith both necessity (2) and possibility (3) operators. Similar work for intuitionistic S4 (IS4) has appeared in [BdP00, AMPR01, GdPR98]. This is a natural logic to consider, if one is determined to push the frontiers of the CurryHoward Isomorphism, as far as they will go. Modal system K is less symmetric than S4 as far as the modality rules are concerned. Modal S4 has introduction and elimination rules for both necessity and ....
....intuitionistic propositional logic. For a proper explanation the reader should consult Lambek and Scott[LS85] To model the 2 modality we need a monoidal endofunctor. The monoidicity of the functor corresponds to the modelling of the K characteristic axiom 2(A B) 2A 2B. In previous work [BdP00] it was shown that to model the S4 necessity 2 operator one needs a monoidal comonad. Here we have less structure and hence only the monoidal endofunctor remains. For precise mathematical de nitions we refer the reader to previous work[BdP00, AMPR01] De nition 2. A IK2 category consists of a ....
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G. M. Bierman and V. de Paiva. On an Intuitionistic Modal Logic. Studia Logica, 65: 383-416, 2000.
Modal Logics with Existential Modality, Finite-iteration.. - Shkatov (2005) (Correct)
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G. M. Bierman and V. de Paiva. On an intuitionistic modal logic. Studia Logica, 65(3):383--416, 2000.
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