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Modal model theory

Maarten De Rijke

Annals of Pure and Applied Logic (forthcoming)

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The logic of Peirce algebras.Maarten De Rijke - 1995 - Journal of Logic, Language and Information 4 (3):227-250.details Peirce algebras combine sets, relations and various operations linking the two in a unifying setting. This paper offers a modal perspective on Peirce algebras. Using modal logic a characterization of the full Peirce algebras is given, as well as a finite axiomatization of their equational theory that uses so-called unorthodox derivation rules. In addition, the expressive power of Peirce algebras is analyzed through their connection with first-order logic, and the fragment of first-order logic corresponding to Peirce algebras is described in (...) terms of bisimulations. (shrink) Download Export citation Bookmark 8 citations
A system of dynamic modal logic.Maarten de Rijke - 1998 - Journal of Philosophical Logic 27 (2):109-142.details In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations (...) Download Export citation Bookmark 10 citations
A System of Dynamic Modal Logic.Maarten Rijkdee - 1998 - Journal of Philosophical Logic 27 (2):109-142.details In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations (...) Download Export citation Bookmark 1 citation
Bisimulations for temporal logic.Natasha Kurtonina & Maarten de Rijke - 1997 - Journal of Logic, Language and Information 6 (4):403-425.details We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief discussion of the wider applicability of our ideas. Download Export citation Bookmark 8 citations

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