Propositional State Transition Logics
PESONEN, RENNE (2008)
2008
Matematiikka - Mathematics
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Hyväksymispäivämäärä
2008-02-04
Julkaisun pysyvä osoite on
http://urn.fi/urn:nbn:fi:uta-1-17690
http://urn.fi/urn:nbn:fi:uta-1-17690
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This paper is an introduction to a class of multimodal logics with an algebraic structure associated with modal operators. The discussion focuses on model theory, especially on the interpretation of several syntactic operators on modalities. First part of the paper discusses definitions of languages and models and considers conceptual issues on modal definability of operations on relations. Also in this context the concept of foundations, which is an abstraction level between domains and frames, is introduced. Then some general results on the expressive power of the class of logics in question is covered.
The core of the article consists of several definability results establishing correspondences between formulae and interpretations of syntactic operators within various languages. The correspondence results are divided into two sections discussing operator definability on the level of frames and foundations respectively. It will be demonstrated that all the operations of the calculus of relations are foundation definable, and moreover that all the common closures (reflexive, symmetric and transitive) are definable on the level of frames and foundations.
This paper is an introduction to a class of multimodal logics with an algebraic structure associated with modal operators. The discussion focuses on model theory, especially on the interpretation of several syntactic operators on modalities. First part of the paper discusses definitions of languages and models and considers conceptual issues on modal definability of operations on relations. Also in this context the concept of foundations, which is an abstraction level between domains and frames, is introduced. Then some general results on the expressive power of the class of logics in question is covered.
The core of the article consists of several definability results establishing correspondences between formulae and interpretations of syntactic operators within various languages. The correspondence results are divided into two sections discussing operator definability on the level of frames and foundations respectively. It will be demonstrated that all the operations of the calculus of relations are foundation definable, and moreover that all the common closures (reflexive, symmetric and transitive) are definable on the level of frames and foundations.