Reference : Introducing reactive Kripke semantics and arc accessibility
Scientific journals : Article
Engineering, computing & technology : Computer science
http://hdl.handle.net/10993/15853
Introducing reactive Kripke semantics and arc accessibility
English
Gabbay, Dov M. [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) > ; King’s College London, London, UK > Department of Computer Science, > > ; Bar-Ilan University, Ramat-Gan, Israel]
2012
Annals of Mathematics & Artificial Intelligence
Springer
66
1-4
7-53
Yes (verified by ORBilu)
1012-2443
[en] Ordinary Kripke models are not reactive. When we evaluate (test/ measure) a formula
A at a model m, the model does not react, respond or change while we evaluate. The model is static and unchanged. This paper studies Kripke models which react to the evaluation process and change themselves during the process. The additional device we add to Kripke semantics to make it reactive is to allow the accessibility relation to access itself. Thus the accessibility relation R of a reactive Kripke model contains not only pairs (a,b)∈R of possible worlds (b is
accessible to a, i.e., there is an accessibility arc from a to b) but also pairs of the form (t ,(a,b))∈R, meaning that the arc (a,b) is accessible to t, or even connections of the form((a,b),(c,d))∈R. This new kind of Kripke semantics allows us to characterise more axiomatic modal logics (with one modality) by a class of reactive frames.
There are logics which cannot be characterised by ordinary frames but which can be
characterised by reactive frames. We also discuss the manifestation of the ‘reactive’
idea in the context of automata theory, where we allow the automaton to react and
change it’s own definition as it responds to input, and in graph theory, where the
graph can change under us as we manipulate it.
http://hdl.handle.net/10993/15853

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
art%3A10.1007%2Fs10472-012-9313-y(1).pdfPublisher postprint905.11 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.