Frank Wolter DECIDABILITY OF TENSE LOGICS
نویسنده
چکیده
transitivity = 2p → 22p, and the axioms for linearity .3 fomulated for both 2 and 2−. Here we call normal extensions of Lin.t simply tense logics. There is a sequence of papers on uni-modal logics of weak orderings. Probably the first one is the famous result of R. Bull [1] that all extensions of S4.3 have the fmp. Then K. Fine [3] proved that all extensions of K4.3 are complete, and recently M. Zakharyaschev [6] proved the decidability of all finitely axiomatizable extensions of K4.3. Contrary to this development research in tense logic was restricted to some important systems (consult [2]). Here we shall continue the modal tradition and explain some steps of the proof of
منابع مشابه
Decidability of Circumscribed Description Logics Revisited
We revisit non-monotonic description logics based on circumscription (with preferences) and prove several decidability results for their satisfiability problem. In particular, we consider circumscribed description logics without the finite model property (DL-LiteF andALCFI) and with fixed roles (DL-LiteF and a fragment of DL-LiteR), improving upon previous decidability results that are limited ...
متن کاملThe product of converse PDL and polymodal K
The product of two modal logics L1 and L2 is the modal logic determined by the class of frames of the form F G such that F and G validate L1 and L2, respectively. This paper proves the decidability of the product of converse PDL and polymodal K. Decidability results for products of modal logics of knowledge as well as temporal logics and polymodal K are discussed. All those products form rather...
متن کاملFusions of Description Logics and Abstract Description Systems
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covere...
متن کاملAxiomatizing Distance Logics
In [8, 6] we introduced a family of ‘modal’ languages intended for talking about distances. These languages are interpreted in ‘distance spaces’ which satisfy some (or all) of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal languages. The aim of this paper is to a...
متن کاملNon-primitive recursive decidability of products of modal logics with expanding domains
We show that—unlike products of ‘transitive’ modal logics which are usually undecidable— their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite...
متن کامل