On some questions of L. ÅqvistArdeshir, Mohammad; Nabavi, Fateme
doi: 10.1093/jigpal/jzk001pmid: N/A
We give answers to some questions raised by L. Åqvist in [6] and [7]. The question raised in [7] which we will answer positively is about the representability of Åqvist's system G in a hierarchy of alethic modal logics Hm, m = 1, 2, …. On the other hand, the questions raised in [6] are about the completeness of some monadic alethic denotic logics with respect to their Kripke semantics.
Admissible Inference Rules in the Linear Logic of Knowledge and Time LTKCalardo, Erica
doi: 10.1093/jigpal/jzk002pmid: N/A
The paper investigates admissible inference rules for the multi-modal logic LTK, which describes a combination of linear time and knowledge. This logic is semantically defined as the set of all ℒ𝒯𝒦-valid formulae, where ℒ𝒯𝒦-frames are multi-modal Kripke-frames combining a linear and discrete representation of the flow of time with special S5-like modalities, defined at each time cluster and representing knowledge. We start by revising the effective finite model property in this particular case, while the central part of the paper is devoted to constructing special n-characterising models for LTK. Such structeres allow us to find an algorithm determining admissible inference rules in LTK; the main result of this work is that LTK is decidable with respect to inference rules.
A Minimal Hybrid Logic for IntervalsHussain, Altaf
doi: 10.1093/jigpal/jzk003pmid: N/A
Taking our inspiration from van Benthem's treatment of temporal interval structures, and Halpern and Shoham's work on intervals, we introduce an interval hybrid temporal logic with two binary relations, precedence and inclusion, for talking about interval temporal structures. This paper can be seen as an continuation of the work began in an earlier paper, in which we undertook a purely modal treatment of interval temporal structures. By introducing an interval hybrid temporal logic, we enrich the logic with nominals, and thereby increase the expressivity of the logic. We study the interval hybrid temporal logic in its full generality and identify two important classes of interval temporal structures: the class of minimal interval structures, and the class of van Benthem minimal interval structures. We present sound and complete tableau calculi for both classes of structures. We prove that the logic of minimal interval structures is decidable, by developing a novel bulldozing technique that handles both the presence of nominals and the interaction between the two relations. We go on to show that the satisfiability problem is EXPTIME-complete. We conclude the paper with the remark that the decidability (or otherwise) and complexity of the logic of van Benthem minimal interval structures remains an interesting open problem
Partially-Elementary Extension Kripke Models: A Characterization and ApplicationsPołacik, Tomasz
doi: 10.1093/jigpal/jzk005pmid: N/A
A Kripke model for a first order language is called a partially-elementary extension model if its accessibility relation is not merely a (weak) submodel relation but a stronger relation of being an elementary submodel with respect to some class of fromulae. As a main result of the paper, we give a characterization of partially-elementary extension Kripke models. Throughout the paper we exploit a generalized version of the hierarchy of first order formulae introduced by W. Burr. We present some applications of partially-elementary extension Kripke models to subtheories of Heyting Arithmetic and provide examples of their models and prove some of their properties. For example, we show that finite models of subtheories in question need not be normal (in the sense of S. Buss). The presented results show that the properties of models of subtheories of Heyting Arithmetic differ much from the properties of models of the full theory.