4,342 research outputs found
Spatial Logics ( Journal of Applied Non-Classical Logics 12-2002)
No full textInternational audience"A Modal Walk Through Space" Marco Aiello, Johan van Benthem ; "Modal Logics for Parallelism, Orthogonality, and Affine Geometries" Philippe Balbiani, Valentin Goranko ; "Modal Logics Based on Mathematical Morphology for Qualitative Spatial Reasoning" Isabelle Bloch ; "Axiomatizing Distance Logics" Oliver Kutz, Holger Sturm, Nobu-Yuki Suzuki, Frank Wolter, Michael Zakharyaschev ; "A Topological Constraint Language with Component Counting" Ian Pratt-Hartmann ; "A Canonical Model of the Region Connection Calculus" Jochen Renz ; "Mereotopology in 2nd-Order and Modal Extensions of Intuitionistic Propositional Logic" Paolo Torrini, John G. Stell, Brandon Bennett ; "A Proximity Approach to Some Region-Based Theories of Space" Dimiter Vakarelov, Georgi Dimov, Ivo Düntsch, Brandon Bennet
A Hierarchy of Modal Logics With Relative Accessibility Relations
No full textIn this paper we introduce and investigate various classes of multimodal logics based on frames with relative accessibility relations. We discuss their applicability to representation and analysis of incomplete information. We provide axiom systems for these logics and we prove their completeness. 1 Introduction The original motivation for introducing and investigating modal logics with relative accessibility relations comes from the theory of information systems. However, as it is shown in this paper, a number of standard multimodal logics can be uniformly presented and investigated within the general framework of relative relations as well. Information systems are the collections of information items that have the form of descriptions of some objects in terms of their properties. More formally, by an information system we mean a structure S = (OB; AT ; fVAL a : a 2 ATg) such that OB is a nonempty set Philippe Balbiani, [email protected], Laboratoire d'informatique de..
Two-sorted point-interval temporal logics
No full textThere are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as particular, duration-less intervals. Here we develop explicitly two-sorted point-interval temporal logical framework whereby time instants (points) and time periods (intervals) are considered on a par, and the perspective can shift between them within the formal discourse. We focus on fragments involving only modal operators that correspond to the inter-sort relations between points and intervals. We analyze their expressiveness, comparative to interval-based logics, and the complexity of their satisfiability problems. In particular, we identify some previously not studied and potentially interesting interval logics. © 2011 Elsevier B.V
A primer on innovation and growth
No full textPhilippe Aghion emphasises that for Europe to stimulate innovation and growth, it is not enough to increase spending on research and development and the protection of intellectual property.
Sahlqvist theorems for precontact logics
No full textPrecontact logics are propositional modal logics that have been recently considered in order to obtain decidable fragments of the region-based theories of space introduced by
De Laguna and Whitehead. We give the definition of Sahlqvist formulas to this region-based setting and we prove correspondence and canonicity results. Together, these results give rise to a completeness result for precontact logics that are axiomatized by Sahlqvist axioms
Definability and computability for PRSPDL
No full textPRSPDL is a variant of PDL with parallel composition. In the Kripke models in which PRSPDL-formulas are evaluated, states have an internal structure. We devote this paper to the definability issue of several classes of frames by means of the language of PRSPDL and to the computability issue of PRSPDL-validity for various fragments of the PRSPDL-language and for various classes of PRSPDL-frames
About intuitionistic public announcement logic
No full textPublic announcement logic (PAL) is a logic for reasoning about the dynamic of knowledge in a multi-agent system in which public announcements are made. Syntactically, public announcements are modal formulas. Semantically, they correspond to restrictions of models. Ma et al. (2014) use the standard toolkit of duality theory in modal logic to define an algebraic semantics for a combination of IPL and PAL into intuitionistic public announcement logic (IPAL). In this paper, grounding our approach on relational semantics rather than on algebraic semantics, we give a sound and complete axiomatization of IPAL and we consider a complete sequent calculus for the associated membership problem
Axiomatizing the lexicographic products of modal logics with linear temporal logic
No full textGiven modal logics L1 and L2, their lexicographic product L1 x L2 is a new logic whose frames are the Cartesian products of an L1-frame and an L2-frame, but with the new accessibility relations reminiscent of a lexicographic ordering. This article considers the lexicographic products of several modal logics with linear temporal logic (LTL) based on ``next'' and ``always in the future''. We provide axiomatizations for logics of the form L x LTL and define cover-simple classes of frames; we then prove that, under fairly general conditions, our axiomatizations are sound and complete whenever the class of L-frames is cover-simple. Finally, we prove completeness for several concrete logics of the form L x LTL
Unification in modal logic Alt1
No full textALT1 is the least modal logic containing the formula characterizing deterministic frames. The unification problem in ALT1 is to determine, given a formula A(x1,...,xn), whether there exists formulas B1, ..., Bn such that A(B1,...,Bn) is in ALT1. In this paper, we show that the unification problem in ALT1 is in PSPACE. We also show that there exists an ALT1-unifiable formula that has no minimal complete set of unifiers. Finally, we study sub-Boolean variants of the unification problem in ALT1
A Natural Intuitionistic Modal Logic: Axiomatization and Bi-Nested Calculus
No full textWe introduce FIK, a natural intuitionistic modal logic specified by Kripke models satisfying the condition of forward confluence. We give a complete Hilbert-style axiomatization of this logic and propose a bi-nested calculus for it. The calculus provides a decision procedure as well as a countermodel extraction: from any failed derivation of a given formula, we obtain by the calculus a finite countermodel of it directly
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