Admissibility and unifiability in contact logics

Contact logics are logics for reasoning about the contact relations between regular subsets in a topological space. Admissible inference rules can be used to improve the performance of any algorithm that handles provability within the context of contact logics. The decision problem of unifiability can be seen as a special case of the decision problem of admissibility. In this paper, we examine the decidability of admissibility problems and unifiability problems in contact logics

Definability and canonicity for Boolean logic with a binary relation

International audienceThis paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical

Ockhamist Propositional Dynamic Logic: a natural link between PDL and CTL

International audienceWe present a new logic called Ockhamist Propositional Dynamic Logic, OPDL, which provides a natural link between PDL and CTL*. We show that both PDL and CTL* can be polynomially embedded into OPDL in a rather simple and direct way. More generally, the semantics on which OPDL is based provides a unifying framework for making the dynamic logic family and the temporal logic family converge in a single logical framework. Decidability of the satisfiability problem for OPDL is studied in the paper

Asynchronous Announcements

We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the logic contains dynamic modalities for making announcements and for receiving them. What an agent believes is a function of her initial uncertainty and of the announcements she has received. Beliefs need not be truthful, because announcements already made may not yet have been received. As announcements are true when sent, certain message sequences can be ruled out, just like inconsistent cuts in distributed computing. We provide a complete axiomatization for this \emph{asynchronous announcement logic} (AA). It is a reduction system that also demonstrates that any formula in $AA$ is equivalent to one without dynamic modalities, just as for public announcement logic. The model checking complexity is in PSPACE. A detailed example modelling message exchanging processes in distributed computing in $AA$ closes our investigation

Axiomatizing the lexicographic products of modal logics with linear temporal logic

Given 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

Algorithms and Complexity of Automata Synthesis by Asynhcronous Orchestration With Applications to Web Services Composition

AbstractComposition of services is necessary for realizing complex tasks on the Web. It has been characterized either as a plan synthesis problem or as a software synthesis problem: given a goal and a set of Web services, generate a composition of the Web services that satisfies the goal. We propose algorithms for performing automated Web service composition. We also examine the composition of services from the perspective of computational complexity

Agents that look at one another

International audienceDespite the fact that epistemic connectives are sometimes interpreted in concrete structures defined by means of runs and clock time functions, one of the things that strikes one when studying multiagent logics is how abstract their semantics are. Contrasting this fact is the fact that real agents like robots in everyday life and virtual characters in video games have strong links with their spatial environment. In this article, we introduce multiagent logics which semantics can be defined by means of purely geometrical notions: possible states are defined by means of the positions in ℝn occupied by agents and the sections of ℝn seen by agents whereas accessibility relations are defined by means of the ability of agents to imagine possible states compatible with what they currently see