A Modal Logic for Termgraph Rewriting

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs allow one to describe classical data-structures (possibly with pointers) such as doubly-linked lists, circular lists etc. We show how the proposed logic can faithfully describe (i) termgraphs as well as (ii) the application of a termgraph rewrite rule (i.e. matching and replacement) and (iii) the computation of normal forms with respect to a given rewrite system. We also show how the proposed logic, which is more expressive than propositional dynamic logic, can be used to specify shapes of classical data-structures (e.g. binary trees, circular lists etc.)

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

Coalition and coalition announcement logic

Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other’s knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and Coalition Announcement Logic. They allow us to reason about what groups of agents can achieve through joint announcements in non-competitive and competitive environments. In this paper, we consider a combination of these logics – Coalition and Group Announcement Logic and provide its complete axiomatisation. Moreover, we partially answer the question of how group and coalition announcement operators interact, and settle some other open problems

Well structured program equivalence is highly undecidable

We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the construction of program equivalence, which returns the value $\mathsf{T}$ precisely when two given programs are equivalent on halting computations. We show that virtually any variant of propositional dynamic logic has $\Pi_1^1$-hard validity problem if it can express even just the equivalence of well-structured programs with the empty program \texttt{skip}. We also show, in these cases, that the set of propositional statements valid over finite models is not recursively enumerable, so there is not even an axiomatisation for finitely valid propositions.Comment: 8 page

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

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