The interpolation property and Robinson's consistency property are important tools for applying logic to software engineering. We provide a uniform technique for proving the Interpolation Property, using the notion of bisimulation. For modal logics, this leads to simple, easy-to-check conditions on the logic which imply interpolation. We apply this result to fibering of modal logics and to modal logics of knowledge and belief.

When giving an nalysis of knowledge in multiagent systems, one needs a framework in which higher-order information and its dynamics can both be represented. A recent tradition stoxting in origina work by Plaza treats all of knowledge, higher-order knowledge, and its dynamics on the sae foot. Our work is in that tradition. It also fits in approaches that not only dynaize the epistemics, but also epistemize the dynamics: the ac- tions that (groups of) agents perform oxe epistemic actions. Different agents may have different information about which action is taking place, including higher-order information. We demonstrate that such information changes require subtle descriptions. Our contribution is to provide a complete axiomatization for n action language of vn Ditmoxsch, where an action is interpreted as a relation between epistemic states (pointed models) and sets of epistemic states. The applicability of the framework is found in every context where multiagent strategic decision making is at stake, and aready demonstrated in gae-like scenoxios such as Cluedo and coxd games.

This paper studies finitary modal logics, interpreted over coalgebras for an endofunctor, and establishes soundness, completeness and decidability results. The logics are studied within the abstract framework of coalgebraic modal logic, which can be instantiated with arbitrary endofunctors on the category of sets. This is achieved through the use of predicate liftings, which generalise atomic propositions and modal operators from Kripke models to arbitrary coalgebras. Predicate liftings also allow us to use induction along the terminal sequence of the underlying endofunctor as a proof principle. This induction principle is systematically exploited to establish soundness, completeness and decidability of the logics. We believe that this induction principle also opens new ways for reasoning about modal logics: Our proof of completeness does not rely on a canonical model construction, and the proof of the finite model property does not use filtrations. 1

In this paper we introduce a modal lan- guage L T for imposing constraints on trees, and an extension LT(L r) for imposing con- straints on trees decorated with feature structures. The motivation for introducing these languages is to provide tools for formalising grammatical frameworks perspicuously, and the paper illustrates this by showing how the leading ideas of arsa can be captured in LT(Lr).

Abstract. XPath 1.0 is a variable free language designed to specify paths between nodes in XML documents. Such paths can alternatively be specified in first-order logic. The logical abstraction of XPath 1.0, usually called Navigational or Core XPath, is not powerful enough to express every first-order definable path. In this paper we show that there exists a natural expansion of Core XPath in which every first-order definable path in XML document trees is expressible. This expansion is called Conditional XPath. It contains additional axis relations of the form (child::n[F])+, denoting the transitive closure of the path expressed by child::n[F]. The difference with XPath’s descendant::n[F] is that the path (child::n[F])+ is conditional on the fact that all nodes in between should be labeled by n and should make the predicate F true. This result can be viewed as the XPath analogue of the expressive completeness of the relational algebra with respect to first-order logic. 1

Cooperation logics have recently begun to attract attention within the multi-agent systems community. Using a cooperation logic, it is possible to represent and reason about the strategic powers of agents and coalitions of agents in game-like multi-agent systems. These powers are generally assumed to be implicitly defined within the structure of the environment, and their origin is rarely discussed. In this paper, we study a cooperation logic in which agents are each assumed to control a set of propositional variables---the powers of agents and coalitions then derive from the allocation of propositions to agents. The basic modal constructs in this Coalition Logic of Propositional Control (CL-PC) allow us to express the fact that a group of agents can cooperate to bring about a certain state of affairs. After motivating and introducing CL-PC, we provide a complete axiom system for the logic, investigate the issue of characterising control in CL-PC with respect to the underlying power structures of the logic, and formally investigate the relationship between CL-PC and Pauly's Coalition Logic. We then show that the model checking and satisfiability problems for CL-PC are both PSPACE-complete, and conclude by discussing our results and how CL-PC sits in relation to other logics of cooperation.

We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new finestructure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering of interesting new questions.

Since it was first proposed by Moses, Shoham, and Tennenholtz, the social laws paradigm has proved to be one of the most compelling approaches to the offline coordination of multiagent systems. In this paper, we make four key contributions to the theory and practice of social laws in multiagent systems. First, we show that the Alternating-time Temporal Logic (atl) of Alur, Henzinger, and Kupferman provides an elegant and powerful framework within which to express and understand social laws for multiagent systems. Second, we show that the effectiveness, feasibility, and synthesis problems for social laws may naturally be framed as atl model checking problems, and that as a consequence, existing atl model checkers may be applied to these problems. Third, we show that the complexity of the feasibility problem in our framework is no more complex in the general case than that of the corresponding problem in the Shoham–Tennenholtz framework (it is np-complete). Finally, we show how our basic framework can easily be extended to permit social laws in which constraints on the legality or otherwise of some action may be explicitly required. We illustrate the concepts and techniques developed by means of a running example.

By representing transition systems as coalgebras, the three main ingredients of their theory: coalgebra, homomorphism, and bisimulation, can be seen to be in a precise correspondence to the basic notions of universal algebra: \Sigma-algebra, homomorphism, and substitutive relation (or congruence). In this paper, some standard results from universal algebra (such as the three isomorphism theorems and facts on the lattices of subalgebras and congruences) are reformulated (using the afore mentioned correspondence) and proved for transition systems. AMS Subject Classification (1991): 68Q10, 68Q55 CR Subject Classification (1991): D.3.1, F.1.2, F.3.2 Keywords & Phrases: Transition system, bisimulation, universal coalgebra, universal algebra, congruence, homomorphism. Note: This paper will appear in `Modal Logic and Process Algebra', edited by Ponse, De Rijke and Venema [PRV95]. 2 Table of Contents 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : ...

Arrow Logic remains PSPACE-complete. Further arrow axioms can easily lead to 36 undecidability. (In private correspondence, Marx has also announced EXP-TIME complexity for the original Guarded Fragment, via a reduction to CRS over 'locally cube' models.) Marx and Venema 1996 is a systematic state-of-the-art presentation of many-dimensional modal logic, including bridges with algebraic logic, as well as many key techniques for dynamic logic, broadly conceived. Ter Meulen 1995 proposes a concise framework for temporal representation in natural language that may be viewed as an alternative dynamification of temporal logic, using an extra, intermediate level of representation. Successive formulas algorithmically generate successive 'dynamic aspect trees', for which there is a notion of 'succesful embedding' into standard temporal models. Valid inference can then be defined as verification of the conclusion by any succesful embedding for the DAT of the premise sequence. This alternative d...