We propose a model

The paper studies many-dimensional modal logics corresponding to products of Kripke frames. It proves results on axiomatisability, the finite model property and decidability for product logics, by applying a rather elaborated modal logic technique: p-morphisms, the finite depth method, normal forms, filtrations. Applications to first order predicate logics are considered too. The introduction and the conclusion contain a discussion of many related results and open problems in the area.

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.

In this paper, we revive the topological interpretation of modal logic, turning it into a general language of patterns in space. In particular, we define a notion of bisimulation for topological models that compares different visual scenes. We refine the comparison by introducing EhrenfeuchtFra iss'e style games between patterns in space. Finally, we consider spatial languages of increased logical power in the direction of geometry. Also, Intelligent Sensory Information Systems, University of Amsterdam 1 Contents 1 Reasoning about Space 3 2 Topological Structure: a Modal Approach 4 2.1 The topological view of space . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Topological spaces . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Special properties of topological spaces . . . . . . . . . . . 6 2.1.3 Structure preserving mappings . . . . . . . . . . . . . . . 7 3 Basic Modal Logic of Space 8 3.1 Topological language and semantics . . . . . . . . . . . . . . . . 8 3.2 Topologi...

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Abstract Tense logics in the bimodal propositional language are investigated with respect to the Finite Model Property (FMP). In order to prove positive results techniques from investigations of modal logics above K4 are extended to tense logic. General negative results show the limits of this transfer. The main result is that the minimal tense extension of a confinal subframe logic \Lambda above K4 has the FMP if and only if the \Lambda-frames form an elementary class.

Agent-based computing in Artificial Intelligence has given rise to a number of diverse and competing proposals for agent programming languages. For several reasons it has been difficult to evaluate and compare those different proposals. One of the main reasons is the lack of a general semantic framework. In this paper, we give a formal embedding of the agent language AgentSpeak(L) in our own agent language 3APL. To this end we define a notion of simulation based on the formal operational semantics of the languages. A main result of the paper is a proof that 3APL can simulate AgentSpeak(L). As a consequence,3APL has at least the same expressive power as AgentSpeak(L). The comparison yields some new insights into the features of the agent languages. One of the results is that AgentSpeak(L) can be substantially simplified.

. In this paper we introduce the two-phase deontic logic 2dl. The preference-based semantics of 2dl is based on an explicit preference ordering between worlds, representing different degrees of ideality. The preference ordering can be used in two ways to evaluate formulas, which we call ordering and minimizing. Ordering uses all preference relations between relevant worlds, whereas minimizing uses the most preferred worlds only. We show that ordering corresponds to the inference pattern strengthening of the antecedent and the conjunction rule for the consequent, and minimizing to the inference pattern weakening of the consequent and the disjunction rule for the antecedent. Moreover, we show that in several problems like the notorious contrary-to-duty paradoxes ordering and minimizing have to be combined to obtain the desirable conclusions, and that in a dyadic deontic logic this can only be done in a so-called two-phase deontic logic. In the first phase the preference ordering is const...

I consider myself very fortunate for having the opportunity to work on this thesis under the supervision of Johan van Benthem and Dick de Jongh. Besides shedding a great deal (of very different!) light upon the problems contained in this thesis, they provided the encouragement and support needed to see this volume through to its completion. Thank you. Thanks to Nick Bezhanishvili and Yde Venema, for serving as members on my defense committee and for useful suggestions along the way. To Benedikt Löwe for the same, and for providing inspiring lecture courses, as well as leaving his door open for conversation. To Darko Sarenac for his helpful skepticism and generous hospitality in Palo Alto. And to Niels Molenaar for handling organizational matters right before I was to defend my thesis. In addition, I would like to thank Thomas, Be, Jill, Charles, Alexandra, Chunlai and Café Reibach for making my time in Amsterdam so enjoyable. This thesis is dedicated to my parents Terry and Therese and sister Teena. Without whom.

Abstract: A class of Kripke models for intuitionistic propositional logic is ‘axiomatic’ if it is the class of all models of some set of formulas (axioms). This paper discusses various structural characterisations of axiomatic classes in terms of closure under certain constructions, including images of bisimulations, disjoint unions, ultrapowers and ‘prime extensions’. The prime extension of a model is a new model whose points are the prime filters of the lattice of upwardly-closed subsets of the original model. We also construct and analyse a ‘definable ’ extension whose points are prime filters of definable sets. A structural explanation is given of why a class that is closed under images of bisimulations and invariant under prime/definable extensions must be invariant under arbitrary ultrapowers. This uses iterated ultrapowers and saturation.