Logic is not just about single-agent notions like reasoning, or zero-agent notions like truth, but also about communication between two or more people. What we tell and ask each other can be just as 'logical' as what we infer in Olympic solitude. We show how such interactive phenomena can be studied systematically by merging epistemic and dynamic logic.

The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multi-agent epistemic language, whose main uses so far have been in reasoning about space. We show that this more geometrical perspective affords greater powers of distinction in the study of common knowledge, defining new collective agents, and merging information for groups of agents.

Abstract. Hybrid logic refers to a group of logics lying between modal and first-order logic in which one can refer to individual states of the Kripke structure. In particular, the hybrid logic HL(@, ↓) is an appealing extension of modal logic that allows one to refer to a state by means of the given names and to dynamically create new names for a state. Unfortunately, as for the richer first-order logic, satisfiability for the hybrid logic

We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig. We point out some consequences in temporal predicate logic and algebraic logic. AMS classification: Primary 03B20; Secondary 03B45, 03C07, 03C13, 03C30, 03G15 Keywords: finite structures, modal logic, modal fragment, packed fragment 1 Introduction Perhaps because beginning students of modal logic are often told that modal logic is more expressive than first-order logic and indeed has some second-order expressive power, or perhaps because they are hoping for something new, it can come as a surprise to them that every modal formula has a `standard translation' into first-order logic. For example, (p !q) is translated to 9y(R(x;y) ^ (P(y) ! 8z(R(y;z) ! Q(z)))): (1) The translation mimics the Kripke semantics for modal logic. Not every first-order formula (with one free variable in the appropriate signature) is the translation of a modal formu...

The guarded fragment (GF) was introduced in [1] as a fragment of first order logic which combines a great expressive power with nice modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. While GF has been established as a particularly well-behaved fragment of first order logic in many respects, interpolation fails in restriction to GF, [9]. In this paper we consider the Beth property of first order logic and show that, despite the failure of interpolation, it is retained in restriction to GF. The Beth property for GF is here established on the basis of a limited form of interpolation, which more closely resembles the interpolation property that is usually studied in modal logics. ¿From this we obtain that, more specifically, even every n-variable guarded fragment with up to nary

We develop a translation-based view dual of modal logic as the study of intensional languages that are at the same time interesting expressive and decidable parts of standard logical systems. This tandem approach improves our understanding of modal logic -- while at the same time, it extends the range of modal notions and techniques into broader areas of standard logic. 1 Translation as a Way of Life 1.1 Basic modal logic and the modal fragment of FOL Modal languages as used to-day can be considered a species of their own, inhabiting the realm of Intensional Logic. But they can also be translated into fragments of standard logical languages, mostly first-order, sometimes higher-order or infinitary. These translations reflect the truth conditions for modal operators in possible worlds models. The ur-example is the basic modal language of possibility and necessity, whose standard translation ST inspired Correspondence Theory (van Benthem 1976, 1985): an existential modality <>p goes to a...

Modal logic becomes action logic by adding programs as in propositional dynamic logic or the µ-- calculus. Modal languages can be seen as decidable fragments of first-order logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of firstorder logic have been identified that enjoy the same pleasant features. The latter can serve as richer action languages as well. We will develop the logic of guarded fragments as a form of process theory. ln particular, moving from sequential to parallel process operations correlates with moving to first-order fragments that are close to, or perhaps just over the decidable--undecidable fence. 1 The modal dynamics of actions We will start by reviewing the basics. Standard polymodal logic is a decidable fragment of the first-order logic of process graphs (labeled transition systems, Kripke models). It can be characterized semantically as consisting, up to logical equivalence, of those firs...

This paper describes a sublanguage of Casl, called Casl-DL, that corresponds to the Web Ontology Language (OWL) being used for the semantic web. OWL can thus benefit from Casl’s strong typing discipline and powerful structuring concepts. Vice versa, the automatic decision procedures available for OWL DL (or more precisely, the underlying description logic SHOIN(D)) become available for a sublanguage of Casl. This is achieved via translations between Casl-DL and SHOIN(D), formalized as so-called institution comorphisms.

Abstract. We prove ExpTime-membership of the satisfiability problem for loosely ∀-guarded first-order formulas with a bounded number of variables and an unbounded number of constants. Guarded fragments with constants are interesting by themselves and because of their connection to hybrid logic.

The first part of the thesis concerns problems related to the question: "when can a regular tree language be defined in first-order logic?" Characterizations in terms of automata of first-order logic and the related chain logic are presented. A decidable property of tree automata called confusion is introduced; it is conjectured that a regular tree language can be defined in chain logic if and only if its minimal automaton does not contain confusion. Furthermore, polynomial time algorithms are presented that decide if a given regular tree language can be defined in any one of the temporal branching logics TL[EX], TL[EF] and TL[EX, EF]. In the second part...