We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterised according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Countable relation algebras with homogeneous representations are characterised by first order formulas. Equivalence games are defined, and are used to establish whether an algebra is !-categorical. We have a simple proof that the perfect extension of a representable relation algebra is completely representable. An important open problem from algebraic logic is addressed by devising another twoplayer game, and using it to derive equational axiomatisations for the classes of all representable relation algebras and representable cylindric algebras. Other instances of this ap...

We introduce quantified interpreted systems, a semantics to reason about knowledge in multi-agent systems in a first-order setting. Quantified interpreted systems may be used to interpret a variety of first-order modal epistemic languages with global and local terms, quantifiers, and individual and distributed knowledge operators for the agents in the system. We define first-order modal axiomatisations for different settings, and show that they are sound and complete with respect to the corresponding semantical classes. The expressibility potential of the formalism is explored by analysing two MAS scenarios: an infinite version of the muddy children problem, a typical epistemic puzzle, and a version of the battlefield game. Furthermore, we apply the theoretical results here presented to the analysis of message passing systems [17,41], and compare the results obtained to their propositional counterparts. By doing so we find that key known meta-theorems of the propositional case can be expressed as validities on the corresponding class of quantified interpreted systems.

This chapter considers theorem proving for discrete temporal logics. We are interested in deciding or at least enumerating the formulas of the logic which are valid, that is, are true in all circumstances. Most of the techniques for temporal theorem-proving have been extensions for methods developed for classical logics but completely novel techniques have also been developed. Initially we concentrate on discrete linear-time temporal logics, describing axiomatic, tableau, automata and resolution based approaches. The application of these approaches to other temporal logics is discussed. 1 Introduction Readers of this handbook will be aware of the wide variety of useful tasks which require reasoning about time. There are many applications of temporal reasoning tasks to problems of knowledge changing, to planning, to processing natural language, to managing the interchange of information, and to developing complex systems. There are a wide variety of temporal logics available in which s...

message passing systems, completeness. We introduce and investigate quantified interpreted systems, a semantics to reason about knowledge and time in a firstorder setting. We provide an axiomatisation, which we show to be sound and complete. We utilise the formalism to study message passing systems (Lamport 1978; Fagin et al 1995) in a first-order setting, and compare the results obtained to those available for the propositional case.

We apply the MetateM executable temporal logic programming language in a distributed system guise to a case study of a hospital patient monitoring system. The purpose is to test MetateM as a framework in which to implement prototypes for developing specifications of complex reactive systems. As it is still in its early stages of development itself we learn a lot about what still needs to be done to make MetateM a successful tool here. Nevertheless we demonstrate its very satisfactory progress and promising potential. 1 The author wishes to thank Marcelo Finger, Michael Fisher, Ian Hodkinson, Tony Hunter, Richard Owens and Ben Strulo for many helpful discussions. The work was supported by the U.K. Science and Engineering Research Council under the MetateM project (GR/F/28526). Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2. Informal Description of PMS : : : : : : : : ...

Abstract. We investigate quantified interpreted systems, a computationally grounded semantics for a first-order temporal epistemic logic on linear time. We report a completeness result for the monodic fragment of a language that includes LTL modalities as well as distributed and common knowledge. We exemplify possible uses of the formalism by analysing message passing systems, a typical framework for distributed systems, in a first-order setting. 1