Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntax-independent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with non-functional features such as control operators and locally-scoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6]. Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in computer-assisted verification and program analysis. Some promising steps have already been taken in this

Abstract. The European Commission’s eEurope initiative aims to bring every citizen, home, school, business and administration online to create a digitally literate Europe. The value lies not in the objective itself, but in its ability to facilitate the advance of Europe into new ways of living and working. Just as in the first literacy revolution, our lives will change in ways never imagined. The vision of eEurope is underpinned by a technological infrastructure that is now taken for granted. Yet it provides us with the ability to pioneer radical new ways of doing business, of undertaking science, and, of managing our everyday activities. Key to this step change is the development of appropriate mechanisms to automate and improve existing tasks, to anticipate desired actions on our behalf (as human users) and to undertake them, while at the same time enabling us to stay involved and retain as much control as required. For many, these mechanisms are now being realised by agent technologies, which are already providing dramatic and sustained benefits in several business and industry domains, including B2B exchanges, supply chain management, car manufacturing, and so on. While there are many real successes of agent technologies to report, there is still much to be done in research and development for the full benefits to be achieved. This is especially true in the context of environments of pervasive computing devices that are envisaged in coming years. This paper describes the current state-of-the-art of agent technologies and

We present the general theory of the method of glueing and associated technique of orthogonality for constructing categorical models of all the structure of linear logic: in particular we treat the exponentials in detail. We indicate simple applications of the methods and show that they cover familiar examples. 1

This paper presents a technique called generic composition to provide a uniform basis for modal operators, sequential composition, di#erent kinds of parallel compositions and various healthiness conditions appearing in a variety of semantic theories. The weak inverse of generic composition is defined. A completeness theorem shows that any predicate can be written in terms of generic composition and its weak inverse. A number of algebraic laws that support reasoning are derived.

Formal dialogue games have been studied in philosophy since at least the time of Aristotle. Recently they have been applied in various contexts in computer science and arti cial intelligence, particularly as the basis for interaction between autonomous software agents. We review these applications and discuss the many open research questions and challenges at this exciting interface between philosophy and computer science.

This paper presents a game model of Second-order Intuitionistic Multiplicative Affine Logic (IMAL2). We extend Lamarche's essential nets to the second-order ane setting and use them to show that the model is fully and faithfully complete.

This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed categories and their relation to intuitionistic logic is followed by a consideration of symmetric monoidal closed, linearly distributive and ∗-autonomous categories and their relation to multiplicative linear logic. We examine nonsymmetric monoidal categories, and consider them as models of noncommutative linear logic. We introduce traced monoidal categories, and discuss their relation to the geometry of interaction. The necessary aspects of the theory of monads is introduced in order to describe the categorical modelling of the exponentials. We conclude by briefly describing the notion of full completeness, a strong form of categorical completeness, which originated in the categorical model theory of linear logic. No knowledge of category theory is assumed, but we do assume knowledge of linear logic sequent calculus and the standard models of linear logic, and modest familiarity with typed lambda calculus. 0

We analyze IF/hyper-classical games by bringing together two viewpoints from Jaakko Hintikka's work: game semantics, and epistemic logic. In the process, we link up between logic and game theory.

: Part I presents a model of interactive computation and a metric for expressiveness, part II relates interactive models of computation to physics, and part III considers empirical models from a philosophical perspective. Interaction machines, which extend Turing machines to interaction, are shown in Part I to be more expressive than Turing machines by a direct proof, by adapting Godel's incompleteness result, and by observability metrics. Observation equivalence provides a tool for measuring expressiveness according to which interactive systems are more expressive than algorithms. Refinement of function equivalence by observation of outer interactive behavior and inner computation steps are examined. The change of focus from algorithms specified by computable functions to interaction specified by observation equivalence captures the essence of empirical computer science. Part II relates interaction in models of computation to observation in the natural sciences. Explanatory power in p...

We discuss how issues of information and computation interact with logic today, and what might be a natural extended agenda of investigation.