Semantic games are an important evaluation method for a wide range of logical languages, and are frequently resorted to when traditional methods do not easily apply. A case in point is a family of independence-friendly (IF) logics which allow regulation over information flow in formulas, and thus perfect information fails in the games associated with such formulas. This mechanism of imperfect information is studied in this paper. It is noted that imperfect information of players often gives rise to the game-theoretic phenomenon of imperfect recall. Furthermore, independence-friendliness in epistemic logic is investigated. We also discuss a couple of misunderstandings that have occurred in the literature concerning IF first-order logics and gametheoretical semantics, related to such issues as intuitionism, constructivism, truth-definitions, mathematical prose, and the status of set theory. By straighten out these misunderstandings, we hope to show the importance of the role semantics ga...

We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But guarding quantification increases worst-case time complexity.

This paper is based on tutorials on “Logic and Games ” at the 7th

Abstract. In this paper we recast the formalism of argumentation formalismknownasDeLP(DefeasibleLogicProgramming)ingame-theoretic terms. By considering a game between a Proponent and an Opponent, in which they present arguments for and against each literal we obtain a bigger gamut of truth values for those literals and their negations as they are defended and attacked. An important role in the determination of warranted literals is assigned to a defeating relation among arguments. We consider first an unrestricted version in which these games may be infinite and then we analyze the underlying assumptions commonly used to make them finite. Under these restrictions the games are always determined-one of the players has a winning strategy. We show how varying the defeating relation may alter the set of truth values reachable under this formalism. We also show how alternative characterizations of the defeating relation may lead to different assignations of truth values to the literals in a DeLP program. 1

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It is only relatively recently that in computer science we have begin to exploit the idea that proofs are essentially executable programs, although it emerged from intuitionistic mathematics some decades before the first digital computers ran programs. One application, as it were from logic to computer science, has been in the design of ever more expressive type systems for programming. The situation is currently that type-checkers have been written for a range of experimental functional programming languages in which the type systems are sufficiently rich to express propositions, logical connectives, predicates, quantifiers, relations, predicate transformers, temporal and modal operators, and everything any one has ever asked for to write fully precise mathematical specifications, or the reasoning that underlies the construction of a program to meet a precise specification. The kind of programs we can write using these type systems are programs that denote mathematical values; they do not of themselves actually do anything or exhibit behaviour. Rather, we do something with them, or make practical application of them, or somehow use a mathematical value as a guide to action. Put crudely, the puzzles

under the supervision of Dr Yde Venema, and submitted to the Board of

The purpose of this paper is to explore the extent in which the idea of using negotiation games in tandem with the theory of semantic games is relevant to the concept of meaning in logical semantics. The need for such negotiations is argued to arise when some formulas are logically non-coherent, which in turn may take place because of conflicts between the players playing the associated non-strictly competitive semantic language-games on these formulas.