Dialogical logic is a game-theoretical approach to logic. Logic is studied with the help of certain games, which can be thought of as idealized argumentations. Two players, the Proponent, who puts forward the initial thesis and tries to defend it, and the Opponent, who tries to attack the Proponent’s thesis, alternately utter argumentative moves according to certain rules. For a long time the dialogical approach had been worked out only for classical and intuitionistic logic. The seven papers of this dissertation (...) show that this narrowness was uncalled for. The initial paper presents an overview and serves as an introduction to the other papers. Those papers are related by one central theme. As each of them presents dialogical formulations of a different non-classical logic, they show that dialogical logic constitutes a powerful and flexible general framework for the development and study of various logical formalisms and combinations thereof. As such it is especially attractive to logical pluralists that reject the idea of “the single correct logic”. The collection contains treatments of free logic, modal logic, relevance logic, connexive logic, linear logic, and multi-valued logic. (shrink)

The aim of the paper is to propose a unified formal account of dialogical cognitive processes so that it allows the analysis of similarities and differences between those processes. Formal dialogue systems constitute two basic categories or paradigms of modelling communication depending on what cognitive process is described by a given system. The first paradigm consists of designing a set of dialogue rules in a similar manner to Lorenzen’s dialogue logic, and according to which players jointly aim to prove the (...) validity of a formula. In such cases we will say that the system describes formal dialogues and the formal cognitive process of proving the validity of a formula. The second paradigm focuses on building a system similar to Hamblin’s formal dialectics, which “simulates” the real-life communication practice. In the type of dialogues described by those systems, players perform “good” argumentation, i.e. argumentation which fulfils certain requirements of rationality such as e.g. the requirement of not committing a fallacy of circular reasoning. In such a case we will be speaking of a natural dialogue and a natural cognitive process of argumentation. (shrink)

We introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game’s chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for (...) the logics of lattices with weak negation and modal operators. (shrink)