This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

Recent work on the development of a dialogical approach to the logic of fiction stresses the notion of existence as choice. Moreover, this approach to existence has been combined with the notion of ontolog-ical dependence as deployed by A. Thomasson’s artifactual theory of fiction. In order to implement such a combination within the dialogical frame several predicates of ontological dependence have been de-fined. However, the definition of such predicates seems to lean on a model-theoretic semantics for mod-al logic after all. (...) The main aim of the present paper is to set a dialogical frame for the study of fictions in the context of the dialogical approach of CTT recently developed by S. Rahman and N. Clerbout where a fully-interpreted language is unfolded. We will herewith develop the idea that in such a setting fiction-al entities are understood as hypothetical objects, that is, objects (functions) the existence of which is dependent upon one or more hypotheses that restrict the scope of choices available. We will finish the paper by suggesting that this provides both a natural and genuinely dialogical way to understand R. Frigg’s take on scientific models as fictions and a new perspective on Thomasson’s notion of generic ontological dependence. Keywords: fiction, dialogues, dialogical logic, hypothetical objects, scientific models. (shrink)

We now move to the demonstration of the left-to-right direction of the equivalence result. Let us assume that there is a winning $$\mathbf {P}$$ P -strategy in the dialogical game for $$\varphi $$ φ.

In the present paper we confront Martin- Löf’s analysis of the axiom of choice with J. Hintikka’s standing on this axiom. Hintikka claims that his game theoretical semantics for Independence Friendly Logic justifies Zermelo’s axiom of choice in a first-order way perfectly acceptable for the constructivists. In fact, Martin- Löf’s results lead to the following considerations:Hintikka preferred version of the axiom of choice is indeed acceptable for the constructivists and its meaning does not involve higher order logic.However, the version acceptable (...) for constructivists is based on an intensional take on functions. Extensionality is the heart of the classical understanding of Zermelo’s axiom and this is the real reason behind the constructivist rejection of it.More generally, dependence and independence features that motivate IF-Logic, can be formulated within the frame of constructive type theory without paying the price of a system that is neither axiomatizable nor has an underlying theory of inference – logic is about inference after all.We conclude pointing out that recent developments in dialogical logic show that the CTT approach to meaning in general and to the axiom of choice in particular is very natural to game theoretical approaches where metalogical features are explicitly displayed at the object language-level. Thus, in some way, this vindicates, albeit in quite of a different manner, Hintikka’s plea for the fruitfulness of game-theoretical semantics in the context of the foundations of mathematics. (shrink)

Pascal Engel distingue globalement deux tendances de concevoir la vérité : les uns défendent une théorie substantialiste selon laquelle la vérité exprime une « caractéristique réelle », les autres, déflationnistes, soutiennent que la vérité n’est pas une propriété authentique des porteurs de vérités. Prenant le réalisme comme option par défaut, Engel cherche une position médiane stable, telle que la vérité est un concept plus substantiel que le déflationnisme ne le prétend et moins substantiel que les théories réalistes ne disent qu’elle (...) est. Dans cet article on développe une solution médiane alternative à la position proposée par Engel en se basant sur une option anti-réaliste et pragmatique (mais non utilitariste). On montre, plus exactement, dans quelle mesure la conception dialogique de la vérité, avancée par Kuno Lorenz, s’oppose aux thèses défendues par Engel tout en poursuivant le même but que lui. (shrink)

Recent literature on dialogical logic discusses the case of tonk and the notion harmony in the context of a rule-based theory of meaning. Now, since the publications of those papers, a dialogical version of constructive type theory has been developed. The aim of the present paper is to show that, from the dialogical point of view, the harmony of the CTT-rules is the consequence of a more fundamental level of meaning characterized by the independence of players. We hope that the (...) following paper will contribute to a better understanding of the dialogical notion of meaning. (shrink)