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)

In its origins Dialogical logic constituted the logical foundations of an overall new movement called the Erlangen School or Erlangen Constructivism that should provide a new start to a general theory of language and of science. In relation to the theory of language, according to the Erlangen-School, language is not just a fact that we discover, but a human cultural accomplishment whose construction reason can and should control. The constructive development of a scientific language was called the Orthosprache-project. Unfortunately, the (...) Orthosprache-project was not further developed and somehow seemed to fade away. Perhaps, one could say that one of the reasons is that the semantic links between dialogical logic, that was restricted to logical constants, and the more general linguistic aspirations of the Orthosprache were not sufficiently developed and then the new theory of meaning of dialogical logic seemed to be cut off from the project of setting the basis for a general theory of meaning.In the present paper we would like to contribute to precise one possible way in which a general dialogical theory of meaning could be linked to dialogical logic. More precisely, the main aim of the article is to set the basis for the meaning of elementary sentences in the context of dialogical interaction. (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)

This volume explores the relation between legal reasoning and logic from both a historical and a systematic perspective. The topics addressed include, among others, conditional legal acts, disjunctions in legal acts, presumptions and conjectures, conflicts of values, Jørgensen´s Dilemma, the Rhetor´s Dilemma, the theory of legal fictions and the categorization of contracts. The unifying problematic of these contributions concerns the conditional structures and, more particularly, the relationship between legal theory and legal reasoning in the context of conditions.

One of the features of John Locke’s moral philosophy is the idea that morality is based on our beliefs concerning the future good. In An Essay Concerning Human Understanding II, xxi, §70, Locke argues that we have to decide between the probability of afterlife and our present temptations. In itself, this kind of decision model is not rare in Early Modern philosophy. Blaise Pascal’s Wager is a famous example of a similar idea of balancing between available options which Marcelo Dascal (...) has discussed in his important 2005 article “The Balance of Reason”. -/- Leibniz, however, was not always satisfied with this kind of simple balancing. In his commentary to Locke’s Essay, Nouveaux essais sur l’entendement humain, II, xxi, §66, he presented an alternative model which is based on an idea of plural, mutually conflicting inclinations. This kind of model, called as vectorial theory of rational decision by Simo Knuuttila, fits well with Leibniz’s theory of the soul where volitions are formed as a kind of compromise between different inclinations to different goods. -/- I will present these two models and show how they illustrate the practical rationality of Locke and Leibniz and how their moral philosophies differ, although being similar in certain respects. The topics include Leibniz’s criticism of Lockean hedonism and the discussion of akratic behaviour in II, xxi of Essay and Nouveaux essais. (shrink)

This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are critically (...) surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning. (shrink)

This volume presents mathematical game theory as an interface between logic and philosophy.

This paper presents a way in which formal logic can be understood and reformulated in terms of argumentation that can help us unify formal and informal reasoning. Classical deductive reasoning will be expressed entirely in terms of notions and concepts from argumentation so that formal logical entailment is equivalently captured via the arguments that win between those supporting concluding formulae and arguments supporting contradictory formulae. This allows us to go beyond Classical Logic and smoothly connect it with human reasoning, thus (...) providing a uniform argumentation-based view of both informal and formal logic. (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)

Dialogue semantics for logic are two-player logic games between a Proponent who puts forward a logical formula φ as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which different logics can be obtained through only small variations of the basic rules. We introduce the composition problem for dialogue games as the problem of resolving, for a set S of rules for dialogue games, whether the set (...) of S-dialogically valid formulas is closed under modus ponens. Solving the composition problem is fundamental for the dialogical approach to logic; despite its simplicity, it often requires an indirect solution with the help of significant logical machinery such as cut-elimination. Direct solutions to the composition problem can, however, sometimes be had. As an example, we give a set N of dialogue rules which is well-justified from the dialogical point of view, but whose set N of dialogically valid formulas is both non-trivial and non-standard. We prove that the composition problem for N can be solved directly, and introduce a tableaux system for N. (shrink)

We present a new proof of soundness/completeness of tableaux with respect to dialogical games in Classical First-Order Logic. As far as we know it is the first thorough result for dialogical games where finiteness of plays is guaranteed by means of what we call repetition ranks.