Dialogues as a Dynamic Framework for Logic

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.LEI Universiteit LeidenPhilosoph

Dialogique temporelle et hybridation

L’objectif de cet article est de donner une interprétation dialogique de la logique temporelle standard. Dans ce cadre, nous utiliserons les langages hybrides dont Patrick Blackburn s’est servi pour caractériser la logique modale comme logique dialogique.The aim of the paper is to offer a dialogical interpretation of standard temporal logic. This interpretation will use hybrid languages which were used by Patrick Blackburn to characterize modal logic as dialogical logic

Necessity, a Leibnizian Thesis, and a Dialogical Semantics

In this paper, an interpretation of "necessity", inspired by a Leibnizian idea and based on the method of dialogical logic, is introduced. The semantic rules corresponding to such an account of necessity are developed, and then some peculiarities, and some potential advantages, of the introduced dialogical explanation, in comparison with the customary explanation offered by the possible worlds semantics, are briefly discussed

Analysis of Dialogical Argumentation via Finite State Machines

Dialogical argumentation is an important cognitive activity by which agents exchange arguments and counterarguments as part of some process such as discussion, debate, persuasion and negotiation. Whilst numerous formal systems have been proposed, there is a lack of frameworks for implementing and evaluating these proposals. First-order executable logic has been proposed as a general framework for specifying and analysing dialogical argumentation. In this paper, we investigate how we can implement systems for dialogical argumentation using propositional executable logic. Our approach is to present and evaluate an algorithm that generates a finite state machine that reflects a propositional executable logic specification for a dialogical argumentation together with an initial state. We also consider how the finite state machines can be analysed, with the minimax strategy being used as an illustration of the kinds of empirical analysis that can be undertaken.Comment: 10 page

Proof Search in Multi-Agent Dialogues for Modal Logic

In computer science, and also in philosophy, modal logics play an important role in various areas. They can be used to model knowledge structures among software-agents, behaviour of computer systems, or ontologies. They also provide mathematical tools to perform reasoning in these models, e.g., to extract common knowledge of agents, check whether security-relevant problems might occur when running a program, or to detect contradictions in a set of terminological definitions. Intuitionistic or constructive propositional logic can be considered as a special kind of modal logic. Constructive modal logics, as a combination of intuitionistic propositional logic and classical modal logics, describe a family of modal systems which are, compared to the classical variant, more restrictive concerning the validity of formulas. To prove validity of a statement formalized in such a logic, various reasoning procedures (also called calculi) have been investigated. There are especially many variants of sequent and tableau systems which can be used easily to find proofs by applying given syntactical rules one after another. Sometimes there are different possibilities to find a proof for the same formula within the same calculus. It also happens that a bad choice of non-invertible rule applications at the wrong time makes it impossible to finish the proof successfully, although the formula is provable. For this reason, a normalization of deductions in a calculus is desired. This restricts the possibilities to apply rules arbitrarily and emphasizes the situations in which significant, non-invertible rule applications are necessary. Such a normalization is enforced in so-called focused sequent systems. Another attempt to find a normalized calculus leads to dialogical logic, a game-theoretic reasoning technique. Usually, two players, one proponent and one opponent, argue about an assertion, expressed as a formula and stated by the proponent at the beginning of the play. The kinds of arguments, namely attacks and defences, are bound to special game rules. These are designed in such a way that the proponent has a winning strategy in the game if and only if his initial statement is a valid formula. The dialogical approach is very flexible as the game rules can be adjusted easily. Sets of rules exist to perform reasoning in many different kinds of logic, however proving soundness and completeness of dialogical calculi is complex and, if at all, often only considered very roughly in the literature. The standard two-player dialogues do not have much potential to enforce normalization like focus sequent systems. However, it turns out that introducing further proponent-players who fight against one opponent in a round-based setting leads to a normalization as described above. The flexibility of two-player games is largely preserved in multi-proponent dialogues. Other ordinary sequent systems can easily be transferred into the dialectic setting to achieve a normalization. Further, the round-based scheduling induces a method to parallelize the reasoning process. Modifying the game rules makes it possible to construct new intermediate or even more restrictive logics. In this work, dialogical systems with multiple proponents are presented for intuitionistic propositional logic and modal logics S4 and CS4. Starting with the former one, it is shown that the normalization can be transferred easily to both the latter systems. Informal game rules are introduced and, to make them concrete and unambiguous, translated into the dialogical sequent-style calculi DiaSeqI, DiaSeqS4, and DiaSeqCS4. An extra system for intuitionistic logic, which guarantees termination in proof searches, even if the target formula is not valid, is also provided. Soundness and completeness of all these presented dialogical sequent calculi is proven formally, by showing that it is always possible to translate derivations in the game-oriented approach into another sound and complete sequent system and vice versa. Thereby, a new (ordinary) multi-conclusion sequent calculus for CS4 is introduced for which adequateness is shown, too. The multi-proponent dialogical systems of this work are compared to different sequent calculi and other dialogical attempts found in literature. A comprehensive survey of such approaches is also part of this thesis

Alternative axiomatics and complexity of deliberative STIT theories

We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of the Chellas STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and the Chellas' STIT.Comment: Submitted to the Journal of Philosophical Logic; 13 pages excluding anne

Negotiating with a logical-linguistic protocol in a dialogical framework

This book is the result of years of reflection. Some time ago, while working in commodities, the author felt how difficult it was to decide the order in which to use arguments during a negotiation process. What would happen if we translated the arguments into cards and played them according to the rules of the Bridge game? The results were impressive. There was potential for improvement in the negotiation process. The investigation went deeper, exploring players, cards, deals and the information concealed in the players´ announcements, in the cards and in the deals. This new angle brought the research to NeuroLinguistic Patterns and cryptic languages, such as Russian Cards. In the following pages, the author shares her discovery of a new application for Logical Dialogues: Negotiations, tackled from basic linguistic structures placed under a dialogue form as a cognitive system which ‘understands’ natural language, with the aim to solve conflicts and even to serve peace

Contextual Epistemic Logic

One of the highlights of recent informal epistemology is its growing theoretical emphasis upon various notions of context. The present paper addresses the connections between knowledge and context within a formal approach. To this end, a "contextual epistemic logic", CEL, is proposed, which consists of an extension of standard S5 epistemic modal logic with appropriate reduction axioms to deal with an extra contextual operator. We describe the axiomatics and supply both a Kripkean and a dialogical semantics for CEL. An illustration of how it may fruitfully be applied to informal epistemological matters is provided

Between sentential and model-based abductions: a dialogical approach

Most of the standard approaches consider abduction in terms of a backward reasoning and miss some of its fundamental features. Overall, they neglect its pragmatic dimension and the conjectural aspect of the conclusion. In this paper, we approach abduction in terms of strategic adjustment process in the context of dialogical logic. This sheds light on the use of conjectures in argumentative interactions. Although abductive dialogues are sometimes based upon sentential conjectures, they can also involve hypotheses about the context of argumentation itself. Indeed, the underlying logic of an argumentative interaction is not always settled since the beginning. In this context, abduction is not only concerned with the introduction of sentential hypotheses, but also with hypotheses concerning the structural rules governing the dialogue itself. We thus emphasize the instrumental dimension of abduction in dialogues.FCT- Portugal Grant number SFRH/BPD/116494/2016FCT CFCUL UID/FIL/00678/2019Universidad de Sevill