Proving Propositional Tautologies in a Natural Dialogue

Abstract

The paper proposes a dialogue system LND which brings together and unifies two traditions in studying dialogue as a game: the dialogical logic introduced by Lorenzen; and persuasion dialogue games as specified by Prakken. The first approach allows the representation of formal dialogues in which the validity of argument is the topic discussed. The second tradition has focused on natural dialogues examining, e.g., informal fallacies typical in real-life communication. Our goal is to unite these two approaches in order to allow communicating agents to benefit from the advantages of both, i.e., to equip them with the ability not only to persuade each other about facts, but also to prove that a formula used in an argument is a classical propositional tautology. To this end, we propose a new description of the dialogical logic which meets the requirements of Prakken's generic specification for natural dialogues, and we introduce rules allowing to embed a formal dialogue in a natural one. We also show the correspondence result between the original and the new version of the dialogical logic, i.e., we show that a winning strategy for a proponent in the original version of the dialogical logic means a winning strategy for a proponent in the new version, and conversely.

Preface: From Pragmatics and Dialectics to Argument Studies

“…From the perspective of dialectics, the Polish School of Argumentation explores various aspects of the dialogical context of argumentation, such as the identification and elimination of formal fallacies (Yaskorska et al 2013; the dynamics of questions in a dialogue (Wiśniewski 1996, Urbański 2001; and game-theoretic accounts of strategies in dialogues (Kacprzak et al in review). The methods of corpus analysis and experimental studies are used to examine issues such as critical analysis of values in political discourse (Sowińska 2013, Kielar 2011, dynamics and structure of argumentation in negotiations (Jochemczyk & Nowak 2010), and argumentative skills in preschoolers' narrative discourse (Rytel 2012).…”

Dialogue Protocols for Formal Fallacies

“…Lorenzen-style Natural Dialogue (LND), introduced in (Yaskorska et al 2013), is a system which provides a method for testing propositional tautologies. This game is based on Lorenzen's dialogical logic (DL) (see Keiff 2011, Lorenz and Lorenzen 1978, Rahman and Tulenheimo 2006.…”

The Polish School of Argumentation: A Manifesto

“…Reason The idea of reason is taken up in the study of the logical structure of everyday argumentation, resulting in formal models of it, such as a dialogue system for the identification and elimination of formal fallacies (Yaskorska et al 2013;Kacprzak and Yaskorska 2014;Kacprzak and Sawicka 2014), probabilistic and inductive models of justification (Kawalec 2003), an account of real premises of argumentation for dynamic epistemic logic (Bryniarski et al 2011), a description of intelligent agent judgement (Gomolińska 2005), and a model of teleological interpretation of statutory legal rules (Ż urek and Araszkiewicz 2013).…”