The Football of Logic

An analogy is made between two rather different domains, namely: logic, and football. Starting from a comparative table between the two activities, an alternative explanation of logic is given in terms of players, ball, goal, and the like. Our main thesis is that, just as the task of logic is preserving truth from premises to the conclusion, footballers strive to keep the ball as far as possible until the opposite goal. Assuming this analogy may help think about logic in the same way as in dialogical logic, but it should also present truth-values in an alternative sense of speech-acts occurring in a dialogue. The relativity of truth-values is focused by this way, thereby leading to an additional way of logical pluralism

The Informal Logic of Mathematical Proof

Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of Stephen Toulmin [The uses of argument, Cambridge University Press, 1958] and the more recent studies of Douglas Walton, [e.g. The new dialectic: Conversational contexts of argument, University of Toronto Press, 1998]. The focus of both of these approaches has largely been restricted to natural language argumentation. However, Walton's method in particular provides a fruitful analysis of mathematical proof. He offers a contextual account of argumentational strategies, distinguishing a variety of different types of dialogue in which arguments may occur. This analysis represents many different fallacious or otherwise illicit arguments as the deployment of strategies which are sometimes admissible in contexts in which they are inadmissible. I argue that mathematical proofs are deployed in a greater variety of types of dialogue than has commonly been assumed. I proceed to show that many of the important philosophical and pedagogical problems of mathematical proof arise from a failure to make explicit the type of dialogue in which the proof is introduced.Comment: 14 pages, 1 figure, 3 tables. Forthcoming in Perspectives on Mathematical Practices: Proceedings of the Brussels PMP2002 Conference (Logic, Epistemology and the Unity of the Sciences Series), J. P. Van Bendegem & B. Van Kerkhove, edd. (Dordrecht: Kluwer, 2004

Using a Logic Programming Framework to Control Database Query Dialogues in Natural Language

We present a natural language question/answering system to interface the University of Évora databases that uses clarification dialogs in order to clarify user questions. It was developed in an integrated logic programming framework, based on constraint logic programming using the GnuProlog(-cx) language [2,11] and the ISCO framework [1]. The use of this LP framework allows the integration of Prolog-like inference mechanisms with classes and inheritance, constraint solving algorithms and provides the connection with relational databases, such as PostgreSQL. This system focus on the questions’ pragmatic analysis, to handle ambiguity, and on an efficient dialogue mechanism, which is able to place relevant questions to clarify the user intentions in a straightforward manner. Proper Nouns resolution and the pp-attachment problem are also handled. This paper briefly presents this innovative system focusing on its ability to correctly determine the user intention through its dialogue capability

Dialogue \u27On The Ground\u27: The Complicated Identities and the Complex Negotiations of Catholics and Hindus in South India

Interreligious dialogue is a vital theological concern for the Catholic Church in India. Over the past three decades, church leaders, progressive theologians, and maverick monastics have experimented with various models and forms of interreligious dialogue. Quite distinct from these contrived institutional initiatives is the dynamic of intimate, subtle, and spontaneous ritual exchange and dialogue between ordinary Hindus and Catholics occurring in the arena of popular piety and rituals at the grassroots level - often in opposition to institutional norms and directives - that may be described as dialogue on the ground. In light of ethnographic research at the shrine of St. Anthony at Uvari in Tamil Nadu - that serves as a representative sample of regional shrines in rural south India - this essay focuses on the logic and grammar of a specific public ritual locally known as asanam as an illustrative case-study of the \u27dialogue on the ground,\u27 delineates the social and religious themes embedded in this ritual, and reflects on its implications for interreligious dialogue

Dialogue Games in Defeasible Logic

In this paper we show how to capture dialogue games in Defeasible Logic. We argue that Defeasible Logic is a natural candidate and general representation formalism to capture dialogue games even with requirements more complex than existing formalisms for this kind of games. We parse the dialogue into defeasible rules with time of the dialogue as time of the rule. As the dialogue evolves we allow an agent to upgrade the strength of unchallenged rules. The proof procedures of (Antoniou, Billington, Governatori, Maher 2001) are used to determine the winner of a dialogue game

On Law, Politics and Contemporary Constitutionalism

Is the political process, with all its difficulties, merely reflective of contemporary constitutionalism? Are the problems an aspect of ongoing inter-communal dialogue? To what extent are existing difficulties exacerbated by a general failure to grasp the difference between the logic of law and political theory and practice? These questions are addressed here in three basic stages: first, the relationship between legal logic and political practice is examined; secondly, the implications of contemporary constitutionalism are explored; and, finally, the agreement and disagreements over its implementation are analyzed

Dialogue Games for Minimal Logic

In this paper, we define a class of dialogue games for Johansson’s minimal logic and prove that it corresponds to the validity of minimal logic. Many authors have stated similar results for intuitionistic and classical logic either with or without actually proving the correspondence. Rahman, Clerbout and Keiff [17] have already specified dialogues for minimal logic; however, they transformed it into Fitch-style natural deduction only. We propose a different specification for minimal logic with the proof of correspondence between the existence of winning strategies for the Proponent in this class of games and the sequent calculus for minimal logic

Speech acts, fallacies and dialogue systems

The paper aims to bring together and unify two traditions in studying dialogue as a game: dialogical logic introduced by Lorenzen (1978); and persuasion dialogue systems as specified by Prakken (2006). We propose a system which allows the elimination of both informal and formal fallacies (van Eemeren & Grootendorst, 2004). To this end, we reconstruct dialogical logic in terms of speech acts as suggested in (Hodges, 2009)