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  1. Dialogue Types, Argumentation Schemes, and Mathematical Practice: Douglas Walton and Mathematics.Andrew Aberdein - 2021 - Journal of Applied Logics 8 (1):159-182.
    Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.
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  • A formal model of adjudication dialogues.Henry Prakken - 2008 - Artificial Intelligence and Law 16 (3):305-328.
    This article presents a formal dialogue game for adjudication dialogues. Existing AI & law models of legal dialogues and argumentation-theoretic models of persuasion are extended with a neutral third party, to give a more realistic account of the adjudicator’s role in legal procedures. The main feature of the model is a division into an argumentation phase, where the adversaries plea their case and the adjudicator has a largely mediating role, and a decision phase, where the adjudicator decides the dispute on (...)
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  • An integrated view on rules and principles.Bart Verheij, Jaap C. Hage & H. Jaap Van Den Herik - 1998 - Artificial Intelligence and Law 6 (1):3-26.
    In the law, it is generally acknowledged that there are intuitive differences between reasoning with rules and reasoning with principles. For instance, a rule seems to lead directly to its conclusion if its condition is satisfied, while a principle seems to lead merely to a reason for its conclusion. However, the implications of these intuitive differences for the logical status of rules and principles remain controversial.A radical opinion has been put forward by Dworkin (1978). The intuitive differences led him to (...)
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  • Why was Alchourrón afraid of snakes?Juliano S. A. Maranhão - 2006 - Análisis Filosófico 26 (1):62-92.
    In the last papers published by Alchourrón, he attacked non-monotonic logics, which he considered philosophically unsound for the representation of defeasible reasoning. Instead of a non-monotonic consequence relation, he proposed a formal representation of defeasibility based on an AGM-like revision of implicit assumptions connected to the premises. Given that this is a procedure to generate non-monotonic logics, it is not clear, from a mathematical standpoint, why he was so suspicious of such logics. In the present paper we try to answer (...)
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  • Law, logic, rhetoric: A procedural model of legal argumentation.Arno R. Lodder - 2004 - In S. Rahman (ed.), Logic, Epistemology, and the Unity of Science. Dordrecht: Kluwer Academic Publishers. pp. 569--588.
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  • Reasoning with Factors.Giovanni Sartor - 2005 - Argumentation 19 (4):417-432.
    The paper proposes an analysis and a formalisation of factor-based reasoning. After examining the relevance of factors in legal reasoning, binary and scalable factors (dimensions) are distinguished and the relations between them are discussed. An account of a fortiori reasoning with both types of factors is developed.
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  • Knowledge Construction in Legal Reasoning: A Three Stage Model of Law’s Evolution in Practical Discourse.Olaf Tans - 2018 - International Journal for the Semiotics of Law - Revue Internationale de Sémiotique Juridique 31 (1):1-19.
    Seeing that socio-legal theory has produced a number of compelling grand theories about law’s development as a body of knowledge, this contribution analyzes legal evolution on the micro-level of decision-making in concrete cases. To that end, law finding is reconstructed as a three stage process of reason-based rule-construction. Legal evolution is argued to stem from the argumentative jumps that are made in this process in order to use what is initially drawn from the body of legal knowledge in new cases. (...)
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