Propositional discourse logic

Synthese 191 (5):1-37 (2014)
Abstract
A novel normal form for propositional theories underlies the logic pdl, which captures some essential features of natural discourse, independent from any particular subject matter and related only to its referential structure. In particular, pdlallows to distinguish vicious circularity from the innocent one, and to reason in the presence of inconsistency using a minimal number of extraneous assumptions, beyond the classical ones. Several, formally equivalent decision problems are identified as potential applications: non-paradoxical character of discourses, admissibility of arguments in argumentation networks, propositional satisfiability, and the existence of kernels of directed graphs. Directed graphs provide the basis for the semantics of pdl and the paper concludes by an overview of relevant graph-theoretical results and their applications in diagnosing paradoxical character of natural discourses
Keywords Semantic paradox  Circularity  Kernels of digraphs  Classical logic  Graph normal form
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DOI 10.1007/s11229-013-0297-x
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References found in this work BETA

Outline of a Theory of Truth.Saul A. Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
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Citations of this work BETA

A Graph-Theoretic Analysis of the Semantic Paradoxes.Timo Beringer & Thomas Schindler - 2017 - Bulletin of Symbolic Logic 23 (4):442-492.
Beliefs Supported by Binary Arguments.Chenwei Shi, Sonja Smets & Fernando R. Velázquez-Quesada - forthcoming - Journal of Applied Non-Classical Logics:1-24.
Resolving Infinitary Paradoxes.Michał Walicki - 2017 - Journal of Symbolic Logic 82 (2):709-723.

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