Propositional discourse logic

Synthese 191 (5):863-899 (2014)
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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.

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Citations of this work

A graph-theoretic analysis of the semantic paradoxes.Timo Beringer & Thomas Schindler - 2017 - Bulletin of Symbolic Logic 23 (4):442-492.
A Unified Theory of Truth and Paradox.Lorenzo Rossi - 2019 - Review of Symbolic Logic 12 (2):209-254.
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Beliefs supported by binary arguments.Chenwei Shi, Sonja Smets & Fernando R. Velázquez-Quesada - 2018 - Journal of Applied Non-Classical Logics 28 (2-3):165-188.

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