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Synthese

, Volume 191, Issue 5, pp 863–899 | Cite as

Propositional discourse logic

  • Sjur Dyrkolbotn
  • Michał Walicki
Article

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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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of InformaticsUniversity of BergenBergenNorway

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