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Graph normal form, GNF, [1], was used in [2, 3] for analyzing paradoxes in propositional discourses, with the semantics—equivalent to the classical one—defined by kernels of digraphs. The paper presents infinitary, resolution-based reasoning with GNF theories, which is refutationally complete for the classical semantics. Used for direct (not refutational) deduction it is not explosive and allows to identify in an inconsistent discourse, a maximal consistent subdiscourse with its classical consequences. Semikernels, generalizing kernels, provide the semantic interpretation.

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[1] Bezem, M., Grabmayer, C., and Walicki, M., Expressive power of digraph solvability . Annals of Pure and Applied Logic, vol. 163 (2012), no. 3, pp. 200212.
[2] Cook, R., Patterns of paradox , this Journal, vol. 69 (2004), no. 3, pp. 767774.
[3] Dyrkolbotn, S. and Walicki, M., Propositional discourse logic . Synthese, vol. 191 (2014), no. 5, pp. 863899.
[4] Richardson, M., Solutions of irreflexive relations . The Annals of Mathematics, Second Series, vol. 58 (1953), no. 3, pp. 573590.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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