Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-08-15T16:59:30.174Z Has data issue: false hasContentIssue false
  • English
  • Français

RESOLVING INFINITARY PARADOXES

Published online by Cambridge University Press:  19 June 2017

MICHAŁ WALICKI
MICHAŁ WALICKI*
Affiliation:
DEPARTMENT OF INFORMATICS UNIVERSITY OF BERGEN PBOX 7803, 5020 BERGEN, NORWAY E-mail: michal@ii.uib.no
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

paradoxinfinitary logicresolutionsubstructural logicdiagraph kernel

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 2 , June 2017 , pp. 709 - 723
Copyright
Copyright © The Association for Symbolic Logic 2017 

References

REFERENCES

Bezem, M., Grabmayer, C., and Walicki, M., Expressive power of digraph solvability . Annals of Pure and Applied Logic, vol. 163 (2012), no. 3, pp. 200–212.CrossRefGoogle Scholar
Cook, R., Patterns of paradox , this Journal, vol. 69 (2004), no. 3, pp. 767–774.Google Scholar
Dyrkolbotn, S. and Walicki, M., Propositional discourse logic . Synthese, vol. 191 (2014), no. 5, pp. 863–899.CrossRefGoogle Scholar
Richardson, M., Solutions of irreflexive relations . The Annals of Mathematics, Second Series, vol. 58 (1953), no. 3, pp. 573–590.CrossRefGoogle Scholar