Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T11:10:16.465Z 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, NORWAYE-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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
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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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