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Journal of Logic and Computation Advance Access published online on September 11, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp050
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Fuzzy Logic Corner

On White's Expansion of Lukasiewicz Logic

Petr Hájek

Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou vezí 2, Prague, 182 07 Czech Republic.
E-mail: hajek{at}cs.cas.cz

Received 2 February 2009.


  Abstract

Avariant of Lukasiewicz logic defined in a remark in White's 1979 paper on the consistency of the axiom of comprehension in the infinite-valued predicate logic of Lukasiewicz is studied; it is shown that the logic in question is an interesting expansion of Lukasiewicz logic which deserves further investigation together with its further expansions. Several formulas are proved in it and some model theory is offered. In the Appendix A, it is shown that a set theory with full comprehension over this logic (claimed consistent by White) is contradictory.

Keywords: Lukasiewicz fuzzy logic; Cantor-Lukasiewicz set theory; full comprehension


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