Sequent Calculi for the classical fragment of Bochvar and Halldén's Nonsense Logics

Marcelo E. Coniglio
(State University of Campinas)
María I. Corbalán
(State University of Campinas)

In this paper sequent calculi for the classical fragment (that is, the conjunction-disjunction-implication-negation fragment) of the nonsense logics B3, introduced by Bochvar, and H3, introduced by Halldén, are presented. These calculi are obtained by restricting in an appropriate way the application of the rules of a sequent calculus for classical propositional logic CPL. The nice symmetry between the provisos in the rules reveal the semantical relationship between these logics. The Soundness and Completeness theorems for both calculi are obtained, as well as the respective Cut elimination theorems.

In Delia Kesner and Petrucio Viana: Proceedings Seventh Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2012), Rio de Janeiro, Brazil, September 29-30, 2012, Electronic Proceedings in Theoretical Computer Science 113, pp. 125–136.
Published: 28th March 2013.

ArXived at: http://dx.doi.org/10.4204/EPTCS.113.12 bibtex PDF
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