Extensions of the basic constructive logic for weak consistency BKc1 defined with a falsity constant

Gemma Robles

doi:10.12775/LLP.2007.010

Authors

Gemma Robles Universidad de La Laguna, Tenerife

DOI:

https://doi.org/10.12775/LLP.2007.010

Keywords

weak consistency, constructive falsity, ternary relational semantics, substructural logics, paraconsistent logics

Abstract

The logic BKc1 is the basic constructive logic for weak consistency (i.e., absence of the negation of a theorem) in the ternary relational semantics without a set of designated points. In this paper, a number of extensions of B Kc1 defined with a propositional falsity constant are defined. It is also proved that weak consistency is not equivalent to negation-consistency or absolute consistency (i.e., non-triviality) in any logic included in positive contractionless intermediate logic LC plus the constructive negation of BKc1 and the (constructive) contraposition axioms.

Author Biography

Gemma Robles, Universidad de La Laguna, Tenerife

Dipto. de Historia y Filosofía de la CC, la Educación y el Lenguaje Facultad de Filosofía

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