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arXiv · 2502.08257

The external version of a subclassical logic

Massimiliano Carrara·Michele Pra Baldi
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Abstract

A three-valued logic L is subclassical when it is defined by a single matrix having the classical two-element matrix as a subreduct. In this case, the language of L can be expanded with special unary connectives, called external operators. The resulting logic L^e is the external version of L, a notion originally introduced by D. Bochvar in 1938 with respect to his weak Kleene logic. In this paper we study the semantic properties of the external version of a three-valued subclassical logic L. We determine sufficient and necessary conditions to turn a model of L into a model of L^e . Moreover, we establish some distinctive semantic properties of L^e.

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Massimiliano Carrara, Michele Pra Baldi. 2025-02-12. The external version of a subclassical logic. https://arxiv.org/abs/2502.08257

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