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arXiv · 2408.04792

Strong completeness for the predicate logic of the continuous t-norms

Diego Castaño·José Patricio Díaz Varela·Gabriel Savoy
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Abstract

The axiomatic system introduced by Hájek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom $(\forall x ϕ)^2 \leftrightarrow \forall x ϕ^2$ and the infinitary rule \[ \frac{ϕ\vee (α\to β^n):n \in \mathbb{N}}{ϕ\vee (α\to α\& β)} \] to achieve strong completeness with respect to continuous t-norms.

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Diego Castaño, José Patricio Díaz Varela, Gabriel Savoy. 2024-08-08. Strong completeness for the predicate logic of the continuous t-norms. https://arxiv.org/abs/2408.04792

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