Gabriel Savoy | Searcharxiv

arXiv2024

Strong standard completeness theorems for S5-modal Lukasiewicz logics

We study the S5-modal expansion of the logic based on the Lukasiewicz t-norm. We exhibit a finitary propositional calculus and show that it is finitely strongly complete with respect to this logic. This propositional calculus is then expanded with an infinitary rule to achieve strong completeness. These results are derived from properties of monadic MValgebras: functional representations of simple and finitely subdirectly irreducible algebras, as well as the finite embeddability property. We also show similar completeness theorems for the extension of the logic based on models with bounded universe.

math.LO↗

arXiv2024

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

The axiomatic system introduced by H\'ajek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom $(\forall x \phi)^2 \leftrightarrow \forall x \phi^2$ and the infinitary rule \[ \frac{\phi \vee (\alpha \to \beta^n):n \in \mathbb{N}}{\phi \vee (\alpha \to \alpha \& \beta)} \] to achieve strong completeness with respect to continuous t-norms.

math.LO↗