Strong completeness for the predicate logic of the continuous t-norms
Diego Castaño, José Patricio Díaz Varela, Gabriel Savoy · arXiv (Cornell University) · 2024
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.