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 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.
连续 t 规范谓词逻辑的强完备性
阿杰克(H\'ajek)引入的公理系统将基于BL-链的一阶逻辑公理化。在本研究中,我们用公理$(forall x \phi)^2 \leftrightarrow \forall x \phi^2$ 和无穷规则来扩展这个系统:n \in \mathbb{N}}{phi \vee (\alpha \to\alpha \& \beta)} \]来实现关于连续规范的强完备性。
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