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A Gentzen System for Conditional Logic: In Memory of Craig Squier

Fernando Guzmán
Studia Logica: An International Journal for Symbolic Logic
Vol. 53, No. 2 (May, 1994), pp. 243-257
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015720
Page Count: 15
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A Gentzen System for Conditional Logic: In Memory of Craig Squier
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Abstract

Conditional logic is the deductive system $\langle \scr{L},\vDash \rangle $ where $\scr{L}$ is the set of propositional connectives $\{\wedge,\vee,^{\prime}\}$ and $\vDash $ is the structural finitary consequence relation on the absolutely free algebra $Fm_{\scr{L}}$ that preserves degrees of truth over the structure of truth values $\langle C,\leq \rangle $. Here C is the non-commutative regular extension of the 2-element Boolean algebra to 3 truth values {t, u, f}, and f < u < t. In this paper we give a Gentzen type axiomatization for conditional logic.

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