Transparent truth-value predicates in multi-valued logics

Nissim Francez, Michael Kaminski

Abstract


The paper defines truth-value assignment predicates $T_i(`\varphi’)$ in multi-valued logics, generalising the classical truth-predicate $T(`\varphi’)$. The meaning of this predicate is that $\varphi$ has the truth-value $v_i$. The paper studies deflational truth-value assignments and their transparency in the form of natural-deduction proof-system. The main technical tool used is {\em poly-sequents} of the form $\Gamma_1 | … | \Gamma_n : \Delta_1 | … | \Delta_n$, interpreted as follows: if for {\em every} $1 \le i \le n$ {\em every} $\alpha \in \Gamma_i$ has truth value $v_i$, then for  {\em some} $1 \le j \le n$ [\some} $\beta \in \Delta_j$ has truth-value $v_j$. The paper proposes a way to identify “real truth” and “real falsity” among the $n$ truth-values.


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