Abstract
In some presentations of classical and intuitionistic logics, the objectlanguage is assumed to contain (two) truth-value constants: ⊤ (verum) and ⊥ (falsum), that are, respectively, true and false under every bivalent valuation. We are interested to define and study analogical constants ‡ , 1 ≤ i ≤ n, that in an arbitrary multi-valued logic over truth-values V = {v1, . . . , vn} have the truth-value vi under every (multi-valued) valuation. As is well known, the absence or presence of such constants has a significant deductive impact on the logics studied. We define such constants proof-theoretically via their associated I/E-rules in a natural-deduction proof system. In particular, we propose a generalization of the notions of contradiction and explosiveness of a logic to the context of multi-valued logics.
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Francez, N., Kaminski, M. (2024). Truth-Value Constants in Multi-Valued Logics. In: Piecha, T., Wehmeier, K.F. (eds) Peter Schroeder-Heister on Proof-Theoretic Semantics. Outstanding Contributions to Logic, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-031-50981-0_14
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DOI: https://doi.org/10.1007/978-3-031-50981-0_14
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