Abstract
I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.
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Restall, G. Truth Values and Proof Theory. Stud Logica 92, 241–264 (2009). https://doi.org/10.1007/s11225-009-9197-y
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DOI: https://doi.org/10.1007/s11225-009-9197-y