Natural deduction rules for a logic of vagueness

Erkenntnis 27 (2):197-229 (1987)
Extant semantic theories for languages containing vague expressions violate intuition by delivering the same verdict on two principles of classical propositional logic: the law of noncontradiction and the law of excluded middle. Supervaluational treatments render both valid; many-Valued treatments, Neither. The core of this paper presents a natural deduction system, Sound and complete with respect to a 'mixed' semantics which validates the law of noncontradiction but not the law of excluded middle
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DOI 10.1007/BF00175369
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Brian Weatherson (2005). True, Truer, Truest. Philosophical Studies 123 (1-2):47-70.

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