Some supervaluation-based consequence relations

Journal of Philosophical Logic 32 (3):225-244 (2003)
Abstract
In this paper, we define some consequence relations based on supervaluation semantics for partial models, and we investigate their properties. For our main consequence relation, we show that natural versions of the following fail: upwards and downwards Lowenheim-Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting consequence relation
Keywords consequence relations  partial models  supervaluations  three-valued logic
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