Hilbert-style axiomatization of first-degree entailment and a family of its extensions |
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Authors: | Yaroslav Shramko |
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Institution: | Department of Philosophy, Kryvyi Rih State Pedagogical University, Kryvyi Rih, 50086, Ukraine |
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Abstract: | This paper presents a Hilbert-style system for the logic of first-degree entailment defined in a Fmla-Fmla framework. The effective use of this formulation as a basis for a whole family of systems extending the logic of first-degree entailment in various directions is shown. By systematizing this family, some new systems are uncovered, and some other well-established logics (such as the first-degree entailment fragment of Priest's Logic of Paradox) obtain new axiomatization. Semantics for the key systems from the family is formulated. |
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Keywords: | Frege rule Hilbert system First-degree entailment Extension of logic |
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