Turnstile Figures of Opposition

Abstract

AbstractWe present many figures of opposition (triangles and hexagons) for simple and double turnstiles. We start with one-sided turnstiles, corresponding to sets of tautologies, and then we go to double-sided turnstiles corresponding to consequence relations. In both cases, we consider proof-theoretic (with the simple turnstile) and model-theoretic (with the double turnstile) figures. By so doing, we discuss various central aspects of notations and conceptualizations of modern logic.KeywordsSquare of oppositionTurnstileTautologyTruthProofConsequenceModelMathematics Subject ClassificationPrimary: 03-01 Secondary 03A05; 03B22;03B45;03F99: 03 C99