Turnstile Figures of Opposition

Por • 19 oct, 2022 • Sección: Educacion

Jean-Yves Beziau

Abstract We present many figures of opposition (triangles and hexagons) for simple and double turnstiles. We start with one-sided turnstiles, corresponding to sets of tautologies, 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 doing so we discuss various central aspects of notations and conceptualizations of modern logic.

 Mathematics Subject Classification Primary: 03-01 Secondary 03A05; 03B22;03B45;03F99: 03 C99

Keywords Square of Opposition, Turnstile, Tautology, Truth, Proof, Consequence, Model.

http://www.jyb-logic.org/TURNSTYLE.pdf

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