Classical model existence and left resolution
DOI:
https://doi.org/10.12775/LLP.2007.011Keywords
classical propositional logic, classical model existence theorem, Gentzen system, resolutionAbstract
By analyzing what are necessary conditions in the proof [4] of the classical model existence theorem CME (every consistent set has a classical model), we present the left resolution Gentzen systems R(¬,-), which proof-theoretically characterize CME.References
Béziau. J.-Y., “Sequents and bivaluations”, Logique et Analyse 176 (2001), 373–94.
Buss, S.R., “An introduction to proof theory”, pp. 1–78 in Handbook of Proof Theory, Stud. Logic Found. Math., 137, North-Holland, Amsterdam, 1998.
Epstein, R.L., The Semantic Foundations of Logic. Vol. 1: Propositional logics, 2nd edn., Oxford University Press, 1995.
Lee, J.-L., “Classical model existence theorem in propositional logics”, pp. 179–197 in Perspectives on Universal Logic, J-Y. Béziau and A. Costa-Leite (eds.), Polimetrica, Monza, Italy, 2007.
Lee, J.-L., “Consistency and satisfiability”, presented in Taiwan Philosophical Association 2007 Annual meeting, on October 21, 2007.
Lee, J.-L., “Classical model existence theorem in subclassical predicate logics. I”, accepted and to appear in Trends in Logic: Towards Mathematical Philosophy, D. Makinson, J. Malinowski and H. Wansing (eds.), in the book series “Trends in Logic” – Studia Logica Library, 2008.
Lee, J.-L., “Glivenko’s Theorem for weak normal modal logics”, submitted to Advances in Modal Logic 2008, 2008.
Tarski, A., “Fundamentale Begriffe der Methodologie der deduktiven Wissenschaften. I.”, Monatshefte für Mathematik und Physik 37 (1930), 361–404.
Tsejtin, G.S., “On the complexity of derivation in propositional logic”, Studies in Constructive Mathematics and Mathematical Logic 2 (1968), 115–125.
Wójcicki, R., Theory of Logical Calculi, Synthese Library, vol. 199, Dordrecht: Kluwer Academic Publishers Group Press, 1988.
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