Abstract
(Non-)deterministic Kripke-style semantics is used to characterize two syntactic properties of single-conclusion canonical sequent calculi: invertibility of rules and axiom-expansion. An alternative matrix-based formulation of such semantics is introduced, which provides an algorithm for checking these properties, and also new insights into basic constructive connectives.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Avron, A., Lev, I.: Non-deterministic Multi-valued Structures. Journal of Logic and Computation 15, 241–261 (2005)
Avron, A., Ciabattoni, A., Zamansky, A.: Canonical calculi: Invertibility, axiom expansion and (Non)-determinism. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds.) CSR 2009. LNCS, vol. 5675, pp. 26–37. Springer, Heidelberg (2009)
Avron, A., Lahav, O.: On Constructive Connectives and Systems. Logical Methods in Computer Science 6(4:12) (2010)
Avron, A., Zamansky, A.: Non-deterministic Semantics for Logical Systems - A Survey. In: Gabbay, D., Guenther, F. (eds.) Handbook of Philosophical Logic. Kluwer, Dordrecht (to appear, 2011)
Bowen, K.A.: An extension of the intuitionistic propositional calculus. Indagationes Mathematicae 33, 287–294 (1971)
Ciabattoni, A., Terui, K.: Towards a semantic characterization of cut-elimination. Studia Logica 82(1), 95–119 (2006)
Gurevich, Y., Neeman, I.: The logic of Infons. Bulletin of European Association for Theoretical Computer Science 98 (June 2009)
Kripke, S.: Semantical analysis of intuitionistic logic I. In: Crossly, J., Dummett, M. (eds.) Formal Systems and Recursive Functions, pp. 92–129 (1965)
McCullough, D.P.: Logical connectives for intuitionistic propositional logic. Journal of Symbolic Logic 36(1), 15–20 (1971)
Mints, G.: A Short Introduction to Intuitionistic Logic. Plenum Publishers, New York (2000)
Urquhart, A.: Many-valued Logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 2, pp. 249–295. Kluwer Academic Publishers, Boston (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ciabattoni, A., Lahav, O., Zamansky, A. (2011). Basic Constructive Connectives, Determinism and Matrix-Based Semantics. In: Brünnler, K., Metcalfe, G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2011. Lecture Notes in Computer Science(), vol 6793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22119-4_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-22119-4_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22118-7
Online ISBN: 978-3-642-22119-4
eBook Packages: Computer ScienceComputer Science (R0)