Abstract
We introduce two different calculi for a first-order extension of inquisitive pair semantics (Groenendijk 2008): Hilbert-style calculus and Tree-sequent calculus. These are first-order generalizations of (Mascarenhas 2009) and (Sano 2009), respectively. First, we show the strong completeness of our Hilbert-style calculus via canonical models. Second, we establish the completeness and soundness of our Tree-sequent calculus. As a corollary of the results, we semantically establish that our Tree-sequent calculus enjoys a cut-elimination theorem.
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References
Groenendijk, J.: Inquisitive semantics: Two possibilities for disjunction. Prepublication Series PP-2008-26, ILLC (2008)
Mascarenhas, S.: Inquisitive semantics and logic. Master’s thesis, Institute for Logic, Language and Computation, University of Amsterdam (2009)
Kashima, R.: Sequent calculi of non-classical logics - Proofs of completeness theorems by sequent calculi. In: Proceedings of Mathematical Society of Japan Annual Colloquium of Foundations of Mathematics, pp. 49–67 (1999) (in Japanese)
Sano, K.: Sound and complete tree-sequent calculus for inquisitive logic. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds.) WoLLIC 2009. LNCS (LNAI), vol. 5514, pp. 365–378. Springer, Heidelberg (2009)
Ciardelli, I., Roelofsen, F.: Inquisitive logic. To appear in Journal of Philosophical Logic, http://sites.google.com/site/inquisitivesemantics/
Ciardelli, I.: A first-order inquisitive semantics. In: Aloni, M., Bastiaanse, H., de Jager, T., Schulz, K. (eds.) Logic, Language and Meaning. LNCS, vol. 6042, pp. 234–243. Springer, Heidelberg (2010)
Ciardelli, I.: Inquisitive semantics and intermediate logics. Master’s thesis, Institute for Logic, Language and Computation, University of Amsterdam (2009)
Gabbay, D.M., Shehtman, V., Skvortsov, D.P.: Quantification in Nonclassical Logic. Studies in logic and the foundations of mathematics, vol. 153. Elsevier, Amsterdam (2009)
Ishigaki, R., Kikuchi, K.: Tree-sequent methods for subintuitionistic predicate logics. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS (LNAI), vol. 4548, pp. 149–164. Springer, Heidelberg (2007)
Gabbay, D.M.: Semantical investigations in Heyting’s intuitionistic logic. Synthese Library, vol. 148. D. Reidel Pub. Co., Dordrecht (1981)
Gabbay, D.M.: Labelled Deductive Systems. Oxford Logic Guides, vol. 33. Clarendon Press/Oxford Science Publications, Oxford (1996)
Hasuo, I., Kashima, R.: Kripke completeness of first-order constructive logics with strong negation. Logic Journal of the IGPL 11(6), 615–646 (2003)
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Sano, K. (2011). First-Order Inquisitive Pair Logic. In: Banerjee, M., Seth, A. (eds) Logic and Its Applications. ICLA 2011. Lecture Notes in Computer Science(), vol 6521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18026-2_13
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DOI: https://doi.org/10.1007/978-3-642-18026-2_13
Publisher Name: Springer, Berlin, Heidelberg
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