Abstract
Labelled tableau systems are developed for subintuitionistic logics \(\mathbf {wK}_\sigma \), \(\mathbf {wKT}_\sigma \) and \(\mathbf {wK4}_\sigma \). These subintuitionistic logics are embedded into corresponding normal modal logics. Hintikka’s model systems are applied to prove the completeness of labelled tableau systems. The finite model property, decidability and disjunction property are obtained by labelled tableau method.
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Beth, E.W.: Semantic entailment and formal derivability. In: Hintikka, J. (ed.), The Philosophy of Mathematics, pp. 9–41. Oxford University Press. Originally published in Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen, Afdeling Letterkunde, N.R. 19 no. 13 (Amsterdam 1955), pp. 309–342 (1969)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Celani, S., Jansana, R.: A closer look at some subintuitionistic logic. Notre Dame J. Form. Logic 42(4), 225–255 (2001)
Corsi, G.: Weak logics with strict implication. Zeitschrift für mathematische Logik u. Grundlagen d 33, 389–406 (1987)
Dos̆en, K.: Modal tanslations into K and D. In: de Rijke, M. (ed.) Diamonds and Defaults, pp. 103–127. Kluwer Academic Publishers, Dordrecht (1993)
Fitting, M.: Proof Methods for Modal and Intuitionistic Logics. D. Reidel, Dordrecht (1983)
Goré, R.: Tableau methods for modal and temporal logics. In: D’Agostino, M., et al. (eds.) Handbook of Tableau Methods, pp. 297–396. Springer, Berlin (1999)
Hintikka, J.: A new approach to sentential logic. Societas Scientiarum Fennica, Commentationes physica-mathematicae, 17(2) (1953)
Hintikka, J.: Form and content in quantification theory. Acta Philosophica Fennica 8, 3–55 (1955)
Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press, Ithaca (1962)
Kripke, S.: A completeness theorem in modal logic. J. Symb. Logic 24(1), 1–14 (1959)
Massacci, F.: Strongly analytic tableaux for modal logics. In: Proceedings of CADE-12, LNAI 814, Bundy, A. (ed.), pp. 723–737. Springer, Berlin (1994)
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This work was supported by Guangdong Province Higher Vocational Colleges and Schools Pearl River Scholar Funded Scheme (2017–2019).
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Ma, M. Labelled Tableau Systems for Some Subintuitionistic Logics. Log. Univers. 13, 273–288 (2019). https://doi.org/10.1007/s11787-018-0201-z
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DOI: https://doi.org/10.1007/s11787-018-0201-z