×

zbMATH — the first resource for mathematics

Hypersequent systems for the admissible rules of modal and intermediate logics. (English) Zbl 1211.03037
Artemov, Sergei (ed.) et al., Logical foundations of computer science. International symposium, LFCS 2009, Deerfield Beach, FL, USA, January 3–6, 2009. Proceedings. Berlin: Springer (ISBN 978-3-540-92686-3/pbk). Lecture Notes in Computer Science 5407, 230-245 (2009).
Summary: The admissible rules of a logic are those rules under which the set of theorems of the logic is closed. In a previous paper by the authors, formal systems for deriving the admissible rules of Intuitionistic Logic and a class of modal logics were defined in a proof-theoretic framework where the basic objects of the systems are sequent rules. Here, the framework is extended to cover derivability of the admissible rules of intermediate logics and a wider class of modal logics, in this case, by taking hypersequent rules as the basic objects.
For the entire collection see [Zbl 1156.03004].

MSC:
03B45 Modal logic (including the logic of norms)
03B55 Intermediate logics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Avron, A.: A constructive analysis of RM. Journal of Symbolic Logic 52(4), 939–951 (1987) · Zbl 0639.03017 · doi:10.2307/2273828
[2] Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford University Press, Oxford (1996) · Zbl 0871.03007
[3] Ciabattoni, A., Ferrari, M.: Hypersequent calculi for some intermediate logics with bounded Kripke models. Journal of Logic and Computation 11(2), 283–294 (2001) · Zbl 0989.03026 · doi:10.1093/logcom/11.2.283
[4] Ghilardi, S.: Unification in intuitionistic logic. Journal of Symbolic Logic 64(2), 859–880 (1999) · Zbl 0930.03009 · doi:10.2307/2586506
[5] Ghilardi, S.: Best solving modal equations. Annals of Pure and Applied Logic 102(3), 184–198 (2000) · Zbl 0949.03010 · doi:10.1016/S0168-0072(99)00032-9
[6] Ghilardi, S., Sacchetti, L.: Filtering unification and most general unifiers in modal logic. Journal of Symbolic Logic 69(3), 879–906 (2004) · Zbl 1069.03011 · doi:10.2178/jsl/1096901773
[7] Iemhoff, R.: On the admissible rules of intuitionistic propositional logic. Journal of Symbolic Logic 66(1), 281–294 (2001) · Zbl 0986.03013 · doi:10.2307/2694922
[8] Iemhoff, R.: Intermediate logics and Visser’s rules. Notre Dame Journal of Formal Logic 46(1), 65–81 (2005) · Zbl 1102.03032 · doi:10.1305/ndjfl/1107220674
[9] Iemhoff, R., Metcalfe, G.: Proof theory for admissible rules. (submitted), http://www.math.vanderbilt.edu/people/metcalfe/publications · Zbl 1174.03024
[10] Jerábek, E.: Admissible rules of modal logics. Journal of Logic and Computation 15, 411–431 (2005) · Zbl 1077.03011 · doi:10.1093/logcom/exi029
[11] Metcalfe, G., Olivetti, N., Gabbay, D.: Proof Theory for Fuzzy Logics. Springer Series in Applied Logic, vol. 36. Springer, Heidelberg (to appear, 2009) · Zbl 1168.03002
[12] Rozière, P.: Regles Admissibles en calcul propositionnel intuitionniste. PhD thesis, Université Paris VII (1992)
[13] Rybakov, V.: Admissibility of Logical Inference Rules. Elsevier, Amsterdam (1997) · Zbl 0872.03002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.