Algebraic characterizations of variable separation properties

• Autorzy: Kihara, H. , Ono, H.
• Języki publikacji: EN

Abstrakty

EN

This paper gives algebraic characterizations of Halld´en completeness (HC), and of Maksimova's variable separa- tion property (MVP) and its deductive form. Though algebraic characterizations of these properties have been already studied for modal and superintuitionistic logics, e.g. in Wroński [12], Maksi- mova [7], [9], a deeper analysis of these properties and non-trivial modifications of these results are needed to extend them to those for substructural logics, because of the lack of some structural rules in them. The first attempt in this direction was made in the dissertation [4] of the first author. Results of this paper are partly announced (sometimes in their weaker form) also in Chapter 5 of the book [2].

• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2008
• Tom: No. 43
• Strony: 43-63
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Kihara, H.

autor

Ono, H.

• Japan Advanced Institute of Science and Technology Asahidai, Nomi, Ishikawa, 923-1292, Japan,

Bibliografia

• [1] G. I. Galanter, Halld´en-completeness for superintuitionistic logics (Russian), Proceedings of IV Soviet-Finland Symposium for Mathematical Logic (1988), pp.81–89.
• [2] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated Lattices: An algebraic glimpse at substructural logics, Studies in Logic and the Foundations of Mathematics, vol.151, Elsevier, 2007.
• [3] N. Galatos and H. Ono, Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL, Studia Logica 83 (2006), pp.279–308.
• [4] H. Kihara, Commutative substructural logics - an algebraic study, Ph.D. Thesis, Japan Advanced Institute of Science and Technology, 2006.
• [5] M. Kracht, Tools and Techniques in modal logic, Studies in Logic and the Foundations of Mathematics, vol. 142, Elsevier, 1999.
• [6] E.J. Lemmon, A note on Halld´en-incompleteness, Notre Dame Journal of Formal Logic 7 (1966), pp.296–300.
• [7] L.L. Maksimova, The principle of separation of variables in propositional logics, Algebra i Logika 15 (1976), pp.168–184.
• [8] L.L. Maksimova, On maximal intermediate logics with the disjunction property, Studia Logica 45 (1986), pp.69–75.
• [9] L.L. Maksimova, On variable separation in modal and superintuitionistic logics, Studia Logica 55 (1995), pp.99–112.
• [10] L.L. Maksimova, Interrelation of algebraic, semantical and logical properties for superintuitionistic and modal logics, in: Logic, Algebra and Computer Science, Banach Center Publications 46, Polish Academy of Science, Warszawa,1999, pp.159–168.
• [11] D. Souma, An algebraic approach to the disjunction property of substructural logics, to appear in Notre Dame Journal of Formal Logic 48 (2007).
• [12] A. Wroński, Remarks on Halldén-completeness of modal and intermediate logics, Bulletin of the Section of Logic 5, 4 (1976), pp.126–129.