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1 Reports on Mathematical Logic

1 2008

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Algebraic characterizations of variable separation properties

100%

Kihara H. , Ono H.

tom No. 43

43-63

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].