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Fusion of sequent modal logic systems labelled with truth values

Rasga, J. ; Roggia, K. ; Sernadas, C.

Logic Journal of the IGPL Vol. 18, Nº 6, pp. 893 - 920, December, 2010.

ISSN (print): 1368-9894
ISSN (online): 1367-0751

Scimago Journal Ranking: 0,35 (in 2010)

Digital Object Identifier: 10.1093/jigpal/jzp081

Fusion is a well-known form of combining normal modal logics endowed with a Hilbert calculi and a Kripke semantics. Herein, fusion is studied over logic systems using sequent calculi labelled with truth values and with a semantics based on a two-sorted algebra allowing, in particular, the representation of general Kripke structures. A wide variety of logics, including non-classical logics like, for instance, modal logics and intuitionistic logic can be presented by logic systems of this kind. A categorical approach of fusion is defined in the context of these logic systems. Preservation of soundness and completeness by fusion is studied. Soundness is preserved without further requirements, completeness is preserved under mild assumptions.