A multimodal logic for reasoning about complementarity

Title:	A multimodal logic for reasoning about complementarity
Authors:	Ivo Düntsch , Dept of Computer Science , Brock University , St Catherines, Ontario, L2S 3A1, Canada Beata Konikowska, Polish Academy of Sciences, Warsaw, Poland
Status:	Journal of Applied Non-Classical Logic 10 (2000), 273-301
Abstract:	Two objects u,v of an information system are said to be complementary with respect to attribute a if a(u)= - a(v), where a(u) is the set of values of attribute a assigned to u. They are said to be complementary with respect to a set of attributes A if they are complementary with respect to each attribute a in A. A multi-modal logical language for reasoning about complementarity relations is presented, with modalities [A] and <A> parameterized by subsets of a given set ATTR of attributes. Two complete deduction system for the language are presented: a Rasiowa-Sikorski style system using signed formulae, and an equivalent sequent calculus system in Gentzen style complete for theories.