Recent studies of the algebraic properties of bilattices have provided insight into their internal structures, and have led to practical results, especially in reducing the computational complexity of bilattice-based multi-valued logic programs. In this paper the representation theorem for interlaced bilattices with negation found in 18] and extended to… (More)
We present the syntax and semantics of a modular ontology language SHOIQP to support context-specific reuse of knowledge from multiple ontologies. A SHOIQP ontology consists of multiple ontology modules (each of which can be viewed as a SHOIQ ontology) and concept, role and nominal names can be shared by " importing " relations among modules. SHOIQP… (More)
The framework and the basic results of Wille on triadic concept analysis, including his Basic Theorem of Triadic Concept Analysis, are here generalized to n-dimensional formal contexts.
Pałasi´nska and Pigozzi developed a theory of partially ordered varieties and quasi-varieties of algebras with the goal of addressing issues pertaining to the theory of algebraizability of logics involving an abstract form of the connective of logical implication. Following their lead, the author has abstracted the theory to cover the case of algebraic… (More)
Algebraic systems play in the theory of algebraizability of π-institutions the role that algebras play in the theory of algebraizable sentential logics. In this same sense, I-algebraic systems are to a π-institution I what S-algebras are to a sentential logic S. More precisely, an (I, N)-algebraic system is the sentence functor reduct of an N-reduced (N,… (More)
An important part of the theory of algebraizable sentential logics consists of studying the algebraic semantics of these logics. As developed by Czelakowski, Blok, and Pigozzi and Font and Jansana, among others, it includes studying the properties of logical matrices serving as models of deductive systems and the properties of abstract logics serving as… (More)
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Protoalgebraic logics are characterized by the monotonicity of the Leibniz operator on their theory lattices and are at the lower end of the Leibniz hierarchy of abstract algebraic logic. They have been shown to be the most primitive among those logics with a strong enough algebraic character to be amenable to algebraic study techniques. Protoalgebraic… (More)