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.
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)
The theory of equivalential deductive systems, as introduced by Prucnal and Wro´nski and further developed by Czelakowski, is abstracted to cover the case of logical systems formalized as π-institutions. More precisely, the notion of an N-equivalence system for a given π-institution is introduced. A characterization theorem for N-equivalence systems,… (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)
In memory of Willem Blok A b s t r a c t. Font and Jansana studied the full models of sentential logics under the presence of a variety of metalogical properties. Their theory of full models was adapted, in recent work by the author, to cover the case of institutional logics. In the present work, the study of metalogical properties is carried out in the… (More)