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)
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)
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)
This paper deals with the algebraization of multi-signature equational logic in the context of the modern theory of categorical abstract algebraic logic. Two are the novelties compared to traditional treatments: First, interpretations between different algebraic types are handled in the object language rather than the metalanguage. Second, rather than… (More)