A representation theorem for universal horn classes categorical in power

Injectives in Finitely Generated Universal Horn Classes

Let K be a finite set of finite structures. We give a syntactic characterization of the property: every element of K is invective in ISP(K). We use this result to establish that 4 is invective in ISP(s) for every two-element algebra i. ?0. Introduction. Let K be a finite set of finite structures for a first-order language. In this paper we give a syntactic characterization (Theorem 4) of the pr...

Tests for injectivity in finitely generated universal Horn classes

Axiomatisability and hardness for universal Horn classes of hypergraphs

We characterise finite axiomatisability and intractability of deciding membership for universal Horn classes generated by finite loop-free hypergraphs. A universal Horn class is a class of model-theoretic structures of the same signature, closed under taking ultraproducts (Pu), direct products over nonempty families (P) and isomorphic copies of substructures (S); see [9, 17, 30, 32] for example...

A universal table model for categorical databases

A consistent categorical database can be viewed as a single contingency table by taking the maximum-entr0p.y extension of its base tables. Such a view, here called the universaf table model, is needed to answer a user who wishes “cross-classified” data, that is, categorical data resulting from the combination of information contained in two or more base tables. In order to implement a universal...

Ologs: A Categorical Framework for Knowledge Representation

In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database sch...