5 research outputs found
Cores and Compactness of Infinite Directed Graphs
AbstractIn this paper we define the property of homomorphic compactness for digraphs. We prove that if a digraphHis homomorphically compact thenHhas a core, although the converse does not hold. We also examine a weakened compactness condition and show that when this condition is assumed, compactness is equivalent to containing a core. We use this result to prove that if a digraphHof sizeÎșis not compact, then there is a digraphGof size at mostÎș+such thatHis not compact with respect toG. We then give examples of some sufficient conditions for compactness
Cores of Countably Categorical Structures
A relational structure is a core, if all its endomorphisms are embeddings.
This notion is important for computational complexity classification of
constraint satisfaction problems. It is a fundamental fact that every finite
structure has a core, i.e., has an endomorphism such that the structure induced
by its image is a core; moreover, the core is unique up to isomorphism. Weprove
that every \omega -categorical structure has a core. Moreover, every
\omega-categorical structure is homomorphically equivalent to a model-complete
core, which is unique up to isomorphism, and which is finite or \omega
-categorical. We discuss consequences for constraint satisfaction with \omega
-categorical templates
Optimal Repairs in the Description Logic EL Revisited
Ontologies based on Description Logics may contain errors, which are usually detected when reasoning produces consequences that follow from the ontology, but do not
hold in the modelled application domain. In previous work, we have introduced repair approaches for EL ontologies that are optimal in the sense that they preserve a maximal
amount of consequences. In this paper, we will, on the one hand, review these approaches, but with an emphasis on motivation rather than on technical details. On the other hand, we will describe new results that address the problems that optimal repairs may become very large or need not even exist unless strong restrictions on the terminological part of the ontology apply. We will show how one can deal with these problems by introducing concise representations of optimal repairs