4 research outputs found
Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics
Belief revision of knowledge bases represented by a set of sentences in a
given logic has been extensively studied but for specific logics, mainly
propositional, and also recently Horn and description logics. Here, we propose
to generalize this operation from a model-theoretic point of view, by defining
revision in an abstract model theory known under the name of satisfaction
systems. In this framework, we generalize to any satisfaction systems the
characterization of the well known AGM postulates given by Katsuno and
Mendelzon for propositional logic in terms of minimal change among
interpretations. Moreover, we study how to define revision, satisfying the AGM
postulates, from relaxation notions that have been first introduced in
description logics to define dissimilarity measures between concepts, and the
consequence of which is to relax the set of models of the old belief until it
becomes consistent with the new pieces of knowledge. We show how the proposed
general framework can be instantiated in different logics such as
propositional, first-order, description and Horn logics. In particular for
description logics, we introduce several concrete relaxation operators tailored
for the description logic \ALC{} and its fragments \EL{} and \ELext{},
discuss their properties and provide some illustrative examples
Query inseparability for ALC ontologies
We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in
a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation,
update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give model-theoretic
criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable
for conjunctive queries (CQs), but 2ExpTime-complete for unions of CQs (UCQs). The same results hold if (U)CQs are
replaced by rooted (U)CQs, where every variable is connected to an answer variable. We also show that inseparability
by CQs is still undecidable if one KB is given in the lightweight DL EL and if no restrictions are imposed on the
signature of the CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query
over any ABox in a given signature and show that, for CQs, this problem is undecidable, too. We then develop
model-theoretic criteria for HornALC TBoxes and show using tree automata that, in contrast, inseparability becomes
decidable and 2ExpTime-complete, even ExpTime-complete when restricted to (unions of) rooted CQs
Revising General Knowledge Bases in Description Logics
Revising knowledge bases (KBs) in description logics (DLs) in a syntax-independent manner is an important and nontrivial problem for ontology management and DL communities. Several attempts have been made to adapt classical modelbased belief revision/update techniques to DLs, but they are restricted in several ways. In particular, they rarely investigate how to deal with revisions of general DL KBs. An important reason for this is that, unlike propositional logic, a DL KB may have infinitely many models with complex (and possibly infinite) structures, making it difficult to define and compute revisions in terms of models. In this paper, we focus on a specific DL in the DL-Lite family, but aim to define and compute revision by general KBs. For this reason, we first develop an alternative semantic characterization for DL-Lite by introducing the concept of a feature (as an alternative to a model) and then define specific revision operators for DL-Lite KBs based on features. We also present an algorithm for computing best approximations for KB revisions in DL-Lite