1,533 research outputs found
Axiom Pinpointing
Axiom pinpointing refers to the task of finding the specific axioms in an
ontology which are responsible for a consequence to follow. This task has been
studied, under different names, in many research areas, leading to a
reformulation and reinvention of techniques. In this work, we present a general
overview to axiom pinpointing, providing the basic notions, different
approaches for solving it, and some variations and applications which have been
considered in the literature. This should serve as a starting point for
researchers interested in related problems, with an ample bibliography for
delving deeper into the details
Axiom Pinpointing in General Tableaux
Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. The pinpointing algorithms described in the DL literature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this paper is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of „tableaux algorithms,' which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures
Blocking and Pinpointing in Forest Tableaux
Axiom pinpointing has been introduced in description logics (DLs) to help the used understand the reasons why consequences hold by computing minimal subsets of the knowledge base that have the consequence in consideration. Several pinpointing algorithms have been described as extensions of the standard tableau-based reasoning algorithms for deciding consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL, using specific traits of them. In the past, we have developed a general approach for extending tableau-based algorithms into pinpointing algorithms. In this paper we explore some issues of termination of general tableaux and their pinpointing extensions. We also define a subclass of tableaux that allows the use of so-called blocking conditions, which stop the execution of the algorithm once a pattern is found, and adapt the pinpointing extensions accordingly, guaranteeing its correctness and termination
On the Complexity of Axiom Pinpointing in Description Logics
We investigate the computational complexity of axiom pinpointing in Description Logics, which is the task of finding minimal subsets of a knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used
Pinpointing in Terminating Forest Tableaux
Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. The pinpointing algorithms described in the DL literature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this paper is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of „tableau algorithms,' which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures
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