On the Computation of Common Subsumers in Description Logics

Description logics (DL) knowledge bases are often build by users with expertise in the application domain, but little expertise in logic. To support this kind of users when building their knowledge bases a number of extension methods have been proposed to provide the user with concept descriptions as a starting point for new concept definitions. The inference service central to several of these approaches is the computation of (least) common subsumers of concept descriptions. In case disjunction of concepts can be expressed in the DL under consideration, the least common subsumer (lcs) is just the disjunction of the input concepts. Such a trivial lcs is of little use as a starting point for a new concept definition to be edited by the user. To address this problem we propose two approaches to obtain "meaningful" common subsumers in the presence of disjunction tailored to two different methods to extend DL knowledge bases. More precisely, we devise computation methods for the approximation-based approach and the customization of DL knowledge bases, extend these methods to DLs with number restrictions and discuss their efficient implementation

Formal Concept Analysis Methods for Description Logics

This work presents mainly two contributions to Description Logics (DLs) research by means of Formal Concept Analysis (FCA) methods: supporting bottom-up construction of DL knowledge bases, and completing DL knowledge bases. Its contribution to FCA research is on the computational complexity of computing generators of closed sets

Polynomial-Time Reasoning Support for Design and Maintenance of Large-Scale Biomedical Ontologies

Description Logics (DLs) belong to a successful family of knowledge representation formalisms with two key assets: formally well-defined semantics which allows to represent knowledge in an unambiguous way and automated reasoning which allows to infer implicit knowledge from the one given explicitly. This thesis investigates various reasoning techniques for tractable DLs in the EL family which have been implemented in the CEL system. It suggests that the use of the lightweight DLs, in which reasoning is tractable, is beneficial for ontology design and maintenance both in terms of expressivity and scalability. The claim is supported by a case study on the renown medical ontology SNOMED CT and extensive empirical evaluation on several large-scale biomedical ontologies

Standard and Non-standard reasoning in Description Logics

The present work deals with Description Logics (DLs), a class of knowledge representation formalisms used to represent and reason about classes of individuals and relations between such classes in a formally well-defined way. We provide novel results in three main directions. (1) Tractable reasoning revisited: in the 1990s, DL research has largely answered the question for practically relevant yet tractable DL formalisms in the negative. Due to novel application domains, especially the Life Sciences, and a surprising tractability result by Baader, we have re-visited this question, this time looking in a new direction: general terminologies (TBoxes) and extensions thereof defined over the DL EL and extensions thereof. As main positive result, we devise EL++(D)-CBoxes as a tractable DL formalism with optimal expressivity in the sense that every additional standard DL constructor, every extension of the TBox formalism, or every more powerful concrete domain, makes reasoning intractable. (2) Non-standard inferences for knowledge maintenance: non-standard inferences, such as matching, can support domain experts in maintaining DL knowledge bases in a structured and well-defined way. In order to extend their availability and promote their use, the present work extends the state of the art of non-standard inferences both w.r.t. theory and implementation. Our main results are implementations and performance evaluations of known matching algorithms for the DLs ALE and ALN, optimal non-deterministic polynomial time algorithms for matching under acyclic side conditions in ALN and sublanguages, and optimal algorithms for matching w.r.t. cyclic (and hybrid) EL-TBoxes. (3) Non-standard inferences over general concept inclusion (GCI) axioms: the utility of GCIs in modern DL knowledge bases and the relevance of non-standard inferences to knowledge maintenance naturally motivate the question for tractable DL formalism in which both can be provided. As main result, we propose hybrid EL-TBoxes as a solution to this hitherto open question

International Workshop on Description Logics : Bonn, May 28/29, 1994

This collection of papers forms the permanent record of the 1994 Description Logic Workshop, that was held at the Gustav Stresemann Institut in Bonn, Germany on 28 and 29 May 1994, immediately after the Fourth International Conference on Principles of Knowledge Representation and Reasoning. The workshop was set up to be as informal as possible, so this collection cannot hope to capture the discussions associated with the workshop. However, we hope that it will serve to remind participants of their discussion at the workshop, and provide non-participants with indications of the topics that were discussed at the workshop. The workshop consisted of seven regular sessions and one panel session. Each regular session had about four short presentations on a single theme, but also had considerable time reserved for discussion. The themes of the sessions were Foundations of Description Logics, Architecture of Description Logics and Description Logic Systems, Language Extensions, Expanding Description Logics, General Applications of Description Logics, Natural Language Applications of Description Logics, Connections between Description Logics and Databases, and the Future of Description Logics and Description Logic Systems. The session on Foundations of Description Logics concentrated on computational properties of description logics, correspondences between description logics and other formalisms, and on semantics of description logics, Similarly, there is discussion on how to develop tractable desription logics, for some notion of tractable, and whether it is useful to worry about achieving tractability at all. Several of the participants argued in favour of a very expressive description logic. This obviously precludes tractability or even decidability of complete reasoning. Klaus Schild proposed that for some purposes one could employ "model checking" (i .e., a closed world assumption) instead of "theorem proving," and has shown that this is still tractable for very large languages. Maurizio Lenzerini's opinion was that it is important to have decidable languages. Tractability cannot be achieved in several application areas because there one needs very expressive constructs: e.g., axioms, complex role constructors, and cycles with fixed-point semantics. For Bob MacGregor, not even decidability is an issue since he claims that Loom's incomplete reasoner is sufficient for his applications. The discussion addressed the question of whether there is still need for foundations, and whether the work on foundation done until now really solved the problems that the designers of early DL systems had. Both questions were mostly answered in the affirmative, with the caveat that new research on foundations should make sure that it is concerned with "real" problems, and not just generates new problems. In the session on Architecture of Description Logics and Description Logic Systems the participants considered different ways of putting together description logics and description logic systems. One way of doing this is to have a different kind of inference strategy for description logics, such as one based on intuitionistic logics or one based directly on rules of inference-thus allowing variant systems. Another way of modifying description logic systems is to divide them up in different ways, such as making a terminology consist of a schema portion and a view portion. Some discussion in this session concerned whether architectures should be influenced by application areas, or even by particular applications. There was considerable discussion at the workshop on how Description Logics should be extended or expanded to make them more useful. There are several methods to do this. The first is to extend the language of descriptions, e.g ., to represent n-ary relations, temporal information, or whole-part relationships, all of which were discussed at the workshop. The second is to add in another kind of reasoning, such as default reasoning, while still keeping the general framework of description logic reasoning. The third is to incorporate descriptions or description-like constructs in a larger reasoner, such as a first order reasoner. This was the approach taken in OMEGA and is the approach being taken in the Loom project. There have been many extensions of the first two kinds proposed for description logics, including several presented at the workshop. One quest ion discussed at the workshop was whether these extensions fit in well with the philosophy of description logic. Another question was whether the presence of many proposals for extensions means that description logics are easy to expand, or that description logics are inadequate representation formalisms? The general consensus was that description logics adequately capture a certain kind of core reasoning and that they lend themselves to incorporation with other kinds of reasoning. Care must be taken, however, to keep the extended versions true to the goals of description logics. The sessions on Applications of Description Logics had presentations on applications of description logics in various areas, including configuration, tutoring, natural language processing, and domain modeling. Most of these applications are research applications, funded by government research programs. There was discussion of what is needed to have more fielded applications of description logics. The session on Connections between Description Logics and Databases considered three kinds of connections between Description Logics and Databases: 1. using Description Logics for expressing database schemas, including local schemas, integrated schemas, and views, integrity constraints, and queries; 2. using Description Logic reasoning for various database-related reasoning, including schema integration and validation, and query optimization, and query validation and organization; and 3. making Description Logic reasoners more like Database Mangagement Systems via optimization. All three of these connections are being actively investigated by the description logic community. The panel session on the Future of Description Logics and Description Logic Systems discussed where the future of description logics will lie. There seems to be a consensus that description logics must forge tighter connections with other formalisms, such as databases or object-oriented systems. In this way, perhaps, description logics will find more real applications

International Workshop on Description Logics : Bonn, May 28/29, 1994

This collection of papers forms the permanent record of the 1994 Description Logic Workshop, that was held at the Gustav Stresemann Institut in Bonn, Germany on 28 and 29 May 1994, immediately after the Fourth International Conference on Principles of Knowledge Representation and Reasoning. The workshop was set up to be as informal as possible, so this collection cannot hope to capture the discussions associated with the workshop. However, we hope that it will serve to remind participants of their discussion at the workshop, and provide non-participants with indications of the topics that were discussed at the workshop. The workshop consisted of seven regular sessions and one panel session. Each regular session had about four short presentations on a single theme, but also had considerable time reserved for discussion. The themes of the sessions were Foundations of Description Logics, Architecture of Description Logics and Description Logic Systems, Language Extensions, Expanding Description Logics, General Applications of Description Logics, Natural Language Applications of Description Logics, Connections between Description Logics and Databases, and the Future of Description Logics and Description Logic Systems. The session on Foundations of Description Logics concentrated on computational properties of description logics, correspondences between description logics and other formalisms, and on semantics of description logics, Similarly, there is discussion on how to develop tractable desription logics, for some notion of tractable, and whether it is useful to worry about achieving tractability at all. Several of the participants argued in favour of a very expressive description logic. This obviously precludes tractability or even decidability of complete reasoning. Klaus Schild proposed that for some purposes one could employ "model checking" (i .e., a closed world assumption) instead of "theorem proving," and has shown that this is still tractable for very large languages. Maurizio Lenzerini\u27s opinion was that it is important to have decidable languages. Tractability cannot be achieved in several application areas because there one needs very expressive constructs: e.g., axioms, complex role constructors, and cycles with fixed-point semantics. For Bob MacGregor, not even decidability is an issue since he claims that Loom\u27s incomplete reasoner is sufficient for his applications. The discussion addressed the question of whether there is still need for foundations, and whether the work on foundation done until now really solved the problems that the designers of early DL systems had. Both questions were mostly answered in the affirmative, with the caveat that new research on foundations should make sure that it is concerned with "real" problems, and not just generates new problems. In the session on Architecture of Description Logics and Description Logic Systems the participants considered different ways of putting together description logics and description logic systems. One way of doing this is to have a different kind of inference strategy for description logics, such as one based on intuitionistic logics or one based directly on rules of inference-thus allowing variant systems. Another way of modifying description logic systems is to divide them up in different ways, such as making a terminology consist of a schema portion and a view portion. Some discussion in this session concerned whether architectures should be influenced by application areas, or even by particular applications. There was considerable discussion at the workshop on how Description Logics should be extended or expanded to make them more useful. There are several methods to do this. The first is to extend the language of descriptions, e.g ., to represent n-ary relations, temporal information, or whole-part relationships, all of which were discussed at the workshop. The second is to add in another kind of reasoning, such as default reasoning, while still keeping the general framework of description logic reasoning. The third is to incorporate descriptions or description-like constructs in a larger reasoner, such as a first order reasoner. This was the approach taken in OMEGA and is the approach being taken in the Loom project. There have been many extensions of the first two kinds proposed for description logics, including several presented at the workshop. One quest ion discussed at the workshop was whether these extensions fit in well with the philosophy of description logic. Another question was whether the presence of many proposals for extensions means that description logics are easy to expand, or that description logics are inadequate representation formalisms? The general consensus was that description logics adequately capture a certain kind of core reasoning and that they lend themselves to incorporation with other kinds of reasoning. Care must be taken, however, to keep the extended versions true to the goals of description logics. The sessions on Applications of Description Logics had presentations on applications of description logics in various areas, including configuration, tutoring, natural language processing, and domain modeling. Most of these applications are research applications, funded by government research programs. There was discussion of what is needed to have more fielded applications of description logics. The session on Connections between Description Logics and Databases considered three kinds of connections between Description Logics and Databases: 1. using Description Logics for expressing database schemas, including local schemas, integrated schemas, and views, integrity constraints, and queries; 2. using Description Logic reasoning for various database-related reasoning, including schema integration and validation, and query optimization, and query validation and organization; and 3. making Description Logic reasoners more like Database Mangagement Systems via optimization. All three of these connections are being actively investigated by the description logic community. The panel session on the Future of Description Logics and Description Logic Systems discussed where the future of description logics will lie. There seems to be a consensus that description logics must forge tighter connections with other formalisms, such as databases or object-oriented systems. In this way, perhaps, description logics will find more real applications

International Workshop on Description Logics : Bonn, May 28/29, 1994

This collection of papers forms the permanent record of the 1994 Description Logic Workshop, that was held at the Gustav Stresemann Institut in Bonn, Germany on 28 and 29 May 1994, immediately after the Fourth International Conference on Principles of Knowledge Representation and Reasoning. The workshop was set up to be as informal as possible, so this collection cannot hope to capture the discussions associated with the workshop. However, we hope that it will serve to remind participants of their discussion at the workshop, and provide non-participants with indications of the topics that were discussed at the workshop. The workshop consisted of seven regular sessions and one panel session. Each regular session had about four short presentations on a single theme, but also had considerable time reserved for discussion. The themes of the sessions were Foundations of Description Logics, Architecture of Description Logics and Description Logic Systems, Language Extensions, Expanding Description Logics, General Applications of Description Logics, Natural Language Applications of Description Logics, Connections between Description Logics and Databases, and the Future of Description Logics and Description Logic Systems. The session on Foundations of Description Logics concentrated on computational properties of description logics, correspondences between description logics and other formalisms, and on semantics of description logics, Similarly, there is discussion on how to develop tractable desription logics, for some notion of tractable, and whether it is useful to worry about achieving tractability at all. Several of the participants argued in favour of a very expressive description logic. This obviously precludes tractability or even decidability of complete reasoning. Klaus Schild proposed that for some purposes one could employ "model checking" (i .e., a closed world assumption) instead of "theorem proving," and has shown that this is still tractable for very large languages. Maurizio Lenzerini's opinion was that it is important to have decidable languages. Tractability cannot be achieved in several application areas because there one needs very expressive constructs: e.g., axioms, complex role constructors, and cycles with fixed-point semantics. For Bob MacGregor, not even decidability is an issue since he claims that Loom's incomplete reasoner is sufficient for his applications. The discussion addressed the question of whether there is still need for foundations, and whether the work on foundation done until now really solved the problems that the designers of early DL systems had. Both questions were mostly answered in the affirmative, with the caveat that new research on foundations should make sure that it is concerned with "real" problems, and not just generates new problems. In the session on Architecture of Description Logics and Description Logic Systems the participants considered different ways of putting together description logics and description logic systems. One way of doing this is to have a different kind of inference strategy for description logics, such as one based on intuitionistic logics or one based directly on rules of inference-thus allowing variant systems. Another way of modifying description logic systems is to divide them up in different ways, such as making a terminology consist of a schema portion and a view portion. Some discussion in this session concerned whether architectures should be influenced by application areas, or even by particular applications. There was considerable discussion at the workshop on how Description Logics should be extended or expanded to make them more useful. There are several methods to do this. The first is to extend the language of descriptions, e.g ., to represent n-ary relations, temporal information, or whole-part relationships, all of which were discussed at the workshop. The second is to add in another kind of reasoning, such as default reasoning, while still keeping the general framework of description logic reasoning. The third is to incorporate descriptions or description-like constructs in a larger reasoner, such as a first order reasoner. This was the approach taken in OMEGA and is the approach being taken in the Loom project. There have been many extensions of the first two kinds proposed for description logics, including several presented at the workshop. One quest ion discussed at the workshop was whether these extensions fit in well with the philosophy of description logic. Another question was whether the presence of many proposals for extensions means that description logics are easy to expand, or that description logics are inadequate representation formalisms? The general consensus was that description logics adequately capture a certain kind of core reasoning and that they lend themselves to incorporation with other kinds of reasoning. Care must be taken, however, to keep the extended versions true to the goals of description logics. The sessions on Applications of Description Logics had presentations on applications of description logics in various areas, including configuration, tutoring, natural language processing, and domain modeling. Most of these applications are research applications, funded by government research programs. There was discussion of what is needed to have more fielded applications of description logics. The session on Connections between Description Logics and Databases considered three kinds of connections between Description Logics and Databases: 1. using Description Logics for expressing database schemas, including local schemas, integrated schemas, and views, integrity constraints, and queries; 2. using Description Logic reasoning for various database-related reasoning, including schema integration and validation, and query optimization, and query validation and organization; and 3. making Description Logic reasoners more like Database Mangagement Systems via optimization. All three of these connections are being actively investigated by the description logic community. The panel session on the Future of Description Logics and Description Logic Systems discussed where the future of description logics will lie. There seems to be a consensus that description logics must forge tighter connections with other formalisms, such as databases or object-oriented systems. In this way, perhaps, description logics will find more real applications