Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200

The role of ontologies in biological and biomedical research: a functional perspective.

Ontologies are widely used in biological and biomedical research. Their success lies in their combination of four main features present in almost all ontologies: provision of standard identifiers for classes and relations that represent the phenomena within a domain; provision of a vocabulary for a domain; provision of metadata that describes the intended meaning of the classes and relations in ontologies; and the provision of machine-readable axioms and definitions that enable computational access to some aspects of the meaning of classes and relations. While each of these features enables applications that facilitate data integration, data access and analysis, a great potential lies in the possibility of combining these four features to support integrative analysis and interpretation of multimodal data. Here, we provide a functional perspective on ontologies in biology and biomedicine, focusing on what ontologies can do and describing how they can be used in support of integrative research. We also outline perspectives for using ontologies in data-driven science, in particular their application in structured data mining and machine learning applications.This is the final version of the article. It first appeared from Oxford University Press via http://dx.doi.org/10.1093/bib/bbv01

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

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

Transformation-Based Bottom-Up Computation of the Well-Founded Model

We present a framework for expressing bottom-up algorithms to compute the well-founded model of non-disjunctive logic programs. Our method is based on the notion of conditional facts and elementary program transformations studied by Brass and Dix for disjunctive programs. However, even if we restrict their framework to nondisjunctive programs, their residual program can grow to exponential size, whereas for function-free programs our program remainder is always polynomial in the size of the extensional database (EDB). We show that particular orderings of our transformations (we call them strategies) correspond to well-known computational methods like the alternating fixpoint approach, the well-founded magic sets method and the magic alternating fixpoint procedure. However, due to the confluence of our calculi, we come up with computations of the well-founded model that are provably better than these methods. In contrast to other approaches, our transformation method treats magic set transformed programs correctly, i.e. it always computes a relevant part of the well-founded model of the original program.Comment: 43 pages, 3 figure