## Probabilistic description logic programs (2005)

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Venue: | In Proc. ECSQARU-2005 |

Citations: | 38 - 15 self |

### BibTeX

@INPROCEEDINGS{Lukasiewicz05probabilisticdescription,

author = {Thomas Lukasiewicz},

title = {Probabilistic description logic programs},

booktitle = {In Proc. ECSQARU-2005},

year = {2005},

pages = {737--749},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. In previous work, we have introduced probabilistic description logic programs (or pdl-programs), which are a combination of description logic programs (or dl-programs) under the answer set and well-founded semantics with Poole’s independent choice logic. Such programs are directed towards sophisticated representation and reasoning techniques that allow for probabilistic uncertainty in the Rules, Logic, and Proof layers of the Semantic Web. In this paper, we continue this line of research. We concentrate on the special case of stratified probabilistic description logic programs (or spdl-programs). In particular, we present an algorithm for query processing in such pdl-programs, which is based on a reduction to computing the canonical model of stratified dl-programs. 1

### Citations

879 | The well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...ying. The semantics of dl-programs was defined in [7] and [8] as an extension of the answer set semantics by Gelfond and Lifschitz [12] and the well-founded semantics by Van Gelder, Ross, and Schlipf =-=[29]-=-, respectively, which are the two most widely used semantics for nonmonotonic logic programs. The description logic knowledge bases in dl-programs are specified in the well-known description logics SH... |

520 | From SHIQ and RDF to OWL: The making of a web ontology language
- Horrocks, Patel-Schneider, et al.
(Show Context)
Citation Context ...ly cooperative agent technology for processing the information of the Web. The Semantic Web consists of several hierarchical layers, where the Ontology layer, in form of the OWL Web Ontology Language =-=[30,18]-=- (recommended by the W3C), is currently the highest layer of sufficient maturity. OWL consists of three increasingly expressive sublanguages, namely OWL Lite, OWL DL, and OWL Full. OWL Lite and OWL DL... |

440 | Description logic programs: combining logic programs with description logic - Grosof, Horrocks, et al. - 2003 |

337 |
Weaving the Web
- Berners-Lee
- 1999
(Show Context)
Citation Context ...we present an algorithm for query processing in such pdl-programs, which is based on a reduction to computing the canonical model of stratified dl-programs. 1 Introduction The Semantic Web initiative =-=[2,9]-=- aims at an extension of the current World Wide Web by standards and technologies that help machines to understand the information on the Web so that they can support richer discovery, data integratio... |

329 | Practical reasoning for expressive description logics
- Horrocks, Sattler, et al.
- 1999
(Show Context)
Citation Context ...ship); and (6) a=b (resp., a �= b), where a,b∈I (equality (resp., inequality)). A knowledge base L is a finite set of axioms. For decidability, number restrictions in L are restricted to simple R ∈RA =-=[19]-=-. The syntax of SHIF(D) is as the above syntax of SHOIN(D), but without the oneOf constructor and with the atleast and atmost constructors limited to 0 and 1. For the semantics of SHIF(D) and SHOIN(D)... |

221 | Combining answer set programming with description logics for the semantic web
- Eiter, Lukasiewicz, et al.
- 2004
(Show Context)
Citation Context ...edge bases. Another type of combination is to build ontologies on top of rules, which means that ontological definitions are supplemented by rules or imported from rules. Towards this goal, the works =-=[7,8]-=- have proposed description logic programs (or dlprograms), which are of the form KB = (L,P), where L is a knowledge base in a description logic and P is a finite set of description logic rules (or dl-... |

208 | Reducing OWL Entailment to Description Logic Satisfiability
- Horrocks, Patel-Schneider
- 2003
(Show Context)
Citation Context ...sists of three increasingly expressive sublanguages, namely OWL Lite, OWL DL, and OWL Full. OWL Lite and OWL DL are essentially very expressive description logics with an RDF syntax [18]. As shown in =-=[16]-=-, ontology entailment in OWL Lite (resp., OWL DL) reduces to knowledge base (un)satisfiability in the description logic SHIF(D) (resp., SHOIN(D)). On top of the Ontology layer, the Rules, Logic, and P... |

163 | Reasoning within fuzzy description logics
- Straccia
(Show Context)
Citation Context ...ilistic generalization of the CLASSIC description logic, which uses Bayesian networks as underlying probabilistic reasoning formalism. Note that fuzzy description logics, such as the ones by Straccia =-=[26,27]-=-, are less closely related to probabilistic description logics, since fuzzy uncertainty deals with vagueness, rather than ambiguity and imprecision. As for (c), especially the works by Costa [4], Pool... |

159 | Design rationale of RuleML: A markup language for semantic web rules
- Boley, Tabet, et al.
- 2001
(Show Context)
Citation Context ...Proof layers of the Semantic Web will be developed next, which should offer sophisticated representation and reasoning capabilities. As a first effort in this direction, RuleML (Rule Markup Language) =-=[3]-=- is an XML-based markup language for rules and rule-based systems, whereas the OWL Rules Language [17] is a first proposal for extending OWL by Horn clause rules. A key requirement of the layered arch... |

157 | The Independent Choice Logic for modelling multiple agents under uncertainty
- Poole
- 1997
(Show Context)
Citation Context ...neralize dl-programs under the answer set and well-founded semantics by probabilistic uncertainty. They have been developed as a combination of dl-programs with Poole’s independent choice logic (ICL) =-=[25]-=-. It is important to point out that Poole’s ICL is a powerful representation and reasoning formalism for single- and also multi-agent systems, which combines logic and probability, and which can repre... |

152 | AL-log: Integrating datalog and description logics
- Donini, Lenzerini, et al.
- 1998
(Show Context)
Citation Context ...ic, and (d) approaches to rule-based well-founded reasoning in the Semantic Web. Below we give some representatives for (a)–(d). Further works and details are given in [9]. The works by Donini et al. =-=[8]-=-, Levy and Rousset [21], and Rosati [25] are representatives of hybrid approaches using description logics as input. Donini et al. [8] introduce a combination of (disjunction-, negation-, and function... |

151 | A proposal for an OWL rules language
- Horrocks, Patel-Schneider
- 2004
(Show Context)
Citation Context ...ion and reasoning capabilities. As a first effort in this direction, RuleML (Rule Markup Language) [3] is an XML-based markup language for rules and rule-based systems, whereas the OWL Rules Language =-=[17]-=- is a first proposal for extending OWL by Horn clause rules. A key requirement of the layered architecture of the Semantic Web is to integrate the Rules and the Ontology layer. In particular, it is cr... |

113 | Towards a fuzzy description logic for the semantic web
- Straccia
- 2004
(Show Context)
Citation Context ...ilistic generalization of the CLASSIC description logic, which uses Bayesian networks as underlying probabilistic reasoning formalism. Note that fuzzy description logics, such as the ones by Straccia =-=[26,27]-=-, are less closely related to probabilistic description logics, since fuzzy uncertainty deals with vagueness, rather than ambiguity and imprecision. As for (c), especially the works by Costa [4], Pool... |

109 | P-CLASSIC: A tractable probabilistic description logic
- Koller, Levy, et al.
- 1997
(Show Context)
Citation Context ...arlier work, Heinsohn [15] and Jaeger [20] present probabilistic extensions to the description logic ALC, which are essentially based on probabilistic reasoning in probabilistic logics. Koller et al. =-=[21]-=- present a probabilistic generalization of the CLASSIC description logic, which uses Bayesian networks as underlying probabilistic reasoning formalism. Note that fuzzy description logics, such as the ... |

100 | A probabilistic extension to ontology language OWL
- Ding, Peng
- 2004
(Show Context)
Citation Context ...bilistic description logics, since fuzzy uncertainty deals with vagueness, rather than ambiguity and imprecision. As for (c), especially the works by Costa [4], Pool and Aikin [24], and Ding and Peng =-=[6]-=- present probabilistic extensions to OWL. In particular, Costa’s work [4] is semantically based on multi-entity Bayesian networks, while [6] has a semantics in standard Bayesian networks. In closely r... |

89 |
editors. Spinning the Semantic Web: Bringing the World Wide Web to Its Full Potential
- Fensel, Wahlster, et al.
- 2002
(Show Context)
Citation Context ...we present an algorithm for query processing in such pdl-programs, which is based on a reduction to computing the canonical model of stratified dl-programs. 1 Introduction The Semantic Web initiative =-=[2,9]-=- aims at an extension of the current World Wide Web by standards and technologies that help machines to understand the information on the Web so that they can support richer discovery, data integratio... |

87 | P-SHOQ(D): A probabilistic extension of SHOQ(D) for probabilistic ontologies in the semantic web
- Giugno, Lukasiewicz
- 2002
(Show Context)
Citation Context ...uncertainty using interval annotations. To my knowledge, the present paper and [22] are the first ones on description logic programs with probabilistic uncertainty. As for (b), Giugno and Lukasiewicz =-=[13]-=- present a probabilistic generalization of the expressive description logic SHOQ(D) behind DAML+OIL, which is based on lexicographic probabilistic reasoning. In earlier work, Heinsohn [15] and Jaeger ... |

78 | Probabilistic reasoning in terminological logics
- Jaeger
- 1994
(Show Context)
Citation Context ... present a probabilistic generalization of the expressive description logic SHOQ(D) behind DAML+OIL, which is based on lexicographic probabilistic reasoning. In earlier work, Heinsohn [15] and Jaeger =-=[20]-=- present probabilistic extensions to the description logic ALC, which are essentially based on probabilistic reasoning in probabilistic logics. Koller et al. [21] present a probabilistic generalizatio... |

70 |
Probabilistic description logics
- Heinsohn
- 1994
(Show Context)
Citation Context ...Lukasiewicz [13] present a probabilistic generalization of the expressive description logic SHOQ(D) behind DAML+OIL, which is based on lexicographic probabilistic reasoning. In earlier work, Heinsohn =-=[15]-=- and Jaeger [20] present probabilistic extensions to the description logic ALC, which are essentially based on probabilistic reasoning in probabilistic logics. Koller et al. [21] present a probabilist... |

59 | Well-founded semantics for description logic programs in the semantic web
- Eiter, Lukasiewicz, et al.
- 2004
(Show Context)
Citation Context ...uct, (5) only products are related to each other, (6) tb ai and tb lp are textbooks, which are related to each other, (7) pc ibm and pc hp are personal computers, which are related to each other, and =-=(8)-=- ibm and hp are providers for pc ibm and pc hp, respectively. This knowledge is expressed by the following description logic knowledge base L1: Textbook ⊑ Book; PC ⊔ Camera ⊑ Electronics; Book ⊔ Elect... |

39 |
Web Ontology Language Overview
- OWL
- 2004
(Show Context)
Citation Context ...ly cooperative agent technology for processing the information of the Web. The Semantic Web consists of several hierarchical layers, where the Ontology layer, in form of the OWL Web Ontology Language =-=[30,18]-=- (recommended by the W3C), is currently the highest layer of sufficient maturity. OWL consists of three increasingly expressive sublanguages, namely OWL Lite, OWL DL, and OWL Full. OWL Lite and OWL DL... |

37 |
Combining Horn rules and description logics
- Levy, Rousset
- 1998
(Show Context)
Citation Context ... to rule-based well-founded reasoning in the Semantic Web. Below we give some representatives for (a)–(d). Further works and details are given in [9]. The works by Donini et al. [8], Levy and Rousset =-=[21]-=-, and Rosati [25] are representatives of hybrid approaches using description logics as input. Donini et al. [8] introduce a combination of (disjunction-, negation-, and function-free) datalog with the... |

36 |
Classical negation in logic programs and deductive databases. New generation computing
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...al knowledge (gained in the program) can be supplied to L before querying. The semantics of dl-programs was defined in [7] and [8] as an extension of the answer set semantics by Gelfond and Lifschitz =-=[12]-=- and the well-founded semantics by Van Gelder, Ross, and Schlipf [29], respectively, which are the two most widely used semantics for nonmonotonic logic programs. The description logic knowledge bases... |

32 |
Embedding defaults into terminological representation systems
- Baader, Hollunder
- 1995
(Show Context)
Citation Context .... [28], Alsaç and Baral [1], Swift [27], Grosof et al. [15], and Hufstadt et al. [20]. Early work on dealing with default information in description logics is the approach due to Baader and Hollunder =-=[4]-=-, where Reiter’s default logic is adapted to terminological knowledge bases. Antoniou [2] combines defeasible reasoning with description logics for the Semantic Web. In [3], Antoniou and Wagner summar... |

32 |
Reasoning for Description Logics around SHIQ in a Resolution Framework
- Hustadt, Motik, et al.
(Show Context)
Citation Context ...mantics.sSome approaches reducing description logic reasoning to logic programming are the works by Van Belleghem et al. [28], Alsaç and Baral [1], Swift [27], Grosof et al. [15], and Hufstadt et al. =-=[20]-=-. Early work on dealing with default information in description logics is the approach due to Baader and Hollunder [4], where Reiter’s default logic is adapted to terminological knowledge bases. Anton... |

25 |
Nonmonotonic rule systems on top of ontology layers
- Antoniou
- 2002
(Show Context)
Citation Context ...ue, denoted ⊥ and ⊤, respectively, and all atoms are classical formulas. If φ and ψ are classical formulas, then also ¬φ and (φ ∧ ψ). A conditional constraint is of the form (ψ|φ)[l,u] with reals l,u∈=-=[0,1]-=- and classical formulas φ and ψ. We define probabilistic formulas inductively as follows. Every conditional constraint is a probabilistic formula. If F and G are probabilistic formulas, then also ¬F a... |

25 | Uncertainty in description logic programs
- Straccia
- 2004
(Show Context)
Citation Context ...iption logics, and (c) probabilistic generalizations of web ontology languages. Note that related work on description logic programs without uncertainty is discussed in [7,8,22].sAs for (a), Straccia =-=[28]-=- combines description logic programs with non-probabilistic uncertainty using interval annotations. To my knowledge, the present paper and [22] are the first ones on description logic programs with pr... |

24 |
Reasoning in description logics using declarative logic programming
- Alsaç, Baral
- 1997
(Show Context)
Citation Context ...denoted ⊥ and ⊤, respectively, and all atoms are classical formulas. If φ and ψ are classical formulas, then also ¬φ and (φ ∧ ψ). A conditional constraint is of the form (ψ|φ)[l, u] with reals l, u ∈ =-=[0, 1]-=- and classical formulas φ and ψ. We define probabilistic formulas inductively as follows. Every conditional constraint is a probabilistic formula. If F and G are probabilistic formulas, then also ¬F a... |

24 | Towards expressive KR systems integrating datalog and description logics: Preliminary report
- Rosati
- 1999
(Show Context)
Citation Context ...ll-founded reasoning in the Semantic Web. Below we give some representatives for (a)–(d). Further works and details are given in [9]. The works by Donini et al. [8], Levy and Rousset [21], and Rosati =-=[25]-=- are representatives of hybrid approaches using description logics as input. Donini et al. [8] introduce a combination of (disjunction-, negation-, and function-free) datalog with the description logi... |

19 |
Representing probabilistic knowledge in the Semantic Web
- Fukushige
- 2004
(Show Context)
Citation Context ...extensions to OWL. In particular, Costa’s work [4] is semantically based on multi-entity Bayesian networks, while [6] has a semantics in standard Bayesian networks. In closely related work, Fukushige =-=[11]-=- proposes a basic framework for representing probabilistic relationships in RDF. Finally, Nottelmann and Fuhr [23] present pDAML+OIL, which is a probabilistic generalization of the web ontology langua... |

17 |
Deduction in ontologies via ASP
- Swift
- 2004
(Show Context)
Citation Context ... which is based on a generalized answer set semantics.sSome approaches reducing description logic reasoning to logic programming are the works by Van Belleghem et al. [28], Alsaç and Baral [1], Swift =-=[27]-=-, Grosof et al. [15], and Hufstadt et al. [20]. Early work on dealing with default information in description logics is the approach due to Baader and Hollunder [4], where Reiter’s default logic is ad... |

14 | Structure-based causes and explanations in the independent choice logic
- Finzi, Lukasiewicz
(Show Context)
Citation Context ...s, Bayesian networks, Markov decision processes, and normal form games [25]. Furthermore, Poole’s ICL also allows for natural notions of causes and explanations as in Pearl’s structural causal models =-=[10]-=-. In this paper, we continue this line of research. We concentrate on the special case of stratified pdl-programs (or spdl-programs). In particular, as a main new contribution, we present an algorithm... |

14 |
pDAML+OIL: A probabilistic extension to DAML+OIL based on probabilistic datalog
- Nottelmann, Fuhr
- 2004
(Show Context)
Citation Context ...[6] has a semantics in standard Bayesian networks. In closely related work, Fukushige [11] proposes a basic framework for representing probabilistic relationships in RDF. Finally, Nottelmann and Fuhr =-=[23]-=- present pDAML+OIL, which is a probabilistic generalization of the web ontology language DAML+OIL, and a mapping to stratified probabilistic datalog. 6 Summary and Outlook We have continued the resear... |

12 |
KEEPER and Protégé: An elicitation environment for Bayesian inference tools
- Pool, Aikin
- 2004
(Show Context)
Citation Context ...closely related to probabilistic description logics, since fuzzy uncertainty deals with vagueness, rather than ambiguity and imprecision. As for (c), especially the works by Costa [4], Pool and Aikin =-=[24]-=-, and Ding and Peng [6] present probabilistic extensions to OWL. In particular, Costa’s work [4] is semantically based on multi-entity Bayesian networks, while [6] has a semantics in standard Bayesian... |

12 |
Schreye. A strong correspondence between description logics and open logic programs
- Belleghem, Denecker, et al.
- 1997
(Show Context)
Citation Context ...thout function symbols) with ALC, which is based on a generalized answer set semantics.sSome approaches reducing description logic reasoning to logic programming are the works by Van Belleghem et al. =-=[28]-=-, Alsaç and Baral [1], Swift [27], Grosof et al. [15], and Hufstadt et al. [20]. Early work on dealing with default information in description logics is the approach due to Baader and Hollunder [4], w... |

11 |
XSB: A System for Efficiently Computing WFS
- Rao, Sagonas, et al.
- 1997
(Show Context)
Citation Context ...loped, with routines to convert RuleML rule bases to Prolog and vice versa. The compiler supports paraconsistent well-founded semantics with explicit negation; it is planned to be extended to use XSB =-=[24]-=-. 5 Summary and Outlook We have presented probabilistic description logic programs (or pdl-programs), which are a combination of dl-programs under the answer set and the well-founded semantics with Po... |

7 |
Rules and defeasible reasoning on the Semantic Web
- Antoniou, Wagner
- 2003
(Show Context)
Citation Context ...due to Baader and Hollunder [4], where Reiter’s default logic is adapted to terminological knowledge bases. Antoniou [2] combines defeasible reasoning with description logics for the Semantic Web. In =-=[3]-=-, Antoniou and Wagner summarize defeasible and strict reasoning in a single rule formalism. An important approach to rule-based reasoning under the well-founded semantics for the Semantic Web is due t... |

6 |
Bayesian Semantics for the Semantic
- Costa
- 2005
(Show Context)
Citation Context ...a [26,27], are less closely related to probabilistic description logics, since fuzzy uncertainty deals with vagueness, rather than ambiguity and imprecision. As for (c), especially the works by Costa =-=[4]-=-, Pool and Aikin [24], and Ding and Peng [6] present probabilistic extensions to OWL. In particular, Costa’s work [4] is semantically based on multi-entity Bayesian networks, while [6] has a semantics... |