## Description Logic Programs: Combining Logic Programs with Description Logic (2003)

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Citations: | 435 - 42 self |

### BibTeX

@INPROCEEDINGS{Grosof03descriptionlogic,

author = {Benjamin N. Grosof},

title = {Description Logic Programs: Combining Logic Programs with Description Logic},

booktitle = {},

year = {2003},

pages = {48--57},

publisher = {ACM}

}

### Years of Citing Articles

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### Abstract

We show how to interoperate, semantically and inferentially, between the leading Semantic Web approaches to rules (RuleML Logic Programs) and ontologies (OWL/DAML+OIL Description Logic) via analyzing their expressive intersection. To do so, we define a new intermediate knowledge representation (KR) contained within this intersection: Description Logic Programs (DLP), and the closely related Description Horn Logic (DHL) which is an expressive fragment of first-order logic (FOL). DLP provides a significant degree of expressiveness, substantially greater than the RDFSchema fragment of Description Logic.

### Citations

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(Show Context)
Citation Context ...predicate p. The query of the view integrates the explicit information, found in pext with the queries that represent the bodies of those rules where p is the head. The interested reader may refer to =-=[18]-=- for an in-depth description, algorithm and proof. Intuitively, this result follows from the following substitutions: each Datalog-rule can be simulated using the select-from-where construct of SQL; m... |

482 |
editors. The Description Logic Handbook
- Baader, Calvanese, et al.
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Citation Context ...der to eliminate the offending operator(s). For example, negation can always be pushed inwards by using a combination of De Morgan’s laws and equivalences such as ¬∃P.C ≡∀P.¬C and ¬� nP �=-=�� � (n − 1) P [1]. Further simpl-=-ifications are also possible, e.g., using the equivalences C ⊔¬C ≡⊤, and ∀P.⊤ ≡⊤. For the sake of simplicity, however, we will assume that DL expressions are in a canonical form where a... |

347 |
Resource Description Framework (RDF) Schema Speci_cation 1.0, W3C Candidate Recommendation
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(Show Context)
Citation Context ...ectly tackling the union (of DL and Horn) in FOL. DLP provides a significant degree of expressiveness. It is a large fragment of the intersection of DL and LP/Horn, and includes the RDF-Schema (RDFS) =-=[4]-=- fragment of DL. The RDFS fragment of DL permits: stating that a class D is asSubclass of a class E; stating that the Domain of a property P is a class C; stating that the Range of a property P is a c... |

327 | Practical reasoning for expressive description logics
- Horrocks, Sattler, et al.
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(Show Context)
Citation Context ...s well as to DLs. From now on, when we talk about RDFS, we will be referring to the DAML+OIL subset of RDFS. DAML+OIL is equivalent to a very expressive DL—in fact it is equivalent to the SHOIQ(D) D=-=L [17, 15]. In add-=-ition to “abstract” classes and individuals, DAML+OIL also supports the use of “concrete” datatypes and data values (the (D) in SHOIQ(D)). In this paper, however, we will restrict our attentio... |

271 | A correspondence theory for terminological logics
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(Show Context)
Citation Context ...een the two logic based KR formalisms (so as to be able to combine knowledge taken from both): Description Logics (decidable fragments of FOL closely related to propositional modal and dynamic logics =-=[20]-=-), and Logic Programs (see, e.g., [2] for review) which in turn is closely related to the Horn fragment of FOL. We further focus on def-Horn (a large fragment of Horn FOL), and then go on to show how ... |

247 | On the decidability of query containment under constraints
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(Show Context)
Citation Context ...romise the tree model property to some extent, e.g., transitive properties can cause “short-cuts” down branches of the tree. 16 This is not an inherent restriction, and n-ary DLs are known, e.g., =-=DLR [5]-=-. 6 4.2.1 RDFS Statements RDFS provides a subset of the DL statements described in Section 3.1: subclass, subproperty, range, and domain statements (which in a DL setting are often called Tbox axioms)... |

232 | The complexity of concept languages
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Citation Context ...o FOL, where classes correspond to unary predicates (predicates of arity 1), properties correspond to binary predicates (predicates of arity 2), and subclass/property axioms correspond to implication =-=[7, 3]-=-. To be more precise, individuals are equivalent to FOL constants, classes and class expressions are equivalent to FOL formulae with one free variable, and properties (and property expressions when su... |

231 | Logic programming and knowledge representation
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(Show Context)
Citation Context ...(so as to be able to combine knowledge taken from both): Description Logics (decidable fragments of FOL closely related to propositional modal and dynamic logics [20]), and Logic Programs (see, e.g., =-=[2]-=- for review) which in turn is closely related to the Horn fragment of FOL. We further focus on def-Horn (a large fragment of Horn FOL), and then go on to show how both DL and LP are related to def-Hor... |

221 | XSB as an efficient deductive database engine
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(Show Context)
Citation Context ...T [12] or Racer [10]. 1 In tandem with RuleML/LP, we also focus on the (positive) Horn subset of FOL, which is closely related to the positive Horn subset of LP.sLogic programming systems such as XSB =-=[16]-=-, however, can access databases directly through built-in predicates. Furthermore, restricted variants of logic programs, such as the ones established in this paper, can be directly implemented on top... |

150 | On the relative expressiveness of description logics and predicate logics. AIJ
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(Show Context)
Citation Context ...o FOL, where classes correspond to unary predicates (predicates of arity 1), properties correspond to binary predicates (predicates of arity 2), and subclass/property axioms correspond to implication =-=[7, 3]-=-. To be more precise, individuals are equivalent to FOL constants, classes and class expressions are equivalent to FOL formulae with one free variable, and properties (and property expressions when su... |

147 | Ontology reasoning in the SHOQ(D) description logic
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(Show Context)
Citation Context ...s well as to DLs. From now on, when we talk about RDFS, we will be referring to the DAML+OIL subset of RDFS. DAML+OIL is equivalent to a very expressive DL—in fact it is equivalent to the SHOIQ(D) D=-=L [17, 15]. In add-=-ition to “abstract” classes and individuals, DAML+OIL also supports the use of “concrete” datatypes and data values (the (D) in SHOIQ(D)). In this paper, however, we will restrict our attentio... |

146 | Description of the RACER System and its Application
- Haarslev, Möller
(Show Context)
Citation Context ... some chosen ontology. This essentially leads to data that is replicated in order to enable ontology-based processing, e.g., by reading the exported files into a classifier such as FaCT [12] or Racer =-=[10]-=-. 1 In tandem with RuleML/LP, we also focus on the (positive) Horn subset of FOL, which is closely related to the positive Horn subset of LP.sLogic programming systems such as XSB [16], however, can a... |

140 |
Attributive concept descriptions with complements
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- 1991
(Show Context)
Citation Context ...⊤⊑∀P − .C ⊤⊑∀hasParent − .Human itype C i : C john : Man i1 Pi2 〈i1,i2〉 : P 〈john, peter〉 : hasParent (∆ I ×∆ I ). Compound class expressions are interpreted according to =-=the following equations (see [21]) ⊤ I =∆ I (C ⊓ D) I = C I ∩ D I ⊥ I = -=-∅ (C ⊔ D) I = C I ∪ D I ¬C I =∆ I \ C I {i} I = {i I } (∀R.C) I = {x ∈ ∆ I |∀y(x, y) ∈ R I ⇒ y ∈ C I } (∃R.C) I = {x ∈ ∆ I |∃y(x, y) ∈ R I ∧ y ∈ C I } (� nR.C) I... |

124 | On the restraining power of guards
- GRÄDEL
(Show Context)
Citation Context ...irected graph. This requirement severely restricts the way variables and quantifiers can be used. In particular, quantifiers must be relativized via atomic formulae (as in the guarded fragment of FOL =-=[11]),-=- i.e., the quantified variable must occur in a property predicate along with the free variable (recall that DL classes correspond to formulae with one free variable). For example, the DL class ∃P.C ... |

119 | Magic templates: A spellbinding approach to logic programs
- Ramakrishnan
- 1988
(Show Context)
Citation Context ...x, y) ∧ P (y, z). The usual strategy to compute the remaining forms of recursive rules in relational databases is in-memory processing using some iterative strategy, e.g. the magic template procedur=-=e [15]-=-. Indirect Recursion. The remaining cases of non-linear recursion that cannot be rewritten into the SQL:99 constructs are mainly represented by the possibility of having cyclical class and property hi... |

114 | Representing Agent Contracts with Exceptions using
- Grosof, Poon
- 2002
(Show Context)
Citation Context ...Semantic Web Services techniques and to explore their application scenarios include: the DAML-Services effort (DAML-S) 6 , the Web Service Modeling Framework effort (WSMF) 7 , SweetDeal e-contracting =-=[13, 19, 14]-=-, and ECOIN financial knowledge integration [9, 10]. Both the DAML-S and SweetDeal efforts have specifically identified combining rules with ontologies as an important requirement. DAML-S began with D... |

112 |
Why is modal logic so robustly decidable
- Vardi
- 1997
(Show Context)
Citation Context ...subset of DL and def-Horn for which a complete mapping can be defined. DLs are decidable subsets of FOL where the decidability is due in large part to their having (a form of) the tree model property =-=[22]-=-. 15 This property says that a DL class C has a model (an interpretation I in which C I in non-empty) iff C has a tree-shaped model, i.e., one in which the interpretation of properties defines a tree ... |

101 |
Foundations of Logic Programming. Second, extended edition
- Lloyd
- 1987
(Show Context)
Citation Context ... the r.h.s. of a subclass axiom, it becomes conjunction in the head of the corresponding rule: C ⊑ D1 ⊓ D2 ≡ D1(x) ∧ D2(x) ← C(x), This is then easily transformed (via the Lloyd-Topor transf=-=ormations [18]) into a-=- pair of def-Horn rules: Disjunction (DL ⊔) D1(x) ← C(x) D2(x) ← C(x) A DL class can be formed from a disjunction of existing classes, e.g., C ⊔ D. From Figure 5 it can be seen that this corre... |

87 |
Linear time algorithm for testing the satisfiability of propositional horn formula
- Dowling, Gallier
- 1984
(Show Context)
Citation Context ... being expressively extensible in directions that FOL is not, as discussed earlier). For the propositional case of def-LP, exhaustive inferencing is O(n) where n = |RP| — i.e., worst-case linear tim=-=e [8]-=-. For the general case with logical variables, the entire conclusion set of a def-LP RP can be computed in time O(n v+1 ), when there is a constant bound v on the number of logical variables per rule ... |

72 | A declarative approach to business rules in contracts: Courteous logic programs
- Grosof, Labrou, et al.
- 1999
(Show Context)
Citation Context ...Semantic Web Services techniques and to explore their application scenarios include: the DAML-Services effort (DAML-S) 6 , the Web Service Modeling Framework effort (WSMF) 7 , SweetDeal e-contracting =-=[13, 19, 14]-=-, and ECOIN financial knowledge integration [9, 10]. Both the DAML-S and SweetDeal efforts have specifically identified combining rules with ontologies as an important requirement. DAML-S began with D... |

56 | How to decide query containment under constraints using a description logic
- Horrocks, Sattler, et al.
- 2000
(Show Context)
Citation Context ... restriction in DLs is that only unary and binary predicates can usually be captured. 16 This is a less onerous restriction, however, as techniques for reifying higher arity predicates are well known =-=[16]-=-. Definite Horn FOL requires that all variables are universally quantified (at the outer level of the rule), and restricts logical connectives in certain ways. One obvious consequence of the restricti... |

45 | Automated negotiation from declarative contract descriptions
- Reeves, Wellman, et al.
- 2000
(Show Context)
Citation Context ...Semantic Web Services techniques and to explore their application scenarios include: the DAML-Services effort (DAML-S) 6 , the Web Service Modeling Framework effort (WSMF) 7 , SweetDeal e-contracting =-=[13, 19, 14]-=-, and ECOIN financial knowledge integration [9, 10]. Both the DAML-S and SweetDeal efforts have specifically identified combining rules with ontologies as an important requirement. DAML-S began with D... |

26 | Knowledge Integration to overcome Ontological Heterogeneity: Challenges from Financial Information Systems
- Firat, S, et al.
- 2002
(Show Context)
Citation Context ...plication scenarios include: the DAML-Services effort (DAML-S) 6 , the Web Service Modeling Framework effort (WSMF) 7 , SweetDeal e-contracting [13, 19, 14], and ECOIN financial knowledge integration =-=[9, 10]-=-. Both the DAML-S and SweetDeal efforts have specifically identified combining rules with ontologies as an important requirement. DAML-S began with DAML+OIL as its main tool for describing services. D... |

22 | Representing E-Business Rules for the Semantic Web: Situated Courteous Logic Programs in RuleML
- Grosof
- 2001
(Show Context)
Citation Context ...ial case of a rule. A relational database, including its queries, can be viewed as a rulebase. 3 Rule Markup Language Initiativehttp://www.ruleml.org and http://ebusiness.mit.edu/bgrosof/#RuleML; see =-=[12]-=- for a relatively recent overview paper.sFocus KRs: As an ontology language, we focus on DAML+OIL; this is based on the particular KR known as Description Logic (DL) 4 , and is the point of departure ... |

20 |
OWL Web Ontology Language 1.0 reference
- Connolly, Dean, et al.
- 2002
(Show Context)
Citation Context ...formally specified/defined vocabulary. Copyright is held by the author/owner(s). . 1 Ian Horrocks University of Manchester Manchester, UK http://www.cs.man.ac.uk/˜horrocks horrocks@cs.man.ac.uk (OWL)=-= [6]-=- and for SW rules 2 (RuleML). 3 We then develop a semantics for combining such rules with such ontologies, based on a translation between their respective KRs. This semantics exploits correspondences ... |

19 | Financial Information Integration in the Presence of Equational Ontological Conflicts
- Firat, Madnick, et al.
- 2002
(Show Context)
Citation Context ...plication scenarios include: the DAML-Services effort (DAML-S) 6 , the Web Service Modeling Framework effort (WSMF) 7 , SweetDeal e-contracting [13, 19, 14], and ECOIN financial knowledge integration =-=[9, 10]-=-. Both the DAML-S and SweetDeal efforts have specifically identified combining rules with ontologies as an important requirement. DAML-S began with DAML+OIL as its main tool for describing services. D... |