## Typed Hybrid Description Logic Programs with Order-Sorted Semantic Web Type Systems based on (2006)

Venue: | University Munich |

Citations: | 13 - 6 self |

### BibTeX

@TECHREPORT{Paschke06typedhybrid,

author = {Adrian Paschke},

title = {Typed Hybrid Description Logic Programs with Order-Sorted Semantic Web Type Systems based on},

institution = {University Munich},

year = {2006}

}

### OpenURL

### Abstract

Abstract. In the recent years rule-based programming in terms of declarative logic programming has formed the basis for many Artificial Intelligence (AI) applications and is well integrated in the mainstream information technology capturing higher-level decision logics. Typically, the standard rule systems and rule-based logic programming languages such as Prolog derivatives are based on the untyped theory of predicate calculus with untyped logical objects (untyped terms), i.e. the logical reasoning algorithms apply pure syntactical reasoning. From a rule engineering perspective this is a serious restriction which lacks major Software Engineering principles such as data abstraction or modularization, which become more and more important when rule applications grow larger and more complex. To support such principles in logic programming and capture the rule engineer’s intended meaning of a logic program, types and typed objects play an important role. Moreover, from a computational point of view, the use of types drastically reduces the search space, i.e. proofs can be kept at a more abstract level and it offers the option to restrict the application of rules and to

### Citations

936 | A theory of type polymorphism in progra.mming
- Milner
- 1978
(Show Context)
Citation Context ...d to different programming languages such as object-oriented or declarative logic programming languages. Based on this theory one of the most well-known type systems is the Hindley-Milner type system =-=[Mil78]-=-. Different forms of type declarations have been proposed such as declarations which use a rather general constraint language [HS88], logical formulas [Xu188,Nai92], regular sets [Mis84,Mis85,HJ92,DZ9... |

642 | The Description Logic Handbook. Theory, Implementation and Applications - Baader, Calvanese, et al. - 2003 |

476 |
RDF Vocabulary Description Language 1.0
- Brickley, Guha, et al.
(Show Context)
Citation Context ...eans of abstract interpretations [Lu98] or constraint solving techniques [Dem99]. 3 Description Logic Type System Until recently, the use of Semantic Web ontology languages such as OWL [MH04] or RDFS =-=[BG04]-=- has been limited primarily to define meta data vocabularies and add semantic machine-readable meta data to Web pages enabling automated processing of Web contents. Both, Description Logics [NBB + 02]... |

400 | Description Logic Programs: Combining Logic Programs with Description Logic
- Grosof, Horrocks, et al.
- 2003
(Show Context)
Citation Context ...ed LPs [15] and Datalog DL [16]. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneous framework sharing the combined language symbols are e.g. DLP =-=[7]-=-, KAON2 [10] or SWRL [9]. Both integration approaches have pros and cons and different integration strategies such as reductions, SLD resolution extensions or fixpoint iterations are applied with diff... |

375 | Uniform proofs as a foundation for logic programming - Miller, Nadathur, et al. - 1991 |

371 |
SWRL: A Semantic Web Rule Language Combining OWL and RuleML", W3C Member Submission
- Horrocks, Patel-Schneider, et al.
- 2004
(Show Context)
Citation Context ...DL [16]. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneous framework sharing the combined language symbols are e.g. DLP [7], KAON2 [10] or SWRL =-=[9]-=-. Both integration approaches have pros and cons and different integration strategies such as reductions, SLD resolution extensions or fixpoint iterations are applied with different restrictions to en... |

361 |
Y.: A guide to completeness and complexity for modal logics of knowledge and belief
- Halpern, Moses
- 1992
(Show Context)
Citation Context ...er decidable DLs reaching from ALC which corresponds to the fragment of FOL obtained by restricting the syntax to formulas containing only two variables (closely related to the multi-modal language K =-=[14]-=-) up to SHIQ (i.e. ALCR+) extended with property hierarchies (H), inverse roles (I) and qualified number restriction (Q)), which is in EXPTIME and SHOIN(D) with nominals and unqualified number restric... |

332 | An efficient unification algorithm
- Martelli, Montanari
- 1982
(Show Context)
Citation Context ...unifier ι such that θ = σ ∗ ι. For a survey on unification theory see, e.g. [BS01,Sie89]. In the following I first define the rules for untyped unification in terms of equationsolving transformations =-=[MM82]-=- for elimination (E), decomposition (D), variable binding (B) and orientation (O). The judgements beneath the horizontal line is the conclusion of the rule and the judgements below the line are the pr... |

273 | An Initial Algebra Approach to the Specification, Correctness and Implementation of Abstract Data Types - Goguen, Thatcher, et al. - 1978 |

255 |
The Gödel Programming Language
- Hill, Lloyd
- 1994
(Show Context)
Citation Context ...t change the semantics of the pure Prolog program. Dietrich and Hagl’s [Die88] extend this approach with input/output mode declarations and subsorts. In contrast, prescriptive type systems, e.g. Gdel =-=[HL94]-=-, Typed Prolog [Lak91], λ-Prolog [Mil86,MNFS91], consider types as properties of the formulas one wants to give a meaning to, i.e. they use a typed logic for programming leading to languages with high... |

224 | Query answering for OWL-DL with rules
- Motik, Sattler, et al.
- 2005
(Show Context)
Citation Context ...brid KBs [Ric05]. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneous framework sharing the combined language symbols are e.g. DLP [Gro03], KAON2 =-=[MSS05]-=- or SWRL [HPSB + 04]. Both integration approaches have pros and cons and different integration strategies such as reductions or fixpoint iterations are applied with different restrictions to ensure de... |

215 | W.: Unification Theory - Baader, Snyder - 1999 |

204 | Combining answer set programming with description logics for the semantic web
- Eiter, Lukasiewicz, et al.
- 2004
(Show Context)
Citation Context ...eterogeneous approaches, which hybridly use DL reasoning techniques and tools in combination with rule languages and rule/LP engines are e.g. CARIN [2], Life [3], Al-log [4], non-monotonic dlprograms =-=[5]-=-, r-hybrid KBs [6], hybrid DL-typed LPs [15] and Datalog DL [16]. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneous framework sharing the combin... |

156 |
Fundamental concepts in programming languages
- Strachey
- 1967
(Show Context)
Citation Context ... language [Mil78]), adhoc polymorphism or parametric polymorphism haven been introduced into logic programming. For a discussion of the differences between parametric and ad-hoc polymorphism see e.g. =-=[Str00]-=-. In the context of polymorphism terms (variables) are authorized to change their types dynamically at runtime, which makes static compile-time analysis insufficient in general. If the type system per... |

144 | L-log: Integrating Datalog and description logics
- Donini, Lenzerini, et al.
- 1998
(Show Context)
Citation Context ...pthon language [1] among the heterogeneous approaches, which hybridly use DL reasoning techniques and tools in combination with rule languages and rule/LP engines are e.g. CARIN [2], Life [3], Al-log =-=[4]-=-, non-monotonic dlprograms [5], r-hybrid KBs [6], hybrid DL-typed LPs [15] and Datalog DL [16]. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneou... |

142 | Mahr: Fundamentals of Algebraic Specifications 1: Equations and Initial Semantics - Ehrig, B - 1985 |

140 |
A Polymorphic Type System For Prolog
- Mycroft, O'Keefe
- 1984
(Show Context)
Citation Context ... the meaning of logic programs. These descriptive approaches are seeking to approximate the structure of a program for use by an optimizing compiler at compile time. For instance, Mycroft and O’Keefe =-=[MO84]-=- demonstrated that the polymorphic type discipline of Milner [Mil78] can be represented in pure Prolog, where the type declarations for variables occur outside of the clauses and do not change the sem... |

123 | Towards a meaning of LIFE
- Ait-Kaci, Podelski
- 1991
(Show Context)
Citation Context ...he early Krypthon language [1] among the heterogeneous approaches, which hybridly use DL reasoning techniques and tools in combination with rule languages and rule/LP engines are e.g. CARIN [2], Life =-=[3]-=-, Al-log [4], non-monotonic dlprograms [5], r-hybrid KBs [6], hybrid DL-typed LPs [15] and Datalog DL [16]. Among the homogeneous approaches which combine the rule component and the DL component in on... |

108 | Unification theory - Siekmann - 1989 |

97 | CARIN: A Representation Language Combining Horn Rules and Description Logics
- Levy, Rousset
- 1996
(Show Context)
Citation Context ...ing from the early Krypthon language [1] among the heterogeneous approaches, which hybridly use DL reasoning techniques and tools in combination with rule languages and rule/LP engines are e.g. CARIN =-=[2]-=-, Life [3], Al-log [4], non-monotonic dlprograms [5], r-hybrid KBs [6], hybrid DL-typed LPs [15] and Datalog DL [16]. Among the homogeneous approaches which combine the rule component and the DL compo... |

84 | The expressive powers of logic programming semantics
- Schlipf
- 1995
(Show Context)
Citation Context ...eral r.e.-complete much better complexity results can be achieved. In our reference implementation we compute well-founded semantics for normal LPs which has been proven to be ∏1 1-complete (see e.g. =-=[12]-=-). The general untyped unification problem in logic programming is P-complete under logspace reductions and P-hardness was proven e.g. by [13]. We, have optimized the basic untyped unification algorit... |

83 | Definite relations over constraint languages - Hohfeld, Smolka - 1988 |

74 | An essential hybrid reasoning system: knowledge and symbol level accounts of KRYPTON
- Brachman, Pigman, et al.
- 1985
(Show Context)
Citation Context ...ations. Both have pros and cons and the question wether the Semantic Web should adopt a homogeneous or heterogenous view is still very much at the beginning. Starting from the early Krypthon language =-=[1]-=- among the heterogeneous approaches, which hybridly use DL reasoning techniques and tools in combination with rule languages and rule/LP engines are e.g. CARIN [2], Life [3], Al-log [4], non-monotonic... |

61 |
On the sequential nature of unification
- Dwork, Kanellakis, et al.
- 1984
(Show Context)
Citation Context ...l LPs which has been proven to be ∏1 1-complete (see e.g. [12]). The general untyped unification problem in logic programming is P-complete under logspace reductions and P-hardness was proven e.g. by =-=[13]-=-. We, have optimized the basic untyped unification algorithm to almost linear time [19]. We allow the DL languages which are used to describe the order-sorted type hierarchies to range over decidable ... |

58 | Logic Programming over Polymorphically Order-Sorted Types - Smolka - 1989 |

51 |
Web Ontology Language
- Antoniou, Harmelen
- 2003
(Show Context)
Citation Context ...ypes, e.g. by means of abstract interpretations [Lu98] or constraint solving techniques [Dem99]. 3 Description Logic Type System Until recently, the use of Semantic Web ontology languages such as OWL =-=[MH04]-=- or RDFS [BG04] has been limited primarily to define meta data vocabularies and add semantic machine-readable meta data to Web pages enabling automated processing of Web contents. Both, Description Lo... |

51 | A many-sorted calculus based on resolution and paramodulation - Walther - 1987 |

43 |
Dependent types in logic programming
- Pfenning
- 1992
(Show Context)
Citation Context ...88], logical formulas [Xu188,Nai92], regular sets [Mis84,Mis85,HJ92,DZ92,AE93], equational specifications [Han92] or typed terms over a order-sorted structure [MO84,Lak91,SNGM9b,HT92,Han91] (see e.g. =-=[Pfe92]-=- for an overview). In general, the works can be classified into two different views on types in logic programming, namely descriptive types and prescriptive types [Red88] (a.k.a. explicit and implicit... |

36 | clause programs with polymorphic types: semantics and resolution - Horn - 1991 |

26 | Schubert’s steamroller problem: formulations and solutions - Stickel - 1986 |

25 |
The OO jDREW Reference Implementation of RuleML
- Ball, Boley, et al.
- 2005
(Show Context)
Citation Context ...DL-typing are AL-Log [4] and closely related Datalog-DL [16], which use the DL terminological models to define hybrid procedural type functions in constraint clauses and OO-RuleML [17] resp. OO-jDrew =-=[18]-=-, which use RDFS to define external order-sorted type systems. These systems adopt a descriptive typing approach where types are included as extra DL functions which make hybrid calls on the external ... |

22 |
Untersuchungen zur mehrsortigen Quantorenlogik”, Mathematische Annalen
- Oberschelp
(Show Context)
Citation Context ...g polymorphism for untyped variables which asContractLog: A DL-Typed Logic Programming Language 5 sume the type of a unified typed term at runtime. A first order-sorted logic was given by Oberschelp =-=[Obe62]-=- and an order-sorted algebra was developed by Goguen et. al. [GM87,Smo89] which forms the basis for the language Eqlog [GM86]. An extended order-sorted algebra with error-handling was proposed by Gogo... |

22 | Object-Oriented RuleML: User-Level Roles, URIGrounded Clauses, and Order-Sorted Terms
- Boley
- 2003
(Show Context)
Citation Context ...ch directly address DL-typing are AL-Log [4] and closely related Datalog-DL [16], which use the DL terminological models to define hybrid procedural type functions in constraint clauses and OO-RuleML =-=[17]-=- resp. OO-jDrew [18], which use RDFS to define external order-sorted type systems. These systems adopt a descriptive typing approach where types are included as extra DL functions which make hybrid ca... |

20 | A hybrid system with datalog and concept languages
- Donini, Lenzerini, et al.
- 1991
(Show Context)
Citation Context ...guage [Bra85] among the heterogeneous approaches, which hybridly use DL reasoning techniques and tools in combination with rule languages and rule engines are e.g. CARIN [Lev96], Life [Ait91], Al-log =-=[DLNS91]-=-, non-monotonic dl-programs [Eit04] and r-hybrid KBs [Ric05]. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneous framework sharing the combined l... |

18 | Implementing polymorphic typing in a logic programming language
- Kwon, Nadathur, et al.
- 1994
(Show Context)
Citation Context ... the bindings of variables, but also their types. Typed unification has been studied for order-sorted and polymorphic type systems, see e.g. Typed Prolog [Lak91], Protos-L [BB89], λ-Prolog extensions =-=[KNW93]-=-. Order-sorted unification extends the usual term unification with additional dynamic type checking. In a nutshell, the basic idea of sorted unification of two typed variables is to find the greatest ... |

17 | Type Systems. The Computer Science and Engineering Handbook - Cardelli - 1997 |

13 | Efficient run-time type checking of typed logic programs - Dart, Zobel - 1992 |

12 | Polymorphic type analysis in logic programs by abstract interpretation
- Lu
- 1998
(Show Context)
Citation Context ...orks on types for LPs have concentrated on implementation techniques for efficiently checking or inferring types at runtime, in particular polymorphic types, e.g. by means of abstract interpretations =-=[Lu98]-=- or constraint solving techniques [Dem99]. 3 Description Logic Type System Until recently, the use of Semantic Web ontology languages such as OWL [MH04] or RDFS [BG04] has been limited primarily to de... |

12 | The Description Logic Handbook: Theory, Implementation, and Applications - Patel-Schneider - 2003 |

7 | Order-sorted algebra I: Partial and overloaded operators, errors and inheritance - Goguen, Meseguer - 1987 |

7 | Owl web ontology language, http://www.w3.org/tr/owl-features/, 2004. A DL-Typed Logic Programming Language 25 - McGuinness, Harmelen - 1978 |

5 |
Datalog-DL: Datalog Rules Parameterized by Description Logics
- Mei, Boley, et al.
- 2006
(Show Context)
Citation Context ...ques and tools in combination with rule languages and rule/LP engines are e.g. CARIN [2], Life [3], Al-log [4], non-monotonic dlprograms [5], r-hybrid KBs [6], hybrid DL-typed LPs [15] and Datalog DL =-=[16]-=-. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneous framework sharing the combined language symbols are e.g. DLP [7], KAON2 [10] or SWRL [9]. Bo... |

3 |
Ã?ber partiell geordnete Sortenmengen und deren Anwendung zur Fehlerbehandlung in abstrakten Datentypen
- Gogolla
- 1986
(Show Context)
Citation Context ... an order-sorted algebra was developed by Goguen et. al. [GM87,Smo89] which forms the basis for the language Eqlog [GM86]. An extended order-sorted algebra with error-handling was proposed by Gogolla =-=[Gog86]-=-. Several other order-sorted approaches have been described using order-sorted unification [Wal87,Hub87]. Different forms of polymorphism such as generic polymorphism (see e.g. ML programming language... |

2 |
PROTOS-L: Towards a knowledge base programming language
- Beierle, BÃttcher
- 1989
(Show Context)
Citation Context ... to queries not only display the bindings of variables, but also their types. Typed unification has been studied for order-sorted and polymorphic type systems, see e.g. Typed Prolog [Lak91], Protos-L =-=[BB89]-=-, λ-Prolog extensions [KNW93]. Order-sorted unification extends the usual term unification with additional dynamic type checking. In a nutshell, the basic idea of sorted unification of two typed varia... |

2 |
Types in Logic Programming, chapter Types and the Intended Meaning of Logic Programs
- Naish
- 1992
(Show Context)
Citation Context ...e of the logical functions and their arguments in a logic program. It has been demonstrated that types play an important role to capture the programmer’s intended meaning of a logic program, see e.g. =-=[Nai92]-=- and that they can be used to dramatically reduce the rule search space - see e.g. Schubert’s Steamroller Problem which used to illustrate this advantage [Sti86]. The theory of types in LP has been st... |

2 |
On the decidability and complexity of integrating ontologies and rules
- Riccardo
(Show Context)
Citation Context ...dly use DL reasoning techniques and tools in combination with rule languages and rule engines are e.g. CARIN [Lev96], Life [Ait91], Al-log [DLNS91], non-monotonic dl-programs [Eit04] and r-hybrid KBs =-=[Ric05]-=-. Among the homogeneous approaches which combine the rule component and the DL component in one homogeneous framework sharing the combined language symbols are e.g. DLP [Gro03], KAON2 [MSS05] or SWRL ... |

2 |
The ContractLog Inference Engine: A configurable inference service for logic programming with linear resolution, goal memoization, loop prevention, and hybrid Semantic Web typed unification supporting selectable SLDNF related and well-founded semantics
- unknown authors
(Show Context)
Citation Context ...ification problem in logic programming is P-complete under logspace reductions and P-hardness was proven e.g. by [13]. We, have optimized the basic untyped unification algorithm to almost linear time =-=[19]-=-. We allow the DL languages which are used to describe the order-sorted type hierarchies to range over decidable DLs reaching from ALC which corresponds to the fragment of FOL obtained by restricting ... |

1 |
An essential hybrid reasoning system: Knowledge and symbol level accounts for krypton
- orgtrrdf-schema
- 1985
(Show Context)
Citation Context ...osed recently. The works on combining rules and ontologies can be basically classified into two basic approaches: homogeneous and heterogeneous integrations. Starting from the early Krypthon language =-=[Bra85]-=- among the heterogeneous approaches, which hybridly use DL reasoning techniques and tools in combination with rule languages and rule engines are e.g. CARIN [Lev96], Life [Ait91], Al-log [DLNS91], non... |

1 |
Type Systems. The Computer Science and Engineering Handbook
- Press
- 1997
(Show Context)
Citation Context ...the ContractLog approach towards a hybrid DL-typed logic. Finally, I will conclude this paper with a short summary in section 7. 2 Types in Logic Programming Definition 1. (Type System) A type system =-=[Car97]-=- is responsible for assigning types to variables and expressions. It uses the type expressions for static type checking at compile time and/or dynamic type checking at runtime. Type systems typically ... |

1 | Types in Logic Programming, chapter A Regular Type Language for Logic Programs - Dart, Zobel - 1992 |