Description Logics with Concrete Domains and Functional Dependencies

Description Logics (DLs) with concrete domains are a useful tool in many applications. To further enhance the expressive power of such DLs, it has been proposed to add database-style key constraints. Up to now, however, only uniqueness constraints have been considered in this context, thus neglecting the second fundamental family of key constraints: functional dependencies. In this paper, we consider the basic DL with concrete domains ALC(D), extend it with functional dependencies, and analyze the impact of this extension on the decidability and complexity of reasoning. Though intuitively the expressivity of functional dependencies seems weaker than that of uniqueness constraints, we are able to show that the former have a similarly severe impact on the computational properties: reasoning is undecidable in the general case, and NEXPTIME-complete in some slightly restricted variants of our logic.

[1]  Carsten Lutz,et al.  Description Logics with Concrete Domains-A Survey , 2002, Advances in Modal Logic.

[2]  Ian Horrocks,et al.  Description Logics as Ontology Languages for the Semantic Web , 2005, Mechanizing Mathematical Reasoning.

[3]  Maja Mili,et al.  Description Logics with Concrete Domains and Functional Dependencies by Maja Miličić , 2019 .

[4]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[5]  Franz Baader,et al.  A Scheme for Integrating Concrete Domains into Concept Languages , 1991, IJCAI.

[6]  Ian Horrocks,et al.  Keys, Nominals, and Concrete Domains , 2003, IJCAI.

[7]  H. Chertkow,et al.  Semantic memory , 2002, Current neurology and neuroscience reports.

[8]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[9]  Yuri Gurevich,et al.  The Classical Decision Problem , 1997, Perspectives in Mathematical Logic.

[10]  Volker Haarslev,et al.  RACER System Description , 2001, IJCAR.

[11]  Emil L. Post.  A variant of a recursively unsolvable problem , 1946 .

[12]  Franz Baader,et al.  Qualifying Number Restrictions in Concept Languages , 1991, KR.

[13]  Ian Horrocks,et al.  Optimizing Description Logic Subsumption , 1999, J. Log. Comput..

[14]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[15]  Frank van Harmelen,et al.  Reviewing the design of DAML+OIL: an ontology language for the semantic web , 2002, AAAI/IAAI.

[16]  Marvin Minsky,et al.  A framework for representing knowledge" in the psychology of computer vision , 1975 .

[17]  Diego Calvanese,et al.  Identification Constraints and Functional Dependencies in Description Logics , 2001, IJCAI.

[18]  Carsten Lutz,et al.  Reasoning about Entity Relationship Diagrams with Complex Attribute Dependencies , 2002, Description Logics.

[19]  Franz Baader,et al.  An Overview of Tableau Algorithms for Description Logics , 2001, Stud Logica.

[20]  Ian Horrocks,et al.  Using an Expressive Description Logic: FaCT or Fiction? , 1998, KR.

[21]  J. Davenport.  Editor , 1960 .

[22]  Maarten Marx,et al.  A Road-Map on Complexity for Hybrid Logics , 1999, CSL.

[23]  Diego Calvanese,et al.  Description Logics for Conceptual Data Modeling , 1998, Logics for Databases and Information Systems.

[24]  David Toman,et al.  On Decidability and Complexity of Description Logics with Uniqueness Constraints , 2001, Description Logics.

[25]  David Toman,et al.  On Reasoning about Structural Equality in XML: A Description Logic Approach , 2003, ICDT.

[26]  Carsten Lutz,et al.  NEXP TIME-complete description logics with concrete domains , 2004, TOCL.

[27]  Ian Horrocks,et al.  A Description Logic with Transitive and Inverse Roles and Role Hierarchies , 1999, J. Log. Comput..

[28]  C. Lutz.  The Complexity of Reasoning with Concrete Domains , 1999 .

[29]  Carsten Lutz.  NEXPTIME-Complete Description Logics with Concrete Domains , 2001, IJCAR.

[30]  Ian Horrocks,et al.  Practical Reasoning for Expressive Description Logics , 1999, LPAR.

[31]  Ulrike Sattler,et al.  The Complexity of Reasoning with Boolean Modal Logics , 2000, Advances in Modal Logic.

[32]  Carsten Lutz,et al.  PSpace Reasoning with the Description Logic ALCF(D) , 2002, Logic Journal of the IGPL.

[33]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[34]  Marvin Minsky,et al.  A framework for representing knowledge , 1974 .

[35]  Alexander Borgida,et al.  Adding Uniqueness Constraints to Description Logics (Preliminary Report) , 1997, DOOD.