Tableau Algorithms for Description Logics

Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system KL-ONE. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of description logics can be decided using tableau-like algorithms. This is not very surprising since description logics have turned out to be closely related to propositional modal logics and logics of programs (such as propositional dynamic logic), for which tableau procedures have been quite successful.

[1]  Francesco M. Donini,et al.  Decidable Reasoning in Terminological Knowledge Representation Systems , 1993, IJCAI.

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

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

[4]  M. de Rijke,et al.  Counting objects in generalized quantifier theory, modal logic and knowledge representation , 1992 .

[5]  Stephan Tobies A PSpace Algorithm for Graded Modal Logic , 1999, CADE.

[6]  Manfred Schmidt-Schauß,et al.  Subsumption in KL-ONE is Undecidable , 1989, KR.

[7]  Maarten de Rijke,et al.  Counting Objects , 1995, J. Log. Comput..

[8]  Peter F. Patel-Schneider,et al.  A Semantics and Complete Algorithm for Subsumption in the CLASSIC Description Logic , 1993, J. Artif. Intell. Res..

[9]  Bernhard Nebel,et al.  Reasoning and Revision in Hybrid Representation Systems , 1990, Lecture Notes in Computer Science.

[10]  Ulrike Sattler,et al.  A Concept Language Extended with Different Kinds of Transitive Roles , 1996, KI.

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

[12]  Hector J. Levesque,et al.  The Tractability of Subsumption in Frame-Based Description Languages , 1984, AAAI.

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

[14]  Ian Horrocks The FaCT System , 1998, TABLEAUX.

[15]  Franz Baader,et al.  A Terminological Knowledge Representation System with Complete Inference Algorithms , 1991, PDK.

[16]  Robert M. MacGregor,et al.  The Evolving Technology of Classification-Based Knowledge Representation Systems , 1991, Principles of Semantic Networks.

[17]  Werner Nutt,et al.  Tractable Concept Languages , 1991, IJCAI.

[18]  Edith Spaan The Complexity of Propositional Tense Logics , 1993 .

[19]  Jaime G. Carbonell,et al.  Automated Deduction — CADE-16 , 2002, Lecture Notes in Computer Science.

[20]  Fabio Grandi,et al.  On Expressive Number Restrictions in Description Logics , 2001, Description Logics.

[21]  Christof Peltason The BACK system—an overview , 1991, SGAR.

[22]  Franz Baader Augmenting Concept Languages by Transitive Closure of Roles: An Alternative to Terminological Cycles , 1991, IJCAI.

[23]  Bernhard Nebel,et al.  Terminological Reasoning is Inherently Intractable , 1990, Artif. Intell..

[24]  Ronald J. Brachman,et al.  An Overview of the KL-ONE Knowledge Representation System , 1985, Cogn. Sci..

[25]  W. Nutt,et al.  Subsumption algorithms for concept languages , 1990 .

[26]  Werner Nutt,et al.  The Complexity of Concept Languages , 1997, KR.

[27]  Carsten Lutz,et al.  Complexity of Terminological Reasoning Revisited , 1999, LPAR.

[28]  Bernhard Hollunder,et al.  Subsumption Algorithms for Concept Description Languages , 1990, ECAI.

[29]  Bernhard Nebel,et al.  An Empirical Analysis of Optimization Techniques for Terminological Representation Systems, or Making KRIS Get a Move On , 1992, KR.

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

[31]  Eric Mays,et al.  K-Rep system overview , 1991, SGAR.

[32]  Francesco M. Donini,et al.  Decidable reasoning in terminological knowledge representation systems , 1993 .

[33]  Klaus Schild,et al.  A Correspondence Theory for Terminological Logics: Preliminary Report , 1991, IJCAI.

[34]  Bernhard Nebel,et al.  Terminological Cycles: Semantics and Computational Properties , 1991, Principles of Semantic Networks.

[35]  Maurizio Lenzerini,et al.  Concept Language with Number Restrictions and Fixpoints, and its Relationship with Mu-calculus , 1994, ECAI.

[36]  Maurizio Lenzerini,et al.  TBox and ABox Reasoning in Expressive Description Logics , 1996, KR.

[37]  Manfred Schmidt-Schaubß,et al.  Subsumption in KL-ONE is undecidable , 1989, KR 1989.

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

[39]  Frank Pfenning,et al.  Logic Programming and Automated Reasoning , 1994, Lecture Notes in Computer Science.

[40]  Roy Dyckhoff Automated Reasoning with Analytic Tableaux and Related Methods , 2000, Lecture Notes in Computer Science.

[41]  Giuseppe De Giacomo,et al.  Tableaux and Algorithms for Propositional Dynamic Logic with Converse , 1996, CADE.

[42]  Sergio Tessaris,et al.  Implementing and Testing Expressive Description Logics: a Preliminary Report , 1995 .

[43]  Peter F. Patel-Schneider,et al.  The CLASSIC knowledge representation system: guiding principles and implementation rationale , 1991, SGAR.

[44]  John Haugeland Mind design , 1985 .

[45]  Michael M. Richter,et al.  Processing Declarative Knowledge , 1991, Lecture Notes in Computer Science.

[46]  Franz Baader,et al.  Cardinality Restrictions on Concepts , 1994, KI.

[47]  Werner Nutt,et al.  On the expressivity of feature logics with negation, functional uncertainty, and sort equations , 1993, J. Log. Lang. Inf..

[48]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

[49]  Werner Nutt,et al.  The Complexity of Existential Quantification in Concept Languages , 1992, Artif. Intell..

[50]  Bernhard Hollunder Hybrid Inferences in KL-ONE-Based Knowledge Representation Systems , 1990, GWAI.

[51]  Klaus Schild,et al.  Terminological Cycles and the Propositional µ-Calculus , 1994, KR.

[52]  Peter F. Patel-Schneider,et al.  "Reducing" CLASSIC to Practice: Knowledge Representation Theory Meets Reality , 1999, Artif. Intell..

[53]  M R Quillian,et al.  Word concepts: a theory and simulation of some basic semantic capabilities. , 1967, Behavioral science.

[54]  M. de Rijke,et al.  Diamonds and Defaults , 1993 .

[55]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

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

[57]  Günther Görz,et al.  KI-96: Advances in Artificial Intelligence , 1996, Lecture Notes in Computer Science.

[58]  Philipp Hanschke,et al.  Specifying Role Interaction in Concept Languages , 1992, KR.

[59]  Maurizio Lenzerini,et al.  Boosting the Correspondence between Description Logics and Propositional Dynamic Logics , 1994, AAAI.