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Using tableau to decide description logics with full role negation and identity

Authors:

Renate A. Schmidt,

Dmitry TishkovskyAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 15, Issue 1

Article No.: 7, Pages 1 - 31

https://doi.org/10.1145/2559947

Published: 06 March 2014 Publication History

Abstract

This article presents a tableau approach for deciding expressive description logics with full role negation and role identity. We consider the description logic ALBO^id, which is ALC extended with the Boolean role operators, inverse of roles, the identity role, and includes full support for individuals and singleton concepts. ALBO^id is expressively equivalent to the two-variable fragment of first-order logic with equality and subsumes Boolean modal logic. In this article, we define a sound, complete, and terminating tableau calculus for ALBO^id that provides the basis for decision procedures for this logic and all its sublogics. An important novelty of our approach is the use of a generic unrestricted blocking mechanism. Unrestricted blocking is based on equality reasoning and a conceptually simple rule, which performs case distinctions over the identity of individuals. The blocking mechanism ties the proof of termination of tableau derivations to the finite model property of ALBO^id.

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Cited By

Hustadt UPapacchini FNalon CDixon C(2024)Model Construction for Modal ClausesAutomated Reasoning10.1007/978-3-031-63501-4_1(3-23)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_1
Li JWu XLu CDeng WZhao Y(2021)Computing Views of OWL Ontologies for the Semantic WebProceedings of the Web Conference 202110.1145/3442381.3449881(2624-2635)Online publication date: 19-Apr-2021
https://dl.acm.org/doi/10.1145/3442381.3449881
Baumgartner PSchmidt R(2019)Blocking and Other Enhancements for Bottom-Up Model Generation MethodsJournal of Automated Reasoning10.1007/s10817-019-09515-1Online publication date: 1-Mar-2019
https://doi.org/10.1007/s10817-019-09515-1
Show More Cited By

Index Terms

Using tableau to decide description logics with full role negation and identity
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Theory of computation
  1. Logic
    1. Modal and temporal logics
    2. Proof theory
  2. Models of computation
    1. Computability

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 15, Issue 1

February 2014

279 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/2590829

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Copyright © 2014 Owner/Author.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Publication History

Published: 06 March 2014

Accepted: 01 May 2013

Revised: 01 May 2013

Received: 01 August 2012

Published in TOCL Volume 15, Issue 1

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Cited By

Hustadt UPapacchini FNalon CDixon C(2024)Model Construction for Modal ClausesAutomated Reasoning10.1007/978-3-031-63501-4_1(3-23)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_1
Li JWu XLu CDeng WZhao Y(2021)Computing Views of OWL Ontologies for the Semantic WebProceedings of the Web Conference 202110.1145/3442381.3449881(2624-2635)Online publication date: 19-Apr-2021
https://dl.acm.org/doi/10.1145/3442381.3449881
Baumgartner PSchmidt R(2019)Blocking and Other Enhancements for Bottom-Up Model Generation MethodsJournal of Automated Reasoning10.1007/s10817-019-09515-1Online publication date: 1-Mar-2019
https://doi.org/10.1007/s10817-019-09515-1
Zohar YTishkovsky DSchmidt RZamansky A(2019)Automating Automated ReasoningDescription Logic, Theory Combination, and All That10.1007/978-3-030-22102-7_29(610-638)Online publication date: 1-Jun-2019
https://doi.org/10.1007/978-3-030-22102-7_29
Ahmetaj SCalvanese DOrtiz MŠimkus M(2017)Managing Change in Graph-Structured Data Using Description LogicsACM Transactions on Computational Logic10.1145/314380318:4(1-35)Online publication date: 3-Nov-2017
https://dl.acm.org/doi/10.1145/3143803
Tishkovsky DSchmidt R(2017)Rule Refinement for Semantic Tableau CalculiAutomated Reasoning with Analytic Tableaux and Related Methods10.1007/978-3-319-66902-1_14(228-244)Online publication date: 30-Aug-2017
https://doi.org/10.1007/978-3-319-66902-1_14
Zhao YSchmidt R(2016)Forgetting concept and role symbols in ALCOIHµ+(∇, ∩)-ontologiesProceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence10.5555/3060621.3060808(1345-1352)Online publication date: 9-Jul-2016
https://dl.acm.org/doi/10.5555/3060621.3060808
Stell JSchmidt RRydeheard D(2016)A bi-intuitionistic modal logic: Foundations and automationJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2015.11.00385:4(500-519)Online publication date: Jun-2016
https://doi.org/10.1016/j.jlamp.2015.11.003
Schmidt RWaldmann U(2015)Modal Tableau Systems with Blocking and Congruence ClosureProceedings of the 24th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods - Volume 932310.1007/978-3-319-24312-2_4(38-53)Online publication date: 21-Sep-2015
https://dl.acm.org/doi/10.1007/978-3-319-24312-2_4
Areces CFontaine PMerz S(2015)Modal Satisfiability via SMT SolvingSoftware, Services, and Systems10.1007/978-3-319-15545-6_5(30-45)Online publication date: 2015
https://doi.org/10.1007/978-3-319-15545-6_5
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