Tableau Calculus

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 834 Experts worldwide ranked by ideXlab platform

Linh Anh Nguyen - One of the best experts on this subject based on the ideXlab platform.

Dmitry Tishkovsky - One of the best experts on this subject based on the ideXlab platform.

  • MetTeL2: Towards a prover generation platform
    2020
    Co-Authors: Dmitry Tishkovsky, Mohammad Khodadadi, Renate A Schmidt, R A Papacchini, Frank Schmidt
    Abstract:

    This paper introduces MetTeL2, a Tableau prover generator producing Java code from the specifications of a logical syntax and a Tableau Calculus. It is intended to provide an easy to use system for nontechnical users and allow technical users to extend the implementation of generated provers.

  • Description Logics - An Abstract Tableau Calculus for the Description Logic SHOI Using Unrestricted Blocking and Rewriting
    2016
    Co-Authors: Mohammad Khodadadi, Renate A Schmidt, Dmitry Tishkovsky
    Abstract:

    This paper presents an abstract Tableau Calculus for the description logic SHOI.SHOI is the extension of ALC with singleton concepts, role inverse,transitive roles and role inclusion axioms. The presented Tableau Calculus isinspired by a recently introduced Tableau synthesis framework. Termination isachieved by a variation of the unrestricted blocking mechanism that immediatelyrewrites terms with respect to the conjectured equalities. This approach leadsto reduced search space for decision procedures based on the Calculus. We alsodiscuss restrictions of the application of the blocking rule by means ofadditional side conditions and/or additional premises.

  • a refined Tableau Calculus with controlled blocking for the description logic shoi
    International Workshop Description Logics, 2013
    Co-Authors: Mohammad Khodadadi, Renate A Schmidt, Dmitry Tishkovsky
    Abstract:

    The paper presents a Tableau Calculus with several refinements for reasoning in the description logic \(\mathcal{SHOI}\). The Calculus uses non-standard rules for dealing with TBox statements. Whereas in existing Tableau approaches a fixed rule is used for dealing with TBox statements, we use a dynamically generated set of refined rules. This approach has become practical because reasoners with flexible sets of rules can be generated with the Tableau prover generation prototype MetTel. We also define and investigate variations of the unrestricted blocking mechanism in which equality reasoning is realised by ordered rewriting and the application of the blocking rule is controlled by excluding its application to a fixed, finite set of individual terms. Reasoning with the unique name assumption and excluding ABox individuals from the application of blocking can be seen as two separate instances of the latter. Experiments show the refinements lead to fewer rule applications and improved performance.

  • Description Logics - A Refined Tableau Calculus with Controlled Blocking for the Description Logic SHOI
    Lecture Notes in Computer Science, 2013
    Co-Authors: Mohammad Khodadadi, Renate A Schmidt, Dmitry Tishkovsky
    Abstract:

    The paper presents a Tableau Calculus with several refinements for reasoning in the description logic \(\mathcal{SHOI}\). The Calculus uses non-standard rules for dealing with TBox statements. Whereas in existing Tableau approaches a fixed rule is used for dealing with TBox statements, we use a dynamically generated set of refined rules. This approach has become practical because reasoners with flexible sets of rules can be generated with the Tableau prover generation prototype MetTel. We also define and investigate variations of the unrestricted blocking mechanism in which equality reasoning is realised by ordered rewriting and the application of the blocking rule is controlled by excluding its application to a fixed, finite set of individual terms. Reasoning with the unique name assumption and excluding ABox individuals from the application of blocking can be seen as two separate instances of the latter. Experiments show the refinements lead to fewer rule applications and improved performance.

  • PAAR@IJCAR - MetTeL 2 : Towards a Tableau Prover Generation Platform
    2013
    Co-Authors: Dmitry Tishkovsky, Renate A Schmidt, Mohammad Khodadadi
    Abstract:

    This paper introduces MetTeL 2 , a Tableau prover generator producing Java code from the specication of a logical syntax and a Tableau Calculus. It is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated implementations.

Mohammad Khodadadi - One of the best experts on this subject based on the ideXlab platform.

  • MetTeL2: Towards a prover generation platform
    2020
    Co-Authors: Dmitry Tishkovsky, Mohammad Khodadadi, Renate A Schmidt, R A Papacchini, Frank Schmidt
    Abstract:

    This paper introduces MetTeL2, a Tableau prover generator producing Java code from the specifications of a logical syntax and a Tableau Calculus. It is intended to provide an easy to use system for nontechnical users and allow technical users to extend the implementation of generated provers.

  • Description Logics - An Abstract Tableau Calculus for the Description Logic SHOI Using Unrestricted Blocking and Rewriting
    2016
    Co-Authors: Mohammad Khodadadi, Renate A Schmidt, Dmitry Tishkovsky
    Abstract:

    This paper presents an abstract Tableau Calculus for the description logic SHOI.SHOI is the extension of ALC with singleton concepts, role inverse,transitive roles and role inclusion axioms. The presented Tableau Calculus isinspired by a recently introduced Tableau synthesis framework. Termination isachieved by a variation of the unrestricted blocking mechanism that immediatelyrewrites terms with respect to the conjectured equalities. This approach leadsto reduced search space for decision procedures based on the Calculus. We alsodiscuss restrictions of the application of the blocking rule by means ofadditional side conditions and/or additional premises.

  • a refined Tableau Calculus with controlled blocking for the description logic shoi
    International Workshop Description Logics, 2013
    Co-Authors: Mohammad Khodadadi, Renate A Schmidt, Dmitry Tishkovsky
    Abstract:

    The paper presents a Tableau Calculus with several refinements for reasoning in the description logic \(\mathcal{SHOI}\). The Calculus uses non-standard rules for dealing with TBox statements. Whereas in existing Tableau approaches a fixed rule is used for dealing with TBox statements, we use a dynamically generated set of refined rules. This approach has become practical because reasoners with flexible sets of rules can be generated with the Tableau prover generation prototype MetTel. We also define and investigate variations of the unrestricted blocking mechanism in which equality reasoning is realised by ordered rewriting and the application of the blocking rule is controlled by excluding its application to a fixed, finite set of individual terms. Reasoning with the unique name assumption and excluding ABox individuals from the application of blocking can be seen as two separate instances of the latter. Experiments show the refinements lead to fewer rule applications and improved performance.

  • Description Logics - A Refined Tableau Calculus with Controlled Blocking for the Description Logic SHOI
    Lecture Notes in Computer Science, 2013
    Co-Authors: Mohammad Khodadadi, Renate A Schmidt, Dmitry Tishkovsky
    Abstract:

    The paper presents a Tableau Calculus with several refinements for reasoning in the description logic \(\mathcal{SHOI}\). The Calculus uses non-standard rules for dealing with TBox statements. Whereas in existing Tableau approaches a fixed rule is used for dealing with TBox statements, we use a dynamically generated set of refined rules. This approach has become practical because reasoners with flexible sets of rules can be generated with the Tableau prover generation prototype MetTel. We also define and investigate variations of the unrestricted blocking mechanism in which equality reasoning is realised by ordered rewriting and the application of the blocking rule is controlled by excluding its application to a fixed, finite set of individual terms. Reasoning with the unique name assumption and excluding ABox individuals from the application of blocking can be seen as two separate instances of the latter. Experiments show the refinements lead to fewer rule applications and improved performance.

  • PAAR@IJCAR - MetTeL 2 : Towards a Tableau Prover Generation Platform
    2013
    Co-Authors: Dmitry Tishkovsky, Renate A Schmidt, Mohammad Khodadadi
    Abstract:

    This paper introduces MetTeL 2 , a Tableau prover generator producing Java code from the specication of a logical syntax and a Tableau Calculus. It is intended to provide an easy to use system for non-technical users and allow technical users to extend the generated implementations.

Andrzej Szalas - One of the best experts on this subject based on the ideXlab platform.

Gernot Stenz - One of the best experts on this subject based on the ideXlab platform.

  • The Disconnection Tableau Calculus
    Journal of Automated Reasoning, 2007
    Co-Authors: Reinhold Letz, Gernot Stenz
    Abstract:

    In this paper we give a comprehensive presentation of the disconnection Tableau Calculus, a proof method for formulas in classical first-order clause logic. The distinguishing property of this Calculus is that it uses unification in such a manner that important proof-theoretic advantages of the classical (i.e., Smullyan-style) Tableau Calculus are preserved, specifically the termination and model generation characteristics for certain formula classes. Additionally, the Calculus is well suited for fully automated proof search. The Calculus is described in detail with soundness and completeness proofs, and a number of important Calculus refinements developed over the past years are presented. Referring to the model-finding abilities of the disconnection Calculus, we explain the extraction and representation of models. We also describe the integration of paramodulation-based equality handling. Finally, we give an overview of related methods.

  • LPAR - Automated Theorem Proving Proof and Model Generation with Disconnection Tableaux
    2001
    Co-Authors: Reinhold Letz, Gernot Stenz
    Abstract:

    We present the disconnection Tableau Calculus, which is a free-variable clausal Tableau Calculus where variables are treatedin a nonrigidmanner. The Calculus essentially consists of a single inference rule, the so-calledlinking rule, which strongly restricts the possible clauses in a Tableau. The methodcan also be viewedas an integration of the linking rule as usedin Plaisted's linking approach into a Tableau format. The Calculus has the proof-theoretic advantage that, in the case of a satisfiable formula, one can characterise a model of the formula, a property which most of the free-variable Tableau calculi lack. In the paper, we present a rigorous completeness proof and give a procedure for extracting a model from a finitely failed branch.

  • Proof and Model Generation with Disconnection Tableaux
    Logic for Programming Artificial Intelligence and Reasoning, 2001
    Co-Authors: Reinhold Letz, Gernot Stenz
    Abstract:

    We present the disconnection Tableau Calculus, which is a free-variable clausal Tableau Calculus where variables are treatedin a nonrigidmanner. The Calculus essentially consists of a single inference rule, the so-called linking rule, which strongly restricts the possible clauses in a Tableau. The method can also be viewed as an integration of the linking rule as used in Plaisted’s linking approach into a Tableau format. The Calculus has the proof-theoretic advantage that, in the case of a satisfiable formula, one can characterise a model of the formula, a property which most of the free-variable Tableau calculi lack. In the paper, we present a rigorous completeness proof and give a procedure for extracting a model from a finitely failed branch.

  • dctp a disconnection Calculus theorem prover system abstract
    International Joint Conference on Automated Reasoning, 2001
    Co-Authors: Reinhold Letz, Gernot Stenz
    Abstract:

    We describe the theorem prover DCTP, which is an implementation of the disconnection Tableau Calculus, a confluent Tableau method, in which free variables are treated in a non-rigid manner. In contrast to most other free-variable Tableau variants, the system can also be used for model generation. We sketch the underlying Calculus and its refinements, and present the results of an experimental evaluation.

  • IJCAR - DCTP - A Disconnection Calculus Theorem Prover - System Abstract
    Automated Reasoning, 2001
    Co-Authors: Reinhold Letz, Gernot Stenz
    Abstract:

    We describe the theorem prover DCTP, which is an implementation of the disconnection Tableau Calculus, a confluent Tableau method, in which free variables are treated in a non-rigid manner. In contrast to most other free-variable Tableau variants, the system can also be used for model generation. We sketch the underlying Calculus and its refinements, and present the results of an experimental evaluation.