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Embedding Proof Problems into Query-answering Problems and Problem Solving by Equivalent TransformationTopics: Intelligent Problem Solving; Knowledge Representation

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Ontology
Subjects/Areas/Topics:Artificial Intelligence
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Enterprise Software Technologies
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Intelligent Problem Solving
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Knowledge Engineering and Ontology Development
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Knowledge Representation
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Knowledge-Based Systems
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Software Engineering
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Symbolic Systems

Abstract: A proof problem is a “yes/no” problem concerning with checking whether one logical formula is a logical
consequence of another logical formula, while a query-answering problem (QA problem) is an “all-answers
finding” problem concerning with finding all ground instances of a query atomic formula that are logical
consequences of a given logical formula. In order to establish a precise relation between these two problem
classes, the concept of an embedding mapping is introduced. When one problem class can be embedded into
another problem class at low computational cost, the former class can be regarded as a subclass of the latter
class and, consequently, problems in the former class can be solved through a method for solving problems in
the latter one. Construction of low-cost embedding mappings from proof problems to QA problems is demonstrated.
By such embedding, proof problems can be solved using a procedure for solving QA problems. A
procedure for solving QA problems based on the equivalent transformation principle is presented. Application
of the procedure to the two problem classes is illustrated.(More)

A proof problem is a “yes/no” problem concerning with checking whether one logical formula is a logical consequence of another logical formula, while a query-answering problem (QA problem) is an “all-answers finding” problem concerning with finding all ground instances of a query atomic formula that are logical consequences of a given logical formula. In order to establish a precise relation between these two problem classes, the concept of an embedding mapping is introduced. When one problem class can be embedded into another problem class at low computational cost, the former class can be regarded as a subclass of the latter class and, consequently, problems in the former class can be solved through a method for solving problems in the latter one. Construction of low-cost embedding mappings from proof problems to QA problems is demonstrated. By such embedding, proof problems can be solved using a procedure for solving QA problems. A procedure for solving QA problems based on the equivalent transformation principle is presented. Application of the procedure to the two problem classes is illustrated.

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Akama, K. and Nantajeewarawat, E. (2013). Embedding Proof Problems into Query-answering Problems and Problem Solving by Equivalent Transformation.In Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2013) ISBN 978-989-8565-81-5, pages 253-260. DOI: 10.5220/0004546202530260

@conference{keod13, author={Kiyoshi Akama. and Ekawit Nantajeewarawat.}, title={Embedding Proof Problems into Query-answering Problems and Problem Solving by Equivalent Transformation}, booktitle={Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2013)}, year={2013}, pages={253-260}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0004546202530260}, isbn={978-989-8565-81-5}, }

TY - CONF

JO - Proceedings of the International Conference on Knowledge Engineering and Ontology Development - Volume 1: KEOD, (IC3K 2013) TI - Embedding Proof Problems into Query-answering Problems and Problem Solving by Equivalent Transformation SN - 978-989-8565-81-5 AU - Akama, K. AU - Nantajeewarawat, E. PY - 2013 SP - 253 EP - 260 DO - 10.5220/0004546202530260