Authors:
Kiyoshi Akama
1
and
Ekawit Nantajeewarawat
2
Affiliations:
1
Hokkaido University, Japan
;
2
Thammasat University, Thailand
Keyword(s):
Question-answering Problems, Proof Problems, Equivalent Transformation, Solving Logical Problems.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Enterprise Software Technologies
;
Intelligent Problem Solving
;
Knowledge Engineering and Ontology Development
;
Knowledge Representation
;
Knowledge-Based Systems
;
Software Engineering
;
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 eq
uivalent transformation principle is presented. Application
of the procedure to the two problem classes is illustrated.
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