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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.

Embedding Proof Problems into Query-answering Problems and Problem Solving by Equivalent Transformation