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A query-answering problem (QA problem) is concerned with finding all ground instances of a query atomic formula that are logical consequences of a given logical formula describing the background knowledge of the problem. A method for solving QA problems on full first-order logic has been invented based on the equivalent  transformation (ET) principle, where a given QA problem on first-order logic is converted into a QA problem  on extended clauses and is then further transformed repeatedly and equivalently into simpler forms until its  answer set can be readily obtained. In this paper, such a clause-based solution is extended by proposing  a new method for effectively utilizing a universally quantified if-and-only-if statement defining a predicate,  which is called an iff-formula. The background knowledge of a given QA problem is separated into two parts:  (i) a conjunction of iff-formulas and (ii) other types of knowledge. Special ET rules for manipulating iffformulas  are introduced. The new solution method deals with both iff-knowledge in first-order logic and a set  of extended clauses. Application of this solution method is illustrated.

Solving Query-answering Problems with If-and-Only-If Formulas