# Inventing ET Rules to Improve an MI Solver on KR-logic

### Tadayuki Yoshida, Ekawit Nantajeewarawat, Masaharu Munetomo, Kiyoshi Akama

#### Abstract

We understand that many logical problems cannot be solved by using logic programs. Logic programs have the limited capability of representation. We try to overcome this limitation by adopting KR-logic, an extension to first-order logic. The extension includes function variables. In this paper, we take a problem which is well-described with function variables. We rely on Logical Problem Solving Framework (LPSF) to formalize our problem as a Model-intersection problem. Then we develop a solver for MI problems by adding five new transformation rules concerning function variables. Correctness of each rule is proved.i.e., each rule is an equivalent tranformation (ET) rule. Since each rule is correct, all ET rules can be used together without modification and combinational cost. Thus, the invented rules can be safely reused in other LPSF-based solvers.

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