Algebraic Methods of Automated Reasoning in Monadic Logic

The purpose of this paper is to explain how the theory of Gröbner bases can be used for automated proving in Monadic Logic. The paper is organized as follows: in Section 1 we recall the syntax and semantics of Monadic Logic, and we describe the aim of this paper: the resolution by an algebraic algorithm of the deduction problem in Monadic Logic. Successively, we reduce the deduction problem in Monadic Logic to the propositional calculus (Section 2), to the ideal membership problem (Section 3), and, finally, to find a Gröbner Base (Section 4). In Section 5 we give some algorithms that solve the problems described above. Main sources of the paper are Shoenfield [5] and Boolos & Jeffrey [1] for the sections 1 and 2; Hsiang [3] and Kapur & Narendran [4] for the section 2; and Buchberger [2] for the sections 4 and 5.