Automated Reasoning for the Dialetheic Logic RM3

This paper describes a system for automated reasoning in the dialetheic logic RM3. A dialetheic logic allows formulae to be true, or false, or (differently from classical logic) both true and false, and the connectives are interpreted in terms of these three truth values. Consequently some inference rules of classical logic are invalid in RM3, and some theorems of classical logic are not theorems of RM3. An automated theorem prover for first-order RM3 has been developed, based on translations of RM3 formulae to classical first-order logic, and use of existing first-order reasoning systems to reason over the translated formulae. Examples and results are provided to highlight the differences between reasoning in RM3 and classical logic.