Formalizing Inconsistency-Tolerant Relevant Human Reasoning: A Decidable Paraconsistent Relevant Logic with Constructible Falsity

Formalizing inconsistency-tolerant relevant human reasoning in a philosophically plausible logic is useful for modeling sophisticated agents similar to human. For this aim, the positive fragment of the logic RW of contraction-less relevant implication is extended with the addition of a Para consistent negation connective similar to the strong negation connective in Nelson´s Para consistent four-valued logic N4. This extended para-consistent relevant logic is called RWP, and it has the property of constructible falsity which is known to be useful for representing inexact predicates. A Gentzen-type sequent calculus SRWP for RWP is introduced, and the decidability and cut-elimination theorems for SRWP are proved. An extended Routley-Meyer semantics is introduced for RWP, and the completeness theorem with respect to this semantics is proved.