Analytic Proof-Theory for Prior’s System Q: First Steps

Arthur Prior introduced the three-valued modal logic called the Q system. A few axiom systems for the Q system can be found in the literature, but no analytic proof-theory in the form of tableau-, sequent- or natural deduction systems. In the present paper we demonstrate how to turn a formal semantics for the Q system into a tableau system, whereby we provide a proof system that is suitable for actual reasoning.