A logic L has the disjunction property just in case \(\models _{L} \varphi \vee \psi \) implies \(\models _{L} \varphi \) or \(\models _{L} \psi \) . This property is important to constructivists and is a well-known feature of intuitionistic logic. In this paper we use model-theoretic techniques to show that the disjunction property holds in Urquhart’s operational relevance logics \({\textbf {R}}_U^+\) , \({\textbf {T}}_U^+\) , \({\textbf {RW}}_U^+\) , \({\textbf {TW}}_U^+\) , and \({\textbf {E}}_U^+\) . These results suggest that operational relevance logics merit further attention from a constructivist perspective. Along the way, we also provide a novel proof that the disjunction property holds in intuitionistic logic.
