Daniel West

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.