 From a logical point of view, inquisitive logic can be axiomatised by expanding intuitionistic logic with the Kreisel-Putnam axiom scheme \((\neg \phi \to (\psi_1\vee \psi_2)) \to (\neg \phi \to \psi_1) \vee (\neg \phi \to \psi_2)\) and the double negation axioms restricted to atoms (Ciardelli and Roelofsen 2011), and so is one of the intermediate logics between intuitionistic and classical logic (see the entry on  intuitionistic logic, section 6.1).  As in intuitionistic logic, in inquisitive logic LEM is not provable and the disjunction property holds (\((\phi \vee \psi)\) is inquisitively provable iff \(\phi\) is inquisitively provable or \(\psi\) is). From a model-theoretic point of view, LEM is not inquisitively valid because both \(\phi\) and \(\neg \phi\) may fail to be supported in a state that represents ignorance with respect to \(\phi\). Recall that the main motivation behind inquisitive logic is to capture both informational and inquisitive content of sentences. Intuitively, \((\phi \vee\neg \phi)\) is not valid because while informationally vacuous, it can still raise an issue, namely the issue whether \(\phi\) is the case or not and, therefore, it is not trivial from an inquisitive point of view.