a controversy among the muslim philosophers about the domain of the extensions was that is the subject of the verity-propositions contained the impossible extensions or only all of the actual and possible ones. from ibn-sina to al-khunaji, there are explicit texts to the former view; but later logicians, starting with athir al-din al-abhari, were inclined to the latter. in this paper, we attamp...

for the first time in the history of logic, afzal al-din al-khunaji has found tautologies and contradictories among the verity and actuality propositions. these have been formalized and investigated in first-order logic and it has been shown that their perpetual truth requires the assumption of ‘the presupposed existence of non-existence.’ in this paper, i investigate the tautologies in second-...

Abstract We prove that the first-order logic of CZF is intuitionistic logic. To do so, we introduce a new model transfinite computation (Set Register Machines) and combine resulting notion realisability with Beth semantics. On way, also show propositional admissible rules are exactly those