impossible extensions and the logic of the concepts

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 attampt to support ibn sina and al khunaji's view versus al abhari's. for this we take the extensions as sets of concepts. if an extension is a set of inconsistent concepts we'll regard it impossible and name its logic ‘the logic of the concepts’. for systematizing the logic we introduce a semantics similar to that of predicate logic and construct a formal system in the first order language. we show that the logical system can be collapsed to a fraction of the second order logic concluding that ibn sina and al khunaji's view can be supported by the second order logic.