Abstract We can measure the complexity of a logical formula by counting number alternations between existential and universal quantifiers. Suppose that an elementary first-order $\varphi $ (in $\mathcal {L}_{\omega ,\omega }$ ) is equivalent to infinitary language {L}_{\infty with n prove finitary Thus using logic does not allow us express in simpler way.

the logical treatise al-muhja has been attributed to avicenna in some bibliographies of logical treatises. since a proper understanding of the development of avicennian logic rests on the identification and consideration of the entire corpus of his logical works, the task of the present study is to investigate the validity of ascription of this treatise to avicenna. in carrying out an analysis ...