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**Truth, Proof and Provability**

دکتر محمد اردشیر

دانشگاه صنعتی شریف

We review the notions of truth, proof and provability in constructive logic. Then we examine these notions in Heyting Arithmetic HA, as a constructive mathematical theory. We argue that Heyting Arithmetic as is formalized, is not a “real” constructive arithmetical theory according to Brouwer-Heyting-Kolmogorov BHK proof explanation of the logical connectives. It sounds that, an extension of HA, called HA*, is a “better” approximation to the constructive arithmetic, based on the BHK proof explanation. Then we introduce the \(\Sigma_1\)-provability logic of HA*.

**مکان: **** ****تهران** **، مؤسسة پژوهشی حکمت و فلسفة ایران**

**زمان****: ****دوشنبه،** **26 فروردین 1398،** **ساعت 4 بعد** **از** **ظهر**