Amir Akbar Tabatabai

Department of Philosophy, Utrecht University, the Netherlands

I am a mathematician interested in philosophy and theoretical computer science.

selected publications

Provability Interpretation of Propositional and Modal Logics

Akbar Tabatabai, Amirhossein

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In 1933, Gödel introduced a provability interpretation of the propositional intuitionistic logic to establish a formalization for the BHK interpretation. He used the modal system, S4, as a formalization of the intuitive concept of provability and then translated IPC to S4. His work suggested the problem to find a concrete provability interpretation of the modal logic S4. In this paper, we will try to answer this problem. In fact, we will generalize Solovay’s provability interpretation of the modal logic GL to capture other modal logics such as K4, KD4 and S4. Then we will use these results to find a formalization for the BHK interpretation and we will show that with different interpretations of the BHK interpretation, we can capture some of the propositional logics such as Intuitionistic logic, minimal logic and Visser-Ruitenburg’s basic logic. Moreover, we will show that there is no provability interpretation for any extension of KD45 and also there is no BHK interpretation for the classical propositional logic.

Implication via Spacetime

Akbar Tabatabai, Amirhossein

Logic, and Their Philosophies: Essays in Honour of Mohammad Ardeshir, Eds. M. Mojtahedi, S. Rahman, M. Zarepour 2021

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In this paper we intend to study implications in their most general form, generalizing different classes of implications including the Heyting implication, sub-structural implications and weak strict implications. Following the topological interpretation of the intuitionistic logic, we will introduce non-commutative spacetimes to provide a more dynamic and subjective interpretation of an intuitionistic proposition. These combinations of space and time are natural sources for well-behaved implications and we will show that their spatio-temporal implications represent any other reasonable abstract implication. Then to provide a faithful well-behaved syntax for abstract implications, we will develop a logical system for the non-commutative spacetimes for which we will present both topological and Kripke semantics. These logics unify sub-structural and sub-intuionistic logics by embracing them as their special fragments.