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Infinitary provability logic
Mojtaba Mojtahedi, Fedor Pakhomov, Giovanni Soldà
Gödel-Löb provability logic $\GL$ is a propositional modal system that on one hand enjoys completeness with respect to conversely well-founded Kripke frames and on the other hand c…
Provability Models
Mojtaba Mojtahedi, Borja Sierra Miranda
In this paper, we study a new Kripke-style semantics for classical modal logic, named as provability models. We study provability models for the propositional modal logics K, K4, S…
Projectivity meets Uniform Post-Interpolant: Classical and Intuitionistic Logic
Mojtaba Mojtahedi, Konstantinos Papafilippou
We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logi…
Relative Unification in Intuitionistic Logic: Towards provability logic of HA
Mojtaba Mojtahedi
This paper studies relative unification and admissibility in the intuitionistic logic. We generalize results of [Ghilardi, 1999; Iemhoff, 2001a] and prove them relative in NNIL(par…
On the Provability Logic of HA
Mojtaba Mojtahedi
We axiomatize the provability logic of $\HA$ and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics…
Hard Provability Logics
Mojtaba Mojtahedi
Let and respectively indicates the provability logic and -provability logic of relative in ${…
Localizing Finite-Depth Kripke Models
Mojtaba Mojtahedi
We can look at a first-order (or propositional) intuitionistic Kripke model as an ordered set of classical models. In this paper, we show that for a finite-depth Kripke model in an…