Mojtaba Mojtahedi

Mojtaba Mojtahedi
University of Tehran | UT ·  School of Mathematics, Statistics and Computer Sciences

PhD

About

15
Publications
945
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35
Citations
Citations since 2017
11 Research Items
32 Citations
2017201820192020202120222023024681012
2017201820192020202120222023024681012
2017201820192020202120222023024681012
2017201820192020202120222023024681012
Additional affiliations
January 2013 - December 2015
Sharif University of Technology
Position
  • Lecturer

Publications

Publications (15)
Article
Full-text available
In this paper we introduce a modal theory $H_{\sigma}$, which is sound and complete for arithmetical $\Sigma$_1 substitutions in ${\bf HA}$, in other words, we will show that $H_{\sigma}$ is the $\Sigma$_1-provability logic of ${\bf HA}$. Moreover we will show that $H_{\sigma}$ is decidable. As a by-product of these results, we show that ${\bf HA}...
Article
Full-text available
We show that the provability logic of PA, GL and the truth provability logic, i.e. the provability logic of PA relative to the standard model ℕ, GLS are reducible to their Σ1-provability logics, GLV and GLSV, respectively, by only propositional substitutions.
Article
Let denote a first-order logic in a language that contains infinitely many constant symbols and also containing intuitionistic logic . By , we mean the associated logic axiomatized by the double negation of the universal closure of the axioms of plus . We shall show that if is strongly complete for a class of Kripke models , then is strongly comple...
Article
We prove that Basic Arithmetic, BA, has the de Jongh property, i.e., for any propositional formula A(p 1,..., p n ) built up of atoms p 1,..., p n , BPC ⊢ A(p 1,..., p n ) if and only if for all arithmetical sentences B 1,..., B n , BA ⊢ A(B 1,..., B n ). The technique used in our proof can easily be applied to some known extensions of BA.
Preprint
Full-text available
We axiomatize the provability logic of HA and show that it is decidable. Moreover we axiomatize the preservativity and relative admissibility for several modal logics extending iK4. As a main tool, we also provide some sort of semantics, called provability semantics, for modal logics extending iGL, which is a mixture of usual Kripke semantics and p...
Article
We prove that $\textbf {K}5$ and some of its extensions that do not contain $\textbf {K}4$ are of unification type $1$.
Article
In this paper, we show that the implication fragment of classical propositional logic is finitary for unification with parameters.
Chapter
Let \(\mathsf{PL}(T,T')\) and \(\mathsf{PL}_{_{\Sigma _1}}(T,T')\) respectively indicate the provability logic and \(\Sigma _1\)-provability logic of \(T\) relative in \(T'\). In this paper we characterise the following relative provability logics: \(\mathsf{PL}_{_{\Sigma _1}}(\mathsf{HA},\mathbb {N})\), \(\mathsf{PL}_{_{\Sigma _1}}(\mathsf{HA},\ma...
Book
This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, inc...
Preprint
Full-text available
Let $\mathcal{PL}({\sf T},{\sf T}')$ and $\mathcal{PL}_{\Sigma_1}({\sf T},{\sf T}')$ respectively indicates the provability logic and $\Sigma_1$-provability logic of ${\sf T}$ relative in ${\sf T}'$. In this paper we characterize the following relative provability logics: $\mathcal{PL}_{\Sigma_1}({\sf HA},\mathbb{N})$, $\mathcal{PL}_{\Sigma_1}({\sf...
Article
For the Heyting Arithmetic HA, $HA^{\text{*}} $ is defined [14, 15] as the theory $\left\{ {A|HA \vdash A^\square } \right\}$ , where $A^\square $ is called the box translation of A (Definition 2.4). We characterize the ${\text{\Sigma }}_1 $ -provability logic of $HA^{\text{*}} $ as a modal theory $iH_\sigma ^{\text{*}} $ (Definition 3.17).
Article
In this paper we introduce a modal theory iHσ which is sound and complete for arithmetical Σ1-interpretations in HA, in other words, we will show that iHσ is the Σ1-provability logic of HA. Moreover we will show that iHσ is decidable. As a by-product of these results, we show that HA+□⊥ has de Jongh property.
Preprint
Full-text available
For the Heyting Arithmetic HA, HA* is defined as the theory $\{A\mid {\sf HA}\vdash A^{\Box}\}$, where $A^{\Box}$ is called the box translation of $A$. We characterize the $\Sigma_1$-provability logic of HA* as a modal theory ${\sf iH}_\sigma^*$.
Article
Full-text available
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 arbitrary first-order language or propositional language, local (classical) truth of a formula is equivalent to non-classical truth (truth in the Kripke semantics) of a...

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