Intuitionistic Axiomatizations for Bounded Extension Kripke Models (2009)
Ardeshir, Mohammad, Ruitenburg, Wim, Salehi, Saeed
We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we...
Mohammad Ardeshir, M. Ardeshir, W. Ruitenburg, Basic Propositional Calculus, H. Barendregt, ...
Basic propositional logic was first introduced by Albert Visser in [6]. Basic logic is a proper subsystem of intuitionistic logic, and can be constructed from it by a weakening of modus ponens. This...
Intuitionistic Axiomatization of the End-Extension Kripke Models (2008)
Mohammad Ardeshir, Wim Ruitenburg, Saeed P. Salehi
We axiomatize two important intermediate logics, classifying end-extension Kripke models and cofinal-extension Kripke models. As applications, we show that Heyting Arithmetic, HA, is complete with...
An Introduction to Basic Arithmetic (2008)
Ardeshir, Mohammad, Hesaam, Bardyaa
We study Basic Arithmetic BA, which is the basic logic BQC equivalent of Heyting Arithmetic HA over intuitionistic logic IQC, and of Peano Arithmetic PA over classical logic CQC. It turns out that...
On some questions of L. Aqvist (2006)
Ardeshir, Mohammad, Nabavi, Fateme
We give answers to some questions raised by L. Åqvist in [6] and [7]. The question raised in [7] which we will answer positively is about the representability of Åqvist's system G in a hierarchy of...
Intuitionistic Open Induction and Least Number Principle and the Buss Operator (1998)
Ardeshir, Mohammad, Moniri, Mojtaba
In "Intuitionistic validity in $T$ -normal Kripke structures," Buss asked whether every intuitionistic theory is, for some classical theory $T$ , that of all $T$ -normal Kripke structures ${\cal...