Curry–Howard–Lambek Correspondence for Intuitionistic Belief

Intuitionistic Correspondence Theory

Algorithmic correspondence for intuitionistic modal mu-calculus

In the present paper, the algorithmic correspondence theory developed in (Conradie and Palmigiano, 2012) is extended to mu-calculi with a non-classical base. We focus in particular on the language of bi-intuitionistic modal mu-calculus. We enhance the algorithm ALBA introduced in (Conradie and Palmigiano, 2012) so as to guarantee its success on the class of recursive muinequalities, which we in...

Intuitionistic common knowledge or belief

Starting off from the usual language of modal logic for multi-agent systems dealing with the agents’ knowledge/belief and common knowledge/belief we define so-called epistemic Kripke structures for intuitionistic (common) knowledge/belief. Then we introduce corresponding deductive systems and show that they are sound and complete with respect to these semantics.

Algorithmic correspondence for intuitionistic modal mu-calculus, Part 2

Sahlqvist-style correspondence results remain a perennial theme and an active topic of research within modal logic. Recently, there has been interest in extending the classical results in this area to the modal mu-calculus [7]. For instance, in [8] van Benthem, Bezhanishvili and Hodkinson define a class of Sahlqvist formulas for the modal mu-calculus, all of which have frame correspondents in f...

Algorithmic correspondence for intuitionistic modal mu-calculus, Part 1

Modal mu-calculus [5] is a logical framework combining simple modalities with fixed point operators, enriching the expressivity of modal logic so as to deal with infinite processes like recursion. It has a simple syntax, an easily given semantics, and is decidable. Many expressive modal and temporal logics such as PDL, CTL and CTL∗ can be seen as fragments of the modal mu-calculus. Sahlqvist-st...