Intuitionistic common knowledge or belief

Hennessy-Milner Properties via Topological Compactness

“…In Subsection 6.3 we apply our results to intuitionistic epistemic logic [33]. The knowledge operators in this logic behave like -modalities.…”

“…Intuitionistic epistemic logic describes a system of the knowledge of n agents [33]. The logical language used for this is EK, and is constructed from propositional variables, intuitionistic connectives, and additional unary modal operators K i for every i ∈ {1, .…”

“…The intuitive meaning of K i φ is "agent i knows that φ" and C φ means that φ is common knowledge. This language can be interpreted in EK-models [33,Definitions 2 and 3]. We give the definition of these models in a slightly reformulated way, so that the connection with Intmodels is easier to see.…”

Modal Intuitionistic Logics as Dialgebraic Logics

“…This dates back to the 1960's [16,17] and includes [15,23,49,66,76,77,88,89] (see [81] for an overview). In addition to the modal intuitionistic logics that have a relational flavour, there is also interest in concurrent dynamic intuitionistic logic [86], epistemic intuitionistic logic [3,44,46,69,87] probabilistic intuitionistic logic [59], and intuitionistic public announcement logic [7,58]. More recently, conditional intuitionistic logic has become prominent [21,84,85].…”