Relational version of the multi-agent computation tree logic $\mathcal{CTLK}$

This paper deals with multi-agent computation tree logic — $\mathcal{CTLK}$ (Computation Tree Logic with Knowledge). Each agent represents its own computational route of the initial problem, and new branches of possible computational routes spawn new agents. The logic $\mathcal{CTLK}$ is a natural enrichment of $\mathcal{CTL}$ by new knowledge operators. We introduce alternative to automata Kripke's relational semantics, describes properties of $\mathcal{CTLK}^{Rel}$-frame and proves finite approximability.