The language of linear temporal logic can be interpreted on the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${\sf ITL}^{\sf c}_{\Diamond \forall }$, recently shown to be decidable by Fernández-Duque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.

In dynamical multi-agent systems, agents are controlled by protocols. In choosing a class of formal protocols, an implicit choice is made concerning the types of agents, actions and dynamics representable. This paper investigates one such choice: An intensional protocol class for agent control in dynamic epistemic logic (DEL), called ‘DEL dynamical systems’. After illustrating how such protocols may be used in formalizing and analyzing information dynamics, the types of epistemic temporal models that they may generate are characterized. This facilitates a (...) formal comparison with the only other formal protocol framework in dynamic epistemic logic, namely the extensional ‘DEL protocols’. The paper concludes with a conceptual comparison, highlighting modeling tasks where DEL dynamical systems are natural. (shrink)

In dynamical multi-agent systems, agents are controlled by protocols. In choosing a class of formal protocols, an implicit choice is made concerning the types of agents, actions and dynamics representable. This paper investigates one such choice: An intensional protocol class for agent control in dynamic epistemic logic, called ‘DEL dynamical systems’. After illustrating how such protocols may be used in formalizing and analyzing information dynamics, the types of epistemic temporal models that they may generate are characterized. This facilitates a formal (...) comparison with the only other formal protocol framework in dynamic epistemic logic, namely the extensional ‘DEL protocols’. The paper concludes with a conceptual comparison, highlighting modeling tasks where DEL dynamical systems are natural. (shrink)

The tangle modality is a propositional connective that extends basic modal logic to a language that is expressively equivalent over certain classes of finite frames to the bisimulation-invariant fragments of both first-order and monadic second-order logic. This paper axiomatises several logics with tangle, including some that have the universal modality, and shows that they have the finite model property for Kripke frame semantics. The logics are specified by a variety of conditions on their validating frames, including local and global connectedness (...) properties. Some of the results have been used to obtain completeness theorems for interpretations of tangled modal logics in topological spaces. (shrink)