Admissible rules for the multi modal logic of knowledge and time LTK1

Multi-modal propositional logics with operators representing both time and knowledge are particularly effective to describe the interaction of agents throughout the flow of time ([1, 2, 3, 4, 5, 6]). These systems are usually generated by adding to an existing propositional logic two sets of modalities: one to model the flow of time and one to describe agents’ knowledge. The interaction of such modalities gives a precise account of the dynamic development of agents’ knowledge. However, despite the power of multi-modal propositional logics, multi-modal languages can only express formulae which are static in a way: the statements only fix a fact, and cannot handle a changing environment, although this is required to model human reasoning, computation and multi-agent environments. Sometimes it might be more useful to discover what follows given some premises, rather than knowing logical truths. For this purpose, inference rules, or logical consecutions, are a core instrument.