Display Calculi for Logics with Relative Accessibility Relations

International audienceWe define cut-free display calculi for knowledge logics where an indiscernibility relation is associated to each set of agents, andwhere agents decide the membership of objects using this indiscernibility relation. To do so, we first translate the knowledge logics into polymodal logics axiomatised by primitive axioms and then use Kracht's results on properly displayable logics to define the display calculi. Apart from these technical results, we argue that Display Logic is a natural framework to define cut-free calculi for many other logics with relative accessibility relations

Display Calculi for Logics with Relative Accessibility Relations

We define cut-free display calculi for knowledge logics where an indiscernibility relation is associated to each set of agents, and where agents decide the membership of objects using this indiscernibility relation. To do so, we first translate the knowledge logics into polymodal logics axiomatised by primitive axioms and then use Kracht's results on properly displayable logics to define the display calculi. Apart from these technical results, we argue that Display Logic is a natural framework to define cut-free calculi for many other logics with relative accessibility relations

Display Calculi for Logics with Relative Accessibility Relations

We define cut-free display calculi for knowledge logics where an indiscernibility relation is associated to each set of agents, and where agents decide the membership of objects using this indiscernibility relation. To do so, we first translate the knowledge logics into polymodal logics axiomatised by primitive axioms and then use Kracht's results on properly displayable logics to define the display calculi. Apart from these technical results, we argue that Display Logic is a natural framework to define cut-free calculi for many other logics with relative accessibility relations. This paper has not been submitted elsewhere in identical or similar form Visit to A.R.P. supported by an Australian Research Council International Fellowship. y Supported by an Australian Research Council Queen Elizabeth II Fellowship. 1 Introduction Background. Formal logic has been used by various authors to analyse and reason about knowledge. The possible-worlds semantics for knowledge logics initia..