On a coalgebraic view on Logic

D. Hofmann, M. A. Martins
2012 Journal of Logic and Computation  
In this paper we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as morphisms in a category. Outline of the paper. We present logic (to be more precise: a consequence relation) on an abstract set rather then a set of formulae. We exhibit various ways to encode this structure which have roots in different fields of mathematics,
more » ... namely topology and (co)algebra. We start by taking a relational approach to the consequence relation; we define appropriated identity and composition to form a monoid that represents the abstract
doi:10.1093/logcom/exs063 fatcat:eze3o2wwyvb6hnlicne2flxtme