Categorical Abstract Algebraic Logic: Meet-Combination of Logical Systems

Abstract

The widespread and rapid proliferation of logical systems in several areas of computer science has led to a resurgence of interest in various methods for combining logical systems and in investigations into the properties inherited by the resulting combinations. One of the oldest such methods is fibring. In fibring the shared connectives of the combined logics inherit properties from both component logical systems, and this leads often to inconsistencies. To deal with such undesired effects, Sernadas et al. (2011, 2012) have recently introduced a novel way of combining logics, called meet-combination, in which the combined connectives share only the common logical properties they enjoy in the component systems. In their investigations they provide a sound and concretely complete calculus for the meet-combination based on available sound and complete calculi for the component systems. In this work, an effort is made to abstract those results to a categorical level amenable to categorical abstract algebraic logic techniques.