Combining and representing logical systems using model-theoretic parchments

Abstract

The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. We adopt the model-theoretic view of logic as captured in the notions of institution and of parchment (an algebraic way of presenting institutions). We propose a new, modified notion of parchment together with parchment morphisms and representations. In contrast to the original parchment definition and our earlier work, in model-theoretic parchments introduced here the universal semantic structure is distributed over individual signatures and models. We lift formal properties of the categories of institutions and their representations to this level: the category of model-theoretic parchments is complete, and their representations may be put together using categorical limits as well. However, model-theoretic parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for combination of various logical features may be introduced either on an ad hoc basis or via representations in a universal logic.

A full version of this paper is available as [11]. It contains all the proofs, complete technicalities and more discussion and examples, omitted here due to space limitations.

This work has been partially supported by KBN grant 8 T11C 01811.