On a General Notion of a Hull

Abstract

In this contribution we give a short presentation of ongoing work in the areas of the general framework and mathematical foundations in MEDLAR II. Our objective is to sketch a brief survey of the problems, the methods and existing results and we conclude with prospects of work in progress. We start with some background information and motivational remarks which form the basis of the subsequent considerations. As mentioned in the following, joint article with K. Stokkermans the logical fiberings (as introduced in Pfalzgraf 1991) provide semantical models for indexed systems of logics and they have (semantical) links to D. Gabbay’s extensive theory of labelled deductive systems (LDS). He sees the logical fiberings as a (general) semantics for LDS and introduced the notion of “fibered semantics.” The LDS form a general framework for the great challenge of “putting logics together” in an integrated system (cf. Gabbay 1990, 1994a, b). This indicates the central interest of fibered structures concerning a general semantics modeling approach. Compare the “sheaf semantics” arising naturally in our subsequent considerations.