# A new type theory for representing logics

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## Abstract

We propose a new type theory for representing logics, called LF^{+} and based on the Edinburgh Logical Framework. The new framework allows us to give, apparently for the first time, general definitions which capture how well a logic has been represented. Using our definitions, we show that, for example, first-order logic can be wellrepresented in LF^{+}, whereas linear and relevant logics cannot. These syntactic definitions of representation have a simple formulation as indexed isomorphisms, which both confirms that our approach is a natural one, and provides a link between type-theoretic and categorical approaches to frameworks.

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© Springer-Verlag Berlin Heidelberg 1993