Chapter

Logic Programming and Automated Reasoning

Volume 698 of the series Lecture Notes in Computer Science pp 146-157

Date:

A new type theory for representing logics

  • Philippa GardnerAffiliated withUniversity of Edinburgh

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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.