A new type theory for representing logics

  • Philippa Gardner
Conference paper

DOI: 10.1007/3-540-56944-8_49

Part of the Lecture Notes in Computer Science book series (LNCS, volume 698)
Cite this paper as:
Gardner P. (1993) A new type theory for representing logics. In: Voronkov A. (eds) Logic Programming and Automated Reasoning. LPAR 1993. Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence), vol 698. Springer, Berlin, Heidelberg

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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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Philippa Gardner
    • 1
  1. 1.University of EdinburghUK

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