## Equivalences between Logics and their Representing Type Theories (1992)

Citations: | 5 - 0 self |

### BibTeX

@MISC{Gardner92equivalencesbetween,

author = {Philippa Gardner},

title = {Equivalences between Logics and their Representing Type Theories},

year = {1992}

}

### OpenURL

### Abstract

We propose a new framework 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. These definitions are possible since we are able to distinguish in a generic way that part of the LF + entailment which corresponds to the underlying logic. This distinction does not seem to be possible with other frameworks. Using our definitions, we show that, for example, natural deduction first-order logic can be well-represented in LF + , whereas linear and relevant logics cannot. We also show that our 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. 1 Introduction Much effort has been devoted to building systems for supporting the construction of f...