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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... (Update)
Context of citations to this paper: More
.... framework can implement any (recursively enumerable) proof system, but the resulting encoding does not necessarily fit well (see [21], where a concept of a natural representation in a framework is formalized and investigated) e.g. Dunn [12] for relevance logics,...
.... framework can implement any (recursively enumerable) proof system, but the resulting encoding does not necessarily fit well (see [13], where a concept of a natural representation in a framework is formalized and investigated) tempts to build ND presentations of non...
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BibTeX entry: (Update)
P. A. Gardner. Equivalences between logics and their representing type theories. Technical Report ECS-LFCS-92-251, LFCS, Deptartment of Computer Science, University of Edinburgh, 1992. Submitted for publication. http://citeseer.ist.psu.edu/1320.html More
@book{ gardnerdidequivalences,
author = "Philippa Gardner",
title = "Equivalences between logics and their representing type theories",
volume = "ECS-LFCS-92-251 Notes: Includes bibliographical references Cover title",
publisher = "LFCS",
pages = "26p",
year = "Dept. of Computer Science",
url = "citeseer.ist.psu.edu/1320.html" }
Citations (may not include all citations):505 Implementing Mathematics with the NuPrl Proof Development Sy.. - Constable - 1986
419 A formulation of the simple theory of types (context) - Church - 1940
343 Modal Logic: an introduction (context) - Chellas - 1980
259 Combinatory Logic (context) - Curry, Feys - 1958
233 The Formulae-as-types Notion of Construction (context) - Howard - 1980
232 Category Theory for Computing Science (context) - Barr, Wells - 1990
191 LEGO Proof Development System: User's Manual (context) - Luo, Pollack - 1992
187 HOL: A Proof Generating System for Higher-Order Logic (context) - Gordon - 1987
101 Higher-order Logic Programming - Miller, Nadathur - 1986
79 Simple Consequence Relations - Avron - 1991
75 Using Typed Lambda Calculus to Implement Formal Systems on a.. - Avron, Honsell et al. - 1992
70 the Meanings of the Logical Constants and the Justifications.. (context) - Martin-Lof - 1985
66 Handbook of Logic in Computer Science (context) - Barendregt, with - 1992
34 Equality in Hyperdoctrines and Comprehension Schema as an Ad.. (context) - Lawvere - 1970
29 A Short Description of Another Logical Framework (context) - Augustsson, Coquand et al. - 1990
20 Abstract Families and the Adjoint Functor Theorems (context) - Par'e, Schumacher
19 Representing Logics in Type Theory (context) - Gardner - 1992
19 Journal of Theoretical Computer Science (context) - Girard - 1987
14 Fibred Categories and the Foundations of Naive Category Theo.. (context) - B'enabou - 1985
9 A Survey of the Project Automath (context) - de Bruijn - 1980
8 Handbook of Philosophical Logic (context) - Dunn, Entailment - 1984
6 long normal form in Type Systems of the Cube (context) - Dowek, Huet et al. - 1993
6 A New Type Theory for Representing Logics (context) - Gardner - 1993
5 The Church--Rosser Property for fij-reduction in Typed Lambd.. (context) - Geuvers - 1992
1 Preliminary version in the Proceedings of the Fourth Annual .. (context) - Harper, Sannella et al. - 1989
1 The Construction of fij-long normal forms in Dependent Type .. (context) - Gardner
1 Pym A Relevant Analysis of Natural Deduction (context) - Miller, Plotkin - 1992
1 Type dependence and constructive mathematics (context) - Beradi - 1990
1 Schematic Consequence - Aczel - 1992
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.cl.cam.ac.uk/users/pag20/): More
Graphical Presentations of Interactive Systems - Gardner (1999) (Correct)
Closed Action Calculi - Gardner (1998) (Correct)
Higher-Order and Reflexive Action Calculi: Their Type Theory .. - Gardner, Hasegawa (1998) (Correct)
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