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Abstract: In the "little theories" version of the axiomatic method, different portions of mathematics are developed in various different formal axiomatic theories. Axiomatic theories may be related by inclusion or by theory interpretation. We argue that the little theories approach is a desirable way to formalize mathematics, and we describe how imps, an Interactive Mathematical Proof System, supports it. (Update)
Context of citations to this paper: More
...more concrete theory, or an equally abstract theory, in a meaning preserving way. Interpretations enable the little theories method [27], in which mathematical knowledge and reasoning is distributed across a network of theories, to be applied to biform theories. EXAMPLE 6.1. Let...
.... of a specific mathematical structure in order to reason about complex Ontology Infrastructure for the Semantic Web problems [16]. They show the advantages of this modular approach in terms of reusability and reduced modelling effort. The idea of reusing and...
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BibTeX entry: (Update)
W. M. Farmer, J. D. Guttman, and F. J. Thayer. Little theories. In D. Kapur, editor, Proceedings of the Eleventh International Conference on Automated Deduction, volume 607 of Lecture Notes in Computer Science, pages 567--581. Springer Verlag, New York, 1992. http://citeseer.ist.psu.edu/farmer92little.html More
@inproceedings{ farmer92little,
author = "William M. Farmer and Joshua D. Guttman and F. Javier Thayer",
title = "Little Theories",
booktitle = "Conference on Automated Deduction",
pages = "567--581",
year = "1992",
url = "citeseer.ist.psu.edu/farmer92little.html" }
Citations (may not include all citations):370 A Mathematical Introduction to Logic (context) - Enderton - 1972
172 An introduction to the theory of lists (context) - Bird - 1986
99 imps: An Interactive Mathematical Proof System - Farmer, Guttman et al. - 1993
63 Basic Algebra (context) - Jacobson - 1985
60 Technical Report sri-csl (context) - Goguen, Winkler - 1988
53 A partial functions version of Church's simple theory of typ.. (context) - Farmer - 1990
52 Foundations of Modern Analysis (context) - Dieudonn - 1960
51 Principles of parameterized programming (context) - Goguen - 1987
24 A simple type theory with partial functions and subtypes (context) - Farmer - 1993
21 Structured theories in lcf (context) - Sannella, Burstall - 1983
18 Mathematical Logic (context) - Shoeneld - 1967
18 a specication language (context) - Burstall, Goguen et al. - 1980
17 Undecidable theories (context) - Tarski, Mostowski et al. - 1953
14 imps: System description - Farmer, Guttman et al. - 1992
13 The Foundations of Geometry (context) - Hilbert - 1902
13 Inference rules using local contexts (context) - Monk - 1988
12 Putting theories together to make speci- cations (context) - Burstall, Goguen - 1977
11 Structure and representation in LF (context) - Harper, Sannella et al. - 1989
7 Introduction to Axiomatic Set Theory (context) - Krivine - 1971
6 Digital Systems Research Center (context) - Guttag, Horning et al. - 1985
6 Two computer-supported proofs in metric space topology - Farmer, Thayer - 1991
6 A proposed interface logic for verication environments (context) - Guttman - 1991
5 The implementation and use of abstract theories in hol (context) - Gunter - 1990
5 The formalization of interpretability (context) - Visser - 1991
2 A lattice of interpretability types of theories (context) - Mycielski - 1977
2 A mathematical characterization of interpretation between th.. (context) - van Bentham, Pearce - 1984
2 An informal introduction to specications using Clear (context) - Burstall, Goguen - 1981
2 Interpretability of elementary theories (context) - Szczerba - 1977
1 Available by ftp from larch (context) - Garland, Guttag et al. - 1991
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://imps.mcmaster.ca/wmfarmer/publications.html): More
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