Results 1 
5 of
5
Little Theories
 Automated DeductionCADE11, volume 607 of Lecture Notes in Computer Science
, 1992
"... 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 wa ..."
Abstract

Cited by 52 (16 self)
 Add to MetaCart
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.
Theory Interpretation in Simple Type Theory
 HIGHERORDER ALGEBRA, LOGIC, AND TERM REWRITING, VOLUME 816 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1993
"... Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admit ..."
Abstract

Cited by 36 (16 self)
 Add to MetaCart
Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admits partial functions and subtypes. The method is patterned on the standard approach to theory interpretation in rstorder logic. Although the method is based on a nonclassical version of simple type theory, it is intended as a guide for theory interpretation in classical simple type theories as well as in predicate logics with partial functions.
unknown title
, 1992
"... 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 ..."
Abstract
 Add to MetaCart
Abstract In the &quot;little theories &quot; 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.
SOME THEOREMS ON THE LATTlCE OF LOCAL INTERPRETABILITY TYPES by JAN KRAJÍÈEK in Prague (Czechoslova,kia)
"... In [4] J. MYCIELSKI introduced a very general notion of multidimensional local interpretability of first ordet theories. If we definethe relation ~ between theories T, S by T ~ S iff Tis multidimensionaly locally interpretable in S, then ~is a. preordering. The induced partia.l ordering is a la.ttic ..."
Abstract
 Add to MetaCart
In [4] J. MYCIELSKI introduced a very general notion of multidimensional local interpretability of first ordet theories. If we definethe relation ~ between theories T, S by T ~ S iff Tis multidimensionaly locally interpretable in S, then ~is a. preordering. The induced partia.l ordering is a la.ttice ordering, it is called tke lattice of