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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 ..."
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Cited by 56 (17 self)
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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.
Two computersupported proofs in metric space topology
 Notices of the American Mathematical Society
, 1991
"... Every mathematician will agree that the discovery, analysis, and communication ..."
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Cited by 8 (3 self)
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Every mathematician will agree that the discovery, analysis, and communication
Integrating External Deduction Tools with ACL2
 Sutcliffe (Eds.), Proceedings of the 6th International Workshop on Implementation of Logics (IWIL 2006
, 2006
"... We present an interface connecting the ACL2 theorem prover with external deduction tools. The logic of ACL2 contains several constructs intended to facilitate structuring of interactive proof development, which complicates the design of such an interface. We discuss some of these complexities and de ..."
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Cited by 7 (5 self)
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We present an interface connecting the ACL2 theorem prover with external deduction tools. The logic of ACL2 contains several constructs intended to facilitate structuring of interactive proof development, which complicates the design of such an interface. We discuss some of these complexities and develop a precise specification of the requirements from external tools for sound connection with ACL2. We also develop constructs within ACL2 to enable the developers of external tools to satisfy our specifications. 1
The Role of Automated Reasoning in Integrated System Verification Environments
, 1992
"... in this document are those of the author(s) and should not be interpreted as representing the official policies, either ..."
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Cited by 3 (2 self)
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in this document are those of the author(s) and should not be interpreted as representing the official policies, either
Should We Begin a Standardization Process for Interface Logics?
, 1992
"... this document are those of the author(s) and should not be interpreted as representing the official policies, either expressed or implied, of Computational Logic, Inc., the Defense Advanced Research Projects Agency or the U.S. Government. ..."
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Cited by 2 (2 self)
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this document are those of the author(s) and should not be interpreted as representing the official policies, either expressed or implied, of Computational Logic, Inc., the Defense Advanced Research Projects Agency or the U.S. Government.
A General Method for Safely Overwriting Theories in Mechanized Mathematics Systems
 Lecture Notes in Computer Science (Proc. Intl. Zurich Sem. Digital Comm.). Spinger
, 1994
"... We propose a general method for overwriting theories with model conservative extensions in mechanized mathematics systems. Model conservative extensions, which include the denition of new constants and the introduction of new abstract datatypes, are \safe" because they preserve models as we ..."
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We propose a general method for overwriting theories with model conservative extensions in mechanized mathematics systems. Model conservative extensions, which include the denition of new constants and the introduction of new abstract datatypes, are \safe" because they preserve models as well as consistency. The method employs the notions of theory interpretation and theory instantiation. It is illustrated using manysorted rstorder logic, but it works for a variety of underlying logics. Supported by the MITRESponsored Research program. 1 1 Introduction Mathematical reasoning is always performed in some mathematical context consisting of vocabulary and assumptions. The formal counterpart of a context is a theory consisting of a formal language plus a set of sentences of the language called axioms. (We will denote a theory T by the pair (L; ) where L is the formal language of T and is the set of axioms of T .) An extension of a theory T is any theory T 0 obtained by ...
Position Paper: Should we begin a standardization process for Interface Logics
, 1992
"... in this document are those of the author(s) and should not be interpreted as representing the official policies, either expressed or implied, of Computational Logic, Inc., the ..."
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Cited by 1 (0 self)
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in this document are those of the author(s) and should not be interpreted as representing the official policies, either expressed or implied, of Computational Logic, Inc., the
Technical Report 72 January, 1992
, 1992
"... this document are those of the author(s) and should not ..."
Open Mechanized Reasoning Systems
, 1992
"... Contents Project Summary . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . Our previous work in mechanized reasoning systems . . . . . . . Existing reasoning systems . . . . . . . . . . . . . . . Existing logical frameworks . . . . . . . . . . . . . . Open mechani ..."
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Contents Project Summary . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . Our previous work in mechanized reasoning systems . . . . . . . Existing reasoning systems . . . . . . . . . . . . . . . Existing logical frameworks . . . . . . . . . . . . . . Open mechanized reasoning systems . . . . . . . . . . . . Project Description . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accomplishments of Previous NSF Support . . . . . . . . . . Budget Pages . . . . . . . . . . . . . . . . . . . Biography of McCarthy . . . . . . . . . . . . . . . . Biography of Giunchiglia . . . . . . . . . . . . . . . Biography of Talcott . . . . . . . . . . . . . . . . i 1. Project summary There is a growing interest in the interconnection and integration of reasoning modules and systems. For example, developers of hardware veri