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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 way to forma ..."
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Cited by 48 (15 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.
Reasoning Theories  Towards an Architecture for Open Mechanized Reasoning Systems
, 1994
"... : Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be ..."
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Cited by 47 (11 self)
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: Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies; and have different interaction capabilities. This paper makes two main contributions towards our goal. First, it proposes a general architecture for a class of reasoning systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a reasoning theory component which is the counterpart of the logical notion of formal system, a control component which consists of a set of inference strategies, and an interaction component which provides an OMRS with the capability of interacting with other systems, including OMRSs and hum...
Structured theory presentations and logic representations
 ANNALS OF PURE AND APPLIED LOGIC
, 1994
"... The purpose of a logical framework such as LF is to provide a language for defining logical systems suitable for use in a logicindependent proof development environment. All inferential activity in an object logic (in particular, proof search) is to be conducted in the logical framework via the ..."
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Cited by 14 (2 self)
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The purpose of a logical framework such as LF is to provide a language for defining logical systems suitable for use in a logicindependent proof development environment. All inferential activity in an object logic (in particular, proof search) is to be conducted in the logical framework via the representation of that logic in the framework. An important tool for controlling search in an object logic, the need for which is motivated by the difficulty of reasoning about large and complex systems, is the use of structured theory presentations. In this paper a rudimentary language of structured theory presentations is presented, and the use of this structure in proof search for an arbitrary object logic is explored. The behaviour of structured theory presentations under representation in a logical framework is studied, focusing on the problem of "lifting" presentations from the object logic to the metalogic of the framework. The topic of imposing structure on logic presentations...
Management of Change in Structured Verification
 In Proceedings 15th IEEE International Conference on Automated Software Engineering, number 2000 in ASE
, 2000
"... The use of formal methods in large complex applications implies the need for an evolutionary formal program development in which specification and verification phases are interleaved. But any change of a specification either by adding new parts or by changing erroneous parts affects existing verific ..."
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Cited by 14 (0 self)
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The use of formal methods in large complex applications implies the need for an evolutionary formal program development in which specification and verification phases are interleaved. But any change of a specification either by adding new parts or by changing erroneous parts affects existing verification work in a subtle way. In this paper we present a truth maintenance system for structured specification and verification. It is based on the simple but powerful notion of a development graph as an underlying datastructure to represent an actual consistent state of a formal development. Based on this notion we try to minimize the consequences of changes of existing verification work. 1. Introduction The application of formal methods in an industrial setting results in an increased complexity of the specification and the corresponding verification. It comprises on the one hand different layers of specifications reflecting the iterated process to refine the requirement specification towa...
Equivalences between Logics and their Representing Type Theories
, 1992
"... 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 abl ..."
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Cited by 5 (0 self)
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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 firstorder logic can be wellrepresented 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 typetheoretic and categorical approaches to frameworks. 1 Introduction Much effort has been devoted to building systems for supporting the construction of f...
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