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32
Ontological Commitments in KnowledgeBased Design Software: A Progress Report
, 1999
"... The increased sensitivity of engineered products to external forces requires new computerbased design tools that can express the richness and complexity of product knowledge. This paper is a progress report of the author's research towards the development of such a knowledgebased design too ..."
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The increased sensitivity of engineered products to external forces requires new computerbased design tools that can express the richness and complexity of product knowledge. This paper is a progress report of the author's research towards the development of such a knowledgebased design tool, called the Design Knowledge Specification Language (DKSL). A key goal is to ensure the maximum possible logical rigor. In order to do this, ontological commitments are constructed to map logical structures to the domain of design knowledge. The first part of the paper discusses a number of ontological commitments the author has discovered for design. The second part of the paper presents the current, incomplete implementation of DKSL. An example of the structural and steadystate thermal analysis of a wall is used to present DKSL's capabilities. Although much work remains to be done, it appears that DKSL may be able to accurately and rigorously describe any design knowledge. Keywords: ...
An automated prover for ZermeloFraenkel set theory in Theorema
 In LMCS02
"... This paper presents some fundamental aspects of the design and the implementation of an automated prover for ZermeloFraenkel set theory within the wellknown Theorema system. The method applies the “ProveComputeSolve”paradigm as its major strategy for generating proofs in a natural style for sta ..."
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This paper presents some fundamental aspects of the design and the implementation of an automated prover for ZermeloFraenkel set theory within the wellknown Theorema system. The method applies the “ProveComputeSolve”paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.
Why sets?
 PILLARS OF COMPUTER SCIENCE: ESSAYS DEDICATED TO BORIS (BOAZ) TRAKHTENBROT ON THE OCCASION OF HIS 85TH BIRTHDAY, VOLUME 4800 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2008
"... Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic foundation of mathematics? Besi ..."
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Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic foundation of mathematics? Besides, set theory seems to play a significant role in computer science; is there a good justification for that? We discuss these and some related issues.
The Creation and Use of a Knowledge Base of Mathematical Theorems and Definitions
, 1995
"... IPR is an automatic theoremproving system intended particularly for use in higherlevel mathematics. It discovers the proofs of theorems in mathematics applying known theorems and definitions. Theorems and definitions are stored in the knowledge base in the form of sequents rather than formulas or ..."
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IPR is an automatic theoremproving system intended particularly for use in higherlevel mathematics. It discovers the proofs of theorems in mathematics applying known theorems and definitions. Theorems and definitions are stored in the knowledge base in the form of sequents rather than formulas or rewrite rules. Because there is more easilyaccessible information in a sequent than there is in the formula it represents, a simple algorithm can be used to search the knowledge base for the most useful theorem or definition to be used in the theoremproving process. This paper describes how the sequents in the knowledge base are formed from theorems stated by the user and how the knowledge base is used in the theoremproving process. An example of a theorem proved and the English proof output are also given.
Formalizing Automata II: Decidable Properties
"... Is it possible to create formal proofs of interesting mathematical theorems which are mechanically checked in every detail and yet are readable and even faithful to the best expositions of those results in the literature? This paper answers that question positively for theorems about decidable prope ..."
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Is it possible to create formal proofs of interesting mathematical theorems which are mechanically checked in every detail and yet are readable and even faithful to the best expositions of those results in the literature? This paper answers that question positively for theorems about decidable properties of nite automata. The exposition is from Hopcroft and Ullman's classic 1969 textbook Formal Languages and Their Relation to Automata. This paper describes a successful formalization which is faithful to that book. The requirement of being faithful to the book has unexpected consequences, namely that the underlying formal theory must include primitive notions of computability. This requirement makes a constructive formalization especially suitable. It also opens the possibility ofusingthe formal proofs to decide properties of automata. The paper shows how to do this. 1
ΩMKRP: A Proof Development Environment
 PROCEEDINGS OF THE 12TH CADE
, 1994
"... In the following we describe the basic ideas underlying\Omega\Gamma mkrp, an interactive proof development environment [6]. The requirements for this system were derived from our experiences in proving an interrelated collection of theorems of a typical textbook on semigroups and automata [3] wi ..."
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In the following we describe the basic ideas underlying\Omega\Gamma mkrp, an interactive proof development environment [6]. The requirements for this system were derived from our experiences in proving an interrelated collection of theorems of a typical textbook on semigroups and automata [3] with the firstorder theorem prover mkrp [11]. An important finding was that although current automated theorem provers have evidently reached the power to solve nontrivial problems, they do not provide sufficient assistance for proving the theorems contained in such a textbook. On account of this, we believe that significantly more support for proof development can be provided by a system with the following two features:  The system must provide a comfortable humanoriented problemsolving environment. In particular, a human user should be able to specify the problem to be solved in a natural way and communicate on proof
Adding Enrichments to Refined Interleavings: A New Model for the πCalculus
, 1999
"... The question of how to model πcalculus name passing has attracted significant interest. Here, this topic is approached with a new fully abstract interleaving model. Its central feature: Every semantic object contains all its transformations under injective name replacements. It is shown how this en ..."
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The question of how to model πcalculus name passing has attracted significant interest. Here, this topic is approached with a new fully abstract interleaving model. Its central feature: Every semantic object contains all its transformations under injective name replacements. It is shown how this enrichment can be used, in a systematic way, to obtain compositional interpretations of the constructors of the πcalculus. The theory of nonwellfounded sets serves as the mathematical basis. Moreover, category theory is used in the form of coalgebras of endofunctors. Not more is needed since transformations under name replacements are not regarded as arrows of a category of partial orders of (unenriched) semantic objects. This approach is a hallmark of previous interleaving models of the πcalculus. It seems to require a lot more category theory than is used here. Also, unlike other related work, the present one does not employ type theory.
SET THEORY FROM CANTOR TO COHEN
"... Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions and gauging their consistency strength. But set theory is also distinguished by having begun int ..."
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Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, set theory has proceeded in the opposite direction, from a web of intensions to a theory of extension par excellence, and like other fields of mathematics its vitality and progress have depended on a steadily growing core of mathematical proofs and methods, problems and results. There is also the stronger contention that from the beginning set theory actually developed through a progression of mathematical moves, whatever and sometimes in spite of what has been claimed on its behalf. What follows is an account of the development of set theory from its beginnings through the creation of forcing based on these contentions, with an avowedly Whiggish emphasis on the heritage that has been retained and developed by the current theory. The