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An Axiomatic Theory of Engineering Design Information
 ENGINEERING WITH COMPUTERS
, 1992
"... Recent research in design theory has sought to formalize the engineering design process without particular concern for the paradigm used to model design information. The authors propose that no correct formalization of the design process can be achieved without first formalizing the semantics of the ..."
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Recent research in design theory has sought to formalize the engineering design process without particular concern for the paradigm used to model design information. The authors propose that no correct formalization of the design process can be achieved without first formalizing the semantics of the information used in the process. To this end, the authors present a new formal theory of design information. The theory, called the Hybrid Model, is an extended form of axiomatic set theory, and relies on it for consistency and logical rigor. The theory is stated as a collection of axioms, using a standard logic notation. Design entities are modeled by formal units called objects. Generalized functions and relations are used to formalize important ordering schemes and abstraction mechanisms relevant to design, including classification by structure and by function, aggregation, specialization and generalization. The hybrid model is meant not only to aid in the study of the design process itself, but also to improve communications between designers, assist standardization of design specifications, and develop new, powerful software tools to aid the designer in his work.
An ArtifactCentered Framework for Modeling Engineering Design
, 1995
"... Successful systems that govern the overall operation of enterprises that conduct concurrent engineering (CE) will integrate all the various aspects of product design and manufacture. Since production of an artifact is the raison d'etre of an engineering enterprise, it follows that consideratio ..."
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Cited by 4 (2 self)
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Successful systems that govern the overall operation of enterprises that conduct concurrent engineering (CE) will integrate all the various aspects of product design and manufacture. Since production of an artifact is the raison d'etre of an engineering enterprise, it follows that consideration of the artifact should be at the heart of any successful CE framework. This paper introduces a logical, ArtifactCentered Modeling framework (ACM), intended to provide a systematic framework to describe and synthesize the systems of an engineering enterprise so that all relevant aspects and relationships between those aspects are accounted for. ACM addresses four functional domains: artifact systems, design systems, engineering management systems, and the environment in which all other domains exist. The framework is constructed from four kinds of building blocks: systems models, modeling languages, and formal language theories. Furthermore, three different, but complementary, perspectives (nam...
Models Of SecondOrder Zermelo Set Theory
, 1999
"... The paper discusses models of secondorder versions of Zermelo set theory that are not given by certain initial segments of the cumulative hierarchy. These models show that common versions of infinity do not, absent replacement, guarantee the existence of the first transfinite stage of the cumulativ ..."
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The paper discusses models of secondorder versions of Zermelo set theory that are not given by certain initial segments of the cumulative hierarchy. These models show that common versions of infinity do not, absent replacement, guarantee the existence of the first transfinite stage of the cumulative hierarchy. Another construction shows that a version of secondorder Zermelo set theory that results when infinity is strengthened to deliver the existence of that stage is satisfied in nonwellfounded models. A variant of secondorder Zermelo set theory is considered all of whose models are given by certain initial segments of the hierarchy.
A New Programming Paradigm for Engineering Design Software
, 1994
"... Currently available programming and database systems are insufficient for engineering applications. The authors contend that a logical progression from a formal conceptual model of the engineering domain to a computational model will lead to new programming paradigms capable of directly supporting e ..."
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Cited by 3 (3 self)
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Currently available programming and database systems are insufficient for engineering applications. The authors contend that a logical progression from a formal conceptual model of the engineering domain to a computational model will lead to new programming paradigms capable of directly supporting engineering applications in a rigorous, concise manner. A formal domain model devised by the authors, the Hybrid Model (HM) of design information, is briefly introduced. It is an extension of axiomatic set theory and is discussed in detail elsewhere. HM forms the basis of Designer, a prototypebased objectoriented programming language supporting a signaturebased canonical message passing mechanism and multiple inheritance. Designer is implemented using the Scheme programming language. Because Designer satisfies a formal conceptual model, and because it is based on a formally specified language, its robustness and logical validity is superior to that of other languages not founded on formal ...
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.
Towards a New Computational Model for Engineering Software Systems
, 1993
"... Currently available programming and database systems are insufficient for engineering applications. The authors contend that a logical progression from a formal conceptual domain model of engineering to a computational model will lead to new software systems capable of supporting design applications ..."
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Currently available programming and database systems are insufficient for engineering applications. The authors contend that a logical progression from a formal conceptual domain model of engineering to a computational model will lead to new software systems capable of supporting design applications in a rigorous, concise manner. A formal domain model devised by the authors, the Hybrid Model (HM) of design information, is briefly introduced. HM is the foundation of Designer, an extension to the Scheme programming language, developed by the authors and presented herein. Designer combines concepts of functional programming and objectorientation to provide the formal rigor and flexibility required in design. Examples demonstrate how this approach impacts on design information modeling. The results of the authors' research with Designer indicate that it can be used to capture design information in an effective and efficient manner. Because Designer satisfies a formal conceptual model (HM)...
How to release Frege’s system from Russell’s antinomy. Abstract presented at 2006
 ASL European Summer Meeting  Logic Colloquium 2006, July 27  August 2
"... Abstract. The conditions for proper definitions in mathematics are given, in terms of the theory of definition, on the basis of the criterions of eliminability and noncreativity. As a definition, Russell’s antinomy is a violation of the criterion of eliminability (Behmann, 1931, [1]; Bochvar, 1943, ..."
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Abstract. The conditions for proper definitions in mathematics are given, in terms of the theory of definition, on the basis of the criterions of eliminability and noncreativity. As a definition, Russell’s antinomy is a violation of the criterion of eliminability (Behmann, 1931, [1]; Bochvar, 1943, [2]). Following the path of the criterion of noncreativity, this paper develops a new analysis of Comprehension schema and, as a consequence, proof that Russell’s antinomy argumentation, despite the words of Frege himself, does not hold in Grundgesetze der Arithmetik. According to Basic Law (III), the class of classes not belonging to themselves is a class defined by a function which can not take as argument its own course of value, „ “ g ⌣ ` ´ ∀ = `ε `ε ( g(ε)) = ε → g(ε) ”« in other words, the class of classes not belonging to themselves is a class whose classes are not identical to the class itself [6].
A Research Program in Design Theory and Computation
, 1993
"... this paper will present a brief overview and status report of the authors' efforts. Each of the three design theoretic tools in figure 1 will be covered in turn. THEORETICAL FOUNDATIONS ..."
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this paper will present a brief overview and status report of the authors' efforts. Each of the three design theoretic tools in figure 1 will be covered in turn. THEORETICAL FOUNDATIONS
On the Use of Impredicative Reasoning to Construct a Class of Partial Models of ZF Within ZF
, 2008
"... Gödel’s incompleteness results show that if ZF is consistent, it is impossible to construct within ZF itself a single object (set) that represents a complete and precise semantic model of ZF. Nevertheless, it has also become clear since then that many kinds of partial models can be constructed withi ..."
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Gödel’s incompleteness results show that if ZF is consistent, it is impossible to construct within ZF itself a single object (set) that represents a complete and precise semantic model of ZF. Nevertheless, it has also become clear since then that many kinds of partial models can be constructed within ZF that reveal interesting characteristics of ZF and related formal systems. We develop here one particular class of partial models of ZF, which rely on an extreme form of impredicative reasoning that nevertheless follow the accepted rules of set theory and firstorder logic and are constructible within exactly the same variant of ZF as the one being modelled. Some study of these partial models yields interesting results.
BEYOND UNCOUNTABLE
, 2003
"... ... The fact is that such a procedure is not applicable. Why? Because their definitions are not predicative and contain within such a vicious circle I already mentioned above; not predicative definitions can not be substituted to defined terms. In this condition, logistics is no longer sterile: it g ..."
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... The fact is that such a procedure is not applicable. Why? Because their definitions are not predicative and contain within such a vicious circle I already mentioned above; not predicative definitions can not be substituted to defined terms. In this condition, logistics is no longer sterile: it generates contradictions. (JulesHenri Poincaré 1902, [10] 211, our translation.) Introduction. By common consent Russell’s antinomy is the reason for which in Zermelo–Fraenkel set theory, there is no set which comprehends all sets. Furthermore, given any set A, there is no set which contains all sets which are not members of A (in particular, there is no set which is the complement of A) ([7] 4041). In other words, given any set A, the absolute complement of A, i.e. {x  x / ∈ A}, cannot