Explicitly Epistemic Contraction by Predicate Abstraction in Automated Theorem Finding: A Case Study in NBG Set Theory

2015 ◽  
pp. 593-602 ◽  
Author(s):  
Hongbiao Gao ◽  
Yuichi Goto ◽  
Jingde Cheng
Keyword(s):  
Set Theory ◽  
Predicate Abstraction

Fuzzy Miner

2011 ◽  
pp. 299-321 ◽  
Author(s):  
Nikos Pelekis ◽  
Babis Theodoulidis ◽  
Ioannis Kopanakis ◽  
Yannis Theodoridis
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Attribute Selection ◽  
Internet Routing ◽  
Data Mining Approach ◽  
New Information

QOSP Quality of Service Open Shortest Path First based on QoS routing has been recognized as a missing piece in the evolution of QoS-based services in the Internet. Data mining has emerged as a tool for data analysis, discovery of new information, and autonomous decision-making. This paper focuses on routing algorithms and their appli-cations for computing QoS routes in OSPF protocol. The proposed approach is based on a data mining approach using rough set theory, for which the attribute-value system about links of networks is created from network topology. Rough set theory offers a knowledge discovery approach to extracting routing-decisions from attribute set. The extracted rules can then be used to select significant routing-attributes and make routing-selections in routers. A case study is conducted to demonstrate that rough set theory is effective in finding the most significant attribute set. It is shown that the algorithm based on data mining and rough set offers a promising approach to the attribute-selection prob-lem in internet routing.

V = L and Intuitive Plausibility in set Theory. A Case Study

2011 ◽  
Vol 17 (3) ◽  
pp. 337-360 ◽  
Author(s):  
Tatiana Arrigoni
Keyword(s):  
Set Theory ◽  
Critical Appraisal ◽  
Philosophy Of Mathematics ◽  
Epistemic Status ◽  
Contemporary Philosophy ◽  
Methodological Principles

AbstractWhat counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of set theoretic axioms and theorems formulated in non-strictly mathematical terms, e.g., by appealing to the iterative concept of set and/or to overall methodological principles, like unify and maximize, and investigate the relation of the latter to success in mathematics.

scholarly journals Experiments with ZF Set Theory in HOL and Isabelle

1995 ◽  
Vol 2 (37) ◽  
Author(s):  
Sten Agerholm ◽  
Mike Gordon
Keyword(s):  
Set Theory ◽  
Lambda Calculus ◽  
General Purpose ◽  
Higher Order ◽  
Proof Assistants ◽  
Higher Order Logic ◽  
First Order ◽  
Advantages And Disadvantages ◽  
Theory Versus

Most general purpose proof assistants support versions of<br />typed higher order logic. Experience has shown that these logics are capable<br />of representing most of the mathematical models needed in Computer<br />Science. However, perhaps there exist applications where ZF-style<br />set theory is more natural, or even necessary. Examples may include<br />Scott's classical inverse-limit construction of a model of the untyped lambda-calculus<br /> (D_inf) and the semantics of parts of the Z specification notation.<br /><br />This paper compares the representation and use of ZF set theory within<br />both HOL and Isabelle. The main case study is the construction of D_inf.<br />The advantages and disadvantages of higher-order set theory versus first-order<br />set theory are explored experimentally. This study also provides a<br />comparison of the proof infrastructure of HOL and Isabelle.

Representation and Interpretation of Sketches in Mechanical Design: Experimental and Theoretical Approaches

2003 ◽  
Author(s):  
Y. Zeng ◽  
A. Pardasani ◽  
H. Antunes ◽  
Z. Li ◽  
J. Dickinson ◽  
...  
Keyword(s):  
Design Process ◽  
Set Theory ◽  
Experimental Approach ◽  
Theoretical Foundation ◽  
Mechanical Design ◽  
Mathematical Structure ◽  
Assembly System ◽  
Automobile Assembly ◽  
Theoretical Approaches

This paper aims to establish a theoretical foundation for representing and interpreting free-hand design sketches throughout the conceptual design process. Both experimental and theoretical approaches are used. In using the experimental approach, one case study from a book and one case study from an automobile assembly system manufacturer are used to illustrate the characteristics of design sketches. These characteristics provide the requirements for models of sketch representation and interpretation. In using the theoretical approach, a mathematical structure of design sketches is established. This mathematical structure can naturally and logically model the evolving sketches generated in the design process, through integrating the strengths of set theory and mereology. Based on the results of these two approaches, a design sketch language is developed to be a formal foundation of sketch representation and interpretation.

Distribution Signals between the Transmitter and Antenna – Event B Model

2017 ◽  
pp. 179-217
Author(s):  
Ivo Lazar ◽  
Said Krayem ◽  
Denisa Hrušecká
Keyword(s):  
Mathematical Modelling ◽  
Set Theory ◽  
Abstract Machine ◽  
Local Conditions ◽  
Digital Video Broadcasting ◽  
Video Broadcasting ◽  
Useful Signal ◽  
To Receive ◽  
Event B Method

What we have solved: the possibility to receive DVB-T (Digital Video Broadcasting Terrestrial) with respect to local conditions for signal. We have deduced: variables that represent a set of so-called useful signal, i.e. the signal suitable for further processing – amplification and distribution. As a case study we have choosed few examples using Event B Method to show possibilty of solving komplex projects by this method. The resulting program can be proven to be correct as for its theoretical backgrounds. It is based on Zermelo-Fraenkel set theory with axion of choice, the concept of generalized substitution and structuring mechanismus (machine, refinement, implementation). B methods are accompanied by mathematical proofs that justify them. Abstract machine in this example connected with mathematical modelling solves an ability to receive DVB-T signal from the plurality of signals, both useful and useless for further processing.

scholarly journals Reliability-Based Multidisciplinary Design Optimization under Correlated Uncertainties

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Huanwei Xu ◽  
Xin Wang ◽  
Wei Li ◽  
Mufeng Li ◽  
Suichuan Zhang ◽  
...  
Keyword(s):  
Design Optimization ◽  
Set Theory ◽  
Multidisciplinary Design Optimization ◽  
Reliability Assessment ◽  
Multidisciplinary Design ◽  
Sequential Optimization ◽  
Engineering System ◽  
First Order ◽  
Reliability Method

Complex mechanical system is usually composed of several subsystems, which are often coupled with each other. Reliability-based multidisciplinary design optimization (RBMDO) is an efficient method to design such complex system under uncertainties. However, the present RBMDO methods ignored the correlations between uncertainties. In this paper, through combining the ellipsoidal set theory and first-order reliability method (FORM) for multidisciplinary design optimization (MDO), characteristics of correlated uncertainties are investigated. Furthermore, to improve computational efficiency, the sequential optimization and reliability assessment (SORA) strategy is utilized to obtain the optimization result. Both a mathematical example and a case study of an engineering system are provided to illustrate the feasibility and validity of the proposed method.

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