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Title: Set-theoretic approach to the concept of type.

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Technical Report
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Other Information: UNCL. Orig. Receipt Date: 30-JUN-73
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Country unknown/Code not available
N80600* -Mathematics & Computers; COMPUTERS; ERRORS; PROGRAMMING LANGUAGES; COMPUTERS/set-theoretic approach to concept of type

Citation Formats

Reynolds, J.C. Set-theoretic approach to the concept of type.. Country unknown/Code not available: N. p., 1969. Web.
Reynolds, J.C. Set-theoretic approach to the concept of type.. Country unknown/Code not available.
Reynolds, J.C. Wed . "Set-theoretic approach to the concept of type.". Country unknown/Code not available. doi:.
title = {Set-theoretic approach to the concept of type.},
author = {Reynolds, J.C.},
abstractNote = {},
doi = {},
journal = {},
number = ,
volume = ,
place = {Country unknown/Code not available},
year = {Wed Jan 01 00:00:00 EST 1969},
month = {Wed Jan 01 00:00:00 EST 1969}

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  • This report by Set Theoretic Information Systems, Inc., was prepared in partial fulfillment of their contractural obligations to the Data Management Research Project of the Lawrence Livermore Laboratory, in behalf of LLL-Contract (RA) 76-12 for the Transportation Systems Center of the U.S. Department of Transportation. The main contract explored efficient means to identify and analyze the large collections of historic data which document the transport of goods and people by ships, planes, trains, and trucks. One approach under consideration was the use of extended set theory and software developed by Set Theoretic Information Systems. In this report the author addressesmore » himself to seven tasks that range from a definition of the set-theoretic data manipulation concepts to the practical task of working with the CAB 586 Flight Service Segment Data Base.« less
  • Extended Set Theory as a data base management discipline has received attention in the data base literature. Set Theoretic Information Systems Corporation has, for some time, marketed a data base system based on the foundation of Extended Set Theory. This system is called Set Theoretic Data Structures (STDS). A series of examples shows that STDS is similar to relational algebraic data base management systems. The advantages of STDS are its straight-forward data base design, compact data representation, and flexible, powerful data manipulation operators, while its limitations are its low-level primitive user interface and the partial implementation of the Extended Setmore » Theoretic concepts. To make STDS very attractive, a ''user-friendly'' interface should be developed, and some distinctive features of extended Set Theory (such as sets of sets) should be implemented. 8 figures, 1 table.« less
  • A simple set of axioms is given for a class of subsets of an abstract set, Z, called ''intervals'', and an assigned ''measure'' for intervals, from which the basic theorems of measure theory are derived. Such a nontopological formulation is required in introducing a measure in a set of graphs, and was developed earlier for that purpose in a more complicated way. The theory is shown to apply to the set of all state vectors of an infinite hierarchical inference tree. 1 figure.
  • Successful regional water-resources planning involves an efficiency analysis to find the optimal system that maximizes benefits minus costs, and an equity analysis to apportion project costs. Traditionally, these two problems have been treated separately. A reliable total numerization procedure is used to find the optimal system for regional water-network problems. This procedure is easy to understand and can be implemented using readily available computer software; furthermore, more engineers can use realistic cost functions or perform detailed cost analysis and, also, examine good suboptimal systems. In addition, this procedure finds the optimal system for each individual and each subgroup of individuals;more » hence, an equity analysis can be accomplished using the theory of the core from cooperative n-person game theory on the optimal system as well as good suboptimal systems. A rigorous procedure using core conditions and linear programming is described to unambiguously measure an individual's minimum cost and maximum cost as a basis for the equitable cost allocation. Traditional approaches for quantifying minimum cost and maximum cost assume that either a regional system involving the grand coalition is built or all the individuals will go-it-alone.« less