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Empty carriers: The categorical burden on logic

  • Bernd Mahr
Part 1: Fundamental Categorical Methods In Computer Science
Part of the Lecture Notes in Computer Science book series (LNCS, volume 393)

Abstract

The problems involved in the question whether or not to allow empty carriers in first order structures are discussed. Allowing empty carriers is convenient in algebra and category theory but puts a burden on logic: If truth evaluation of formulas is not considered to be partial (which creates an abundance of problems itself), anomalies in validity, truth, and deduction can not be avoided. Nevertheless, various approaches to first order logic with empty carriers allowed have been made. We discuss some of these and propose a new solution to the problem which, in a sense, mediates between the disadvantages found in the literature. We characterize deduction in terms of conventional deduction and show, how a correct and complete calculus for the conventional counterpart of a given first order specification logic can be adapted to remain correct and complete.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Bernd Mahr
    • 1
  1. 1.Fachbereich Informatik (20)Technische Universität BerlinGermany

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