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Logical fiberings and polycontextural systems

  • J. Pfalzgraf
Part II Selected Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 535)

Abstract

Based on the notion of abstract fiber spaces the concept of a logical fibering is developed. This was motivated by a project where so-called polycontextural logics were discussed. The fiber space approach provides a rather general framework for the modeling of such non classical logics. It gives the possibility to construct a variety of new logical spaces from a given (indexed) system of logics. These spaces are in some sense parallel (inference) systems. We can give a straight forward definition and classification of the so-called transjunctions arising in polycontextural logics. These are bivariate operations having values distributed over different logical subsystems. Univariate, bivariate operations are introduced in functional notation. The group generated by the generalized negation operations and system changes is investigated. We make some remarks on aspects of applicability and links to other work.

Keywords

Base Space Logical Space Fiber Space Input Pair Valuation Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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10 References

Selected Literature on Polycontextural Logic

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Literature on Categories, Logics, Fiberings

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    J.Pfalzgraf. Reasoning on a Möbius Strip. MEDLAR Newsletter No.1, Sept-Nov 1990, J.Cunningham, D.Gabbay, R. de Queiroz (eds.), Imperial College London.Google Scholar
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    J. Pfalzgraf. Representation of geometric spaces as Fibered Structures. Results in Math. Vol.12 (1987), 172–190 (in German).Google Scholar
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    J.Pfalzgraf. On Logical Fiberings and Polycontextural Systems. A First Approach. RISC-Linz Publ. Series No. 91–13.0 (1991).Google Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • J. Pfalzgraf
    • 1
  1. 1.RISC-Linz Johannes Kepler UniversityLinzAustria

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