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On Probability Domains III

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Abstract

Domains of generalized probability have been introduced in order to provide a general construction of random events, observables and states. It is based on the notion of a cogenerator and the properties of product. We continue our previous study and show how some other quantum structures fit our categorical approach. We discuss how various epireflections implicitly used in the classical probability theory are related to the transition to fuzzy probability theory and describe the latter probability theory as a genuine categorical extension of the former. We show that the IF-probability can be studied via the fuzzy probability theory. We outline a “tensor modification” of the fuzzy probability theory.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Roman Frič

  2. Catholic University in Ružomberok, Hrabovská cesta 1, 034 01, Ružomberok, Slovakia

    Roman Frič & Martin Papčo

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Martin Papčo

Authors
  1. Roman Frič
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  2. Martin Papčo
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Correspondence to Roman Frič.

Additional information

This work was supported by the Slovak Research and Development Agency [contract No. APVV-0178-11]; and Slovak Scientific Grant Agency [VEGA project 2/0046/11].

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Frič, R., Papčo, M. On Probability Domains III. Int J Theor Phys 54, 4237–4246 (2015). https://doi.org/10.1007/s10773-014-2471-4

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  • DOI: https://doi.org/10.1007/s10773-014-2471-4

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