Studia Logica

, Volume 94, Issue 2, pp 271–290 | Cite as

A Probability Measure for Partial Events

  • Maurizio NegriEmail author


We introduce the concept of partial event as a pair of disjoint sets, respectively the favorable and the unfavorable cases. Partial events can be seen as a De Morgan algebra with a single fixed point for the complement. We introduce the concept of a measure of partial probability, based on a set of axioms resembling Kolmogoroff’s. Finally we define a concept of conditional probability for partial events and apply this concept to the analysis of the two-slit experiment in quantum mechanics.


non-classical probability partial events partial logic quantum mechanics 


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  1. 1.
    Balbes, R., and P. Dwinger, Distributive Lattices, University of Missouri Press, 1974.Google Scholar
  2. 2.
    Blyth, T.S., and J.C.Varlet, Ockham Algebras, Oxford University Press, 1994.Google Scholar
  3. 3.
    Fine, A., ‘Some Conceptual Problems of Quantum Theory’, in R. A. Colodny (ed.), Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain, University of Pittsburgh Press, 1972.Google Scholar
  4. 4.
    Mundici D.: Averaging the truth-value in Łukasiewicz logic. Studia Logica 55, 1 (1995)CrossRefGoogle Scholar
  5. 5.
    Negri, M., An algebraic completeness proof for Kleene’s 3-valued logic, Boll. Un. Mat. Ital. (6), 5-B (2002), 447–67.Google Scholar
  6. 6.
    Negri M.: Kleene’s logic and De Morgan algebras. In: Ballo, E., Franchella, M. (eds) Logic and Philosophy in Italy, Polimetrica, Milano (2006)Google Scholar
  7. 7.
    Popper K.: Quantum Theory and the Schism in Physics. Hutchinson, London (1982)Google Scholar
  8. 8.
    Putnam, H., Philosophical Papers: Mathematics, Matter and Method, vol. 2, The Logic of Quantum Mechanics, Cambridge 1975, pp. 174–197.Google Scholar

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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dipartimento di FilosofiaUniversità degli Studi di TorinoTorinoItaly

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