Fer-Jan de Vries - Encoding many-valued logic in λ-calculus

lmcs:4900 - Logical Methods in Computer Science, June 29, 2021, Volume 17, Issue 2 - https://doi.org/10.46298/lmcs-17(2:25)2021
Encoding many-valued logic in λ-calculusArticle

Authors: Fer-Jan de Vries

    We will extend the well-known Church encoding of Boolean logic into λ-calculus to an encoding of McCarthy's 3-valued logic into a suitable infinitary extension of λ-calculus that identifies all unsolvables by , where is a fresh constant. This encoding refines to n-valued logic for n{4,5}. Such encodings also exist for Church's original λI-calculus. By way of motivation we consider Russell's paradox, exploiting the fact that the same encoding allows us also to calculate truth values of infinite closed propositions in this infinitary setting.


    Volume: Volume 17, Issue 2
    Published on: June 29, 2021
    Accepted on: March 31, 2021
    Submitted on: October 19, 2018
    Keywords: Computer Science - Logic in Computer Science,68Nxx, 03B50,F.4.1,K.2

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