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    Constant domain quantified modal logics without Boolean negation

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    Author
    RESTALL, GA
    Date
    2005
    Source Title
    The Australasian Journal of Logic
    Publisher
    Victoria University of Wellington
    University of Melbourne Author/s
    Restall, Gregory
    Affiliation
    Philosophy, Anthropology and Social Inquiry
    Metadata
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    Document Type
    Journal Article
    Citations
    RESTALL, G. A. (2005). Constant domain quantified modal logics without Boolean negation. Australasian Journal of Logic, 3, pp.45-62. https://doi.org/10.26686/ajl.v3i0.1772.
    Access Status
    This item is currently not available from this repository
    URI
    http://hdl.handle.net/11343/29126
    DOI
    10.26686/ajl.v3i0.1772
    Description

    C1 - Refereed Journal Article

    Abstract
    This paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a twoplace modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s presentation of the completeness proof quite closely [10]), but with an important twist, to do with the absence of Boolean negation.
    Keywords
    Philosophy

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