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  1. Béziau's Translation Paradox.Lloyd Humberstone - 2005 - Theoria 71 (2):138-181.
    Jean-Yves Béziau (‘Classical Negation can be Expressed by One of its Halves’, Logic Journal of the IGPL 7 (1999), 145–151) has given an especially clear example of a phenomenon he considers a sufficiently puzzling to call the ‘paradox of translation’: the existence of pairs of logics, one logic being strictly weaker than another and yet such that the stronger logic can be embedded within it under a faithful translation. We elaborate on Béziau’s example, which concerns classical negation, as well as (...)
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  • Sentence connectives in formal logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
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  • Modal Logics That Are Both Monotone and Antitone: Makinson’s Extension Results and Affinities between Logics.Lloyd Humberstone & Steven T. Kuhn - 2022 - Notre Dame Journal of Formal Logic 63 (4):515-550.
    A notable early result of David Makinson establishes that every monotone modal logic can be extended to LI, LV, or LF, and every antitone logic can be extended to LN, LV, or LF, where LI, LN, LV, and LF are logics axiomatized, respectively, by the schemas □α↔α, □α↔¬α, □α↔⊤, and □α↔⊥. We investigate logics that are both monotone and antitone (hereafter amphitone). There are exactly three: LV, LF, and the minimum amphitone logic AM axiomatized by the schema □α→□β. These logics, (...)
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  • False though partly true – an experiment in logic.Lloyd Humberstone - 2003 - Journal of Philosophical Logic 32 (6):613-665.
    We explore in an experimental spirit the prospects for extending classical propositional logic with a new operator P intended to be interpreted when prefixed to a formula as saying that formula in question is at least partly true. The paradigm case of something which is, in the sense envisaged, false though still "partly" true is a conjunction one of whose conjuncts is false while the other is true. Ideally, we should like such a logic to extend classical logic - or (...)
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