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  1. Variations on a Theme of Curry.Lloyd Humberstone - 2006 - Notre Dame Journal of Formal Logic 47 (1):101-131.
    After an introduction to set the stage, we consider some variations on the reasoning behind Curry's Paradox arising against the background of classical propositional logic and of BCI logic and one of its extensions, in the latter case treating the "paradoxicality" as a matter of nonconservative extension rather than outright inconsistency. A question about the relation of this extension and a differently described (though possibly identical) logic intermediate between BCI and BCK is raised in a final section, which closes with (...)
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  • For Want of an ‘And’: A Puzzle about Non-Conservative Extension.Lloyd Humberstone - 2005 - History and Philosophy of Logic 26 (3):229-266.
    Section 1 recalls a point noted by A. N. Prior forty years ago: that a certain formula in the language of a purely implicational intermediate logic investigated by R. A. Bull is unprovable in that logic but provable in the extension of the logic by the usual axioms for conjunction, once this connective is added to the language. Section 2 reminds us that every formula is interdeducible with (i.e. added to intuitionistic logic, yields the same intermediate logic as) some conjunction-free (...)
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  • Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCSK Fragment of S5.Lloyd Humberstone - 2006 - Journal of Philosophical Logic 35 (5):435-487.
    We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we (...)
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  • Identical twins, deduction theorems, and pattern functions: Exploring the implicative BCsK fragment of S. [REVIEW]Lloyd Humberstone - 2007 - Journal of Philosophical Logic 36 (5):435 - 487.
    We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we (...)
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