89 found
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  1.  53
    The Connectives.Lloyd Humberstone - 2011 - MIT Press.
    It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.This landmark work offers both ...
  2. Two Notions of Necessity.Martin Davies & Lloyd Humberstone - 1980 - Philosophical Studies 38 (1):1-31.
  3. Two-Dimensional Adventures.Lloyd Humberstone - 2004 - Philosophical Studies 118 (1-2):17--65.
    This paper recalls some applications of two-dimensional modal logic from the 1980s, including work on the logic of Actually and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity. There is some discussion of reactions this material has aroused in commentators since. We also survey related work by Leslie Tharp from roughly the same period.
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  4.  77
    The Revival of Rejective Negation.Lloyd Humberstone - 2000 - Journal of Philosophical Logic 29 (4):331-381.
    Whether assent ("acceptance") and dissent ("rejection") are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege's, rejectivism has undergone something of a revival in (...)
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  5.  82
    Parts and Partitions.Lloyd Humberstone - 2000 - Theoria 66 (1):41-82.
    Our object is to study the interaction between mereology and David Lewis’ theory of subject-matters, elaborating his observation that not every subject matter is of the form: how things stand with such-and-such a part of the world. After an informal introduction to this point in Section 1, we turn to a formal treatment of the partial orderings arising in the two areas – the part-whole relation, on the one hand, and the relation of refinement amongst partitions of the set of (...)
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  6.  40
    Contra-Classical Logics.Lloyd Humberstone - 2000 - Australasian Journal of Philosophy 78 (4):438 – 474.
    Only propositional logics are at issue here. Such a logic is contra-classical in a superficial sense if it is not a sublogic of classical logic, and in a deeper sense, if there is no way of translating its connectives, the result of which translation gives a sublogic of classical logic. After some motivating examples, we investigate the incidence of contra-classicality (in the deeper sense) in various logical frameworks. In Sections 3 and 4 we will encounter, originally as an example of (...)
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  7.  17
    The Modal Logic of Agreement and Noncontingency.Lloyd Humberstone - 2002 - Notre Dame Journal of Formal Logic 43 (2):95-127.
    The formula A (it is noncontingent whether A) is true at a point in a Kripke model just in case all points accessible to that point agree on the truth-value of A. We can think of -based modal logic as a special case of what we call the general modal logic of agreement, interpreted with the aid of models supporting a ternary relation, S, say, with OA (which we write instead of A to emphasize the generalization involved) true at a (...)
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  8. Modality.Lloyd Humberstone - 2005 - In Frank Jackson & Michael Smith (eds.), The Oxford Handbook of Contemporary Philosophy. Oxford University Press.
  9.  16
    Supervenience, Dependence, Disjunction.Lloyd Humberstone - forthcoming - Logic and Logical Philosophy:1.
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  10.  72
    Similarity Relations and the Preservation of Solidity.A. P. Hazen & Lloyd Humberstone - 2004 - Journal of Logic, Language and Information 13 (1):25-46.
    The partitions of a given set stand in a well known one-to-onecorrespondence with the equivalence relations on that set. We askwhether anything analogous to partitions can be found which correspondin a like manner to the similarity relations (reflexive, symmetricrelations) on a set, and show that (what we call) decompositions – of acertain kind – play this role. A key ingredient in the discussion is akind of closure relation (analogous to the consequence relationsconsidered in formal logic) having nothing especially to do (...)
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  11.  78
    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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  12. A Perspective on Modal Sequent Logic.Stephen Blamey & Lloyd Humberstone - 1991 - Publications of the Research Institute for Mathematical Sciences 27 (5):763-782.
  13.  17
    Smiley's Distinction Between Rules of Inference and Rules of Proof.Lloyd Humberstone - 2010 - In T. J. Smiley, Jonathan Lear & Alex Oliver (eds.), The Force of Argument: Essays in Honor of Timothy Smiley. Routledge. pp. 107--126.
  14.  36
    Sufficiency and Excess.Lloyd Humberstone - 2006 - Proceedings of the Aristotelian Society 106 (1):265-320.
    This paper assembles examples and considerations bearing on such questions as the following. Are statements to the effect that someone is too young (for instance) or that someone is old enough always to be understood in terms of someone's being too young or too old for such-and-such-for example, for them to join a particular organization? And when a 'such-and-such' has been specified, is it always at least tacitly modal in force-in the case just given, too young or old enough to (...)
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  15.  29
    Extensionality in Sentence Position.Lloyd Humberstone - 1986 - Journal of Philosophical Logic 15 (1):27 - 54.
  16.  22
    On a Conservative Extension Argument of Dana Scott.Lloyd Humberstone - 2011 - Logic Journal of the IGPL 19 (1):241-288.
    Exegesis, analysis and discussion of an argument deployed by Dana Scott in his 1973 paper ‘Background to Formalization’, rovide an ideal setting for getting clear about some subtleties in the apparently simple idea of conservative extension. There, Scott claimed in respect of two fundamental principles concerning implication that any generalized consequence relation respecting these principles is always extended conservatively by some similarly fundamental principles concerning conjunction and disjunction. This claim appears on the face of it to conflict with cases in (...)
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  17.  49
    Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness.Lloyd Humberstone - 2006 - Journal of Philosophical Logic 36 (1):1-32.
    The logic of 'elsewhere,' i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions, as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which (...)
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  18. Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau).Lloyd Humberstone - 2005 - Theoria 71 (3):241-262.
    We discuss aspects of the logic of negation bearing on an issue raised by Jean-Yves Béziau, recalled in §1. Contrary- and subcontrary-forming operators are introduced in §2, which examines some of their logical behaviour, leading on naturally to a consideration in §3 of dual intuitionistic negation (as well as implication), and some further operators related to intuitionistic negation. In §4, a historical explanation is suggested as to why some of these negation-related connectives have attracted more attention than others. The remaining (...)
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  19.  65
    Invitation to Autoepistemology.Lloyd Humberstone - 2002 - Theoria 68 (1):13-51.
    The phrase ‘autoepistemic logic’ was introduced in Moore [1985] to refer to a study inspired in large part by criticisms in Stalnaker [1980] of a particular nonmonotonic logic proposed by McDermott and Doyle.1 Very informative discussions for those who have not encountered this area are provided by Moore [1988] and the wide-ranging survey article Konolige [1994], and the scant remarks in the present introductory section do not pretend to serve in place of those treatments as summaries of the field. A (...)
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  20.  50
    Replacement in Logic.Lloyd Humberstone - 2013 - Journal of Philosophical Logic 42 (1):49-89.
  21.  24
    An Intriguing Logic with Two Implicational Connectives.Lloyd Humberstone - 2000 - Notre Dame Journal of Formal Logic 41 (1):1-40.
    Matthew Spinks [35] introduces implicative BCSK-algebras, expanding implicative BCK-algebras with an additional binary operation. Subdirectly irreducible implicative BCSK-algebras can be viewed as flat posets with two operations coinciding only in the 1- and 2-element cases, each, in the latter case, giving the two-valued implication truth-function. We introduce the resulting logic (for the general case) in terms of matrix methodology in §1, showing how to reformulate the matrix semantics as a Kripke-style possible worlds semantics, thereby displaying the distinction between the two (...)
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  22.  43
    Can Every Modifier Be Treated as a Sentence Modifier?Lloyd Humberstone - 2008 - Philosophical Perspectives 22 (1):241-275.
  23.  23
    Yet Another "Choice of Primitives" Warning: Normal Modal Logics.Lloyd Humberstone - 2004 - Logique Et Analyse 47.
  24.  34
    Note on Contraries and Subcontraries.Lloyd Humberstone - 2003 - Noûs 37 (4):690–705.
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  25. The Background of Circumstances.Lloyd Humberstone - 1983 - Pacific Philosophical Quarterly 64:19-34.
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  26.  12
    Sentence Connectives in Formal Logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
  27.  39
    The Pleasures of Anticipation: Enriching Intuitionistic Logic. [REVIEW]Lloyd Humberstone - 2001 - Journal of Philosophical Logic 30 (5):395-438.
    We explore a relation we call 'anticipation' between formulas, where A anticipates B (according to some logic) just in case B is a consequence (according to that logic, presumed to support some distinguished implicational connective →) of the formula A → B. We are especially interested in the case in which the logic is intuitionistic (propositional) logic and are much concerned with an extension of that logic with a new connective, written as "a", governed by rules which guarantee that for (...)
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  28.  40
    What Fa Says About A.Lloyd Humberstone - 2000 - Dialectica 54 (1):3–28.
    A sentence mentioning an object can be regarded as saying any one of several things about that object, without thereby being ambiguous. Some of the (logical) repercussions of this commonplace observation are recorded, and some critical discussion is provided of views which would appear to go against it.
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  29.  54
    Variation on a Trivialist Argument of Paul Kabay.Lloyd Humberstone - 2011 - Journal of Logic, Language and Information 20 (1):115-132.
    Impossible worlds are regarded with understandable suspicion by most philosophers. Here we are concerned with a modal argument which might seem to show that acknowledging their existence, or more particularly, the existence of some hypothetical (we do not say “possible”) world in which everything was the case, would have drastic effects, forcing us to conclude that everything is indeed the case—and not just in the hypothesized world in question. The argument is inspired by a metaphysical (rather than modal-logical) argument of (...)
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  30. Modal Formulas True at Some Point in Every Model.Lloyd Humberstone - 2008 - Australasian Journal of Logic 6:70-82.
    In a paper on the logical work of the Jains, Graham Priest considers a consequence relation, semantically characterized, which has a natural analogue in modal logic. Here we give a syntactic/axiomatic description of the modal formulas which are consequences of the empty set by this relation, which is to say: those formulas which are, for every model, true at some point in that model.
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  31.  86
    Plural Logic, by Alex Oliver and Timothy Smiley.Lloyd Humberstone - 2015 - Australasian Journal of Philosophy 93 (1):192-195.
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  32.  16
    Minimally Congruential Contexts: Observations and Questions on Embedding E in K.Lloyd Humberstone - 2012 - Notre Dame Journal of Formal Logic 53 (4):581-598.
    Recently, an improvement in respect of simplicity was found by Rohan French over extant translations faithfully embedding the smallest congruential modal logic (E) in the smallest normal modal logic (K). After some preliminaries, we explore the possibility of further simplifying the translation, with various negative findings (but no positive solution). This line of inquiry leads, via a consideration of one candidate simpler translation whose status was left open earlier, to isolating the concept of a minimally congruential context. This amounts, roughly (...)
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  33.  44
    Inverses for Normal Modal Operators.Lloyd Humberstone & Timothy Williamson - 1997 - Studia Logica 59 (1):33-64.
    Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended (...)
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  34.  13
    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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  35.  6
    Classically Archetypal Rules.Tomasz Połacik & Lloyd Humberstone - 2018 - Review of Symbolic Logic 11 (2):279-294.
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  36.  51
    Co-Instantiation and Identity.Lloyd Humberstone & Aubrey Townsend - 1994 - Philosophical Studies 74 (2):243 - 272.
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  37.  25
    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 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 some results according to which the pure sublogic in either of these connectives is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we show that for the pure logic of one of these (...)
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  38.  14
    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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  39.  30
    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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  40.  25
    Names and Pseudonyms.Lloyd Humberstone - 1995 - Philosophy 70 (274):487 - 512.
    Was there such a person as Lewis Carroll? An affirmative answer is suggested by the thought that Lewis Carroll was Charles Dodgson, and since there was certainly such a person as Charles Dodgson, there was such a person as Lewis Carroll. A negative answer is suggested by the thought that in arguing thus, the two names ‘Lewis Carroll’ and ‘Charles Dodgson’ are being inappropriately treated as though they were completely on a par: a pseudonym is, after all, a false or (...)
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  41.  33
    Partial Confirmation of a Conjecture on the Boxdot Translation in Modal Logic.Rohan French & Lloyd Humberstone - 2009 - Australasian Journal of Logic 7:56-61.
    The purpose of the present note is to advertise an interesting conjecture concerning a well-known translation in modal logic, by confirming a (highly restricted) special case of the conjecture.
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  42.  28
    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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  43.  13
    Collapsing Modalities.Lloyd Humberstone - 2009 - Notre Dame Journal of Formal Logic 50 (2):119-132.
    Sections 1 and 2 respectively raise and settle the question of whether, if an affirmative modality collapses (reduces to the null modality, that is) in a normal modal logic, then all modalities of the same length collapse in that logic, while Section 3 considers some special cases of an analogous phenomenon for congruential modal logics, closing with a general question about collapsing modalities in this broader range of logics.
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  44. Logical Pluralism.Lloyd Humberstone - 2009 - Australasian Journal of Philosophy 87 (1):162 – 168.
  45.  12
    Replacing Modus Ponens With One-Premiss Rules.Lloyd Humberstone - 2008 - Logic Journal of the IGPL 16 (5):431-451.
    After some motivating remarks in Section 1, in Section 2 we show how to replace an axiomatic basis for any one of a broad range of sentential logics having finitely many axiom schemes and Modus Ponens as the sole proper rule, by a basis with the same axiom schemes and finitely many one-premiss rules. Section 3 mentions some questions arising from this replacement procedure , explores another such procedure, and discusses some aspects of the consequence relations associated with the different (...)
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  46.  35
    James W. Garson, Modal Logic for Philosophers. Second Edition, Cambridge University Press, Cambridge, 2013, Pp. 506. ISBN: 978-1107609525 $44.99. [REVIEW]Lloyd Humberstone - 2016 - Studia Logica 104 (2):365-379.
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  47.  31
    Valuational Semantics of Rule Derivability.Lloyd Humberstone - 1996 - Journal of Philosophical Logic 25 (5):451 - 461.
    If a certain semantic relation (which we call 'local consequence') is allowed to guide expectations about which rules are derivable from other rules, these expectations will not always be fulfilled, as we illustrate. An alternative semantic criterion (based on a relation we call 'global consequence'), suggested by work of J.W. Garson, turns out to provide a much better - indeed a perfectly accurate - guide to derivability.
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  48.  28
    Investigations Into a Left-Structural Right-Substructural Sequent Calculus.Lloyd Humberstone - 2007 - Journal of Logic, Language and Information 16 (2):141-171.
    We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we (...)
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  49.  56
    Logical Relations.Lloyd Humberstone - 2013 - Philosophical Perspectives 27 (1):175-230.
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  50. Review of 'Multi-Dimensional Modal Logic'by Maarten Marx and Yde Venema. [REVIEW]Lloyd Humberstone - 2000 - Studia Logica 65:278-282.
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