94 found
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  1.  70
    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 ...
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  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. Philosophical Applications of Modal Logic.Lloyd Humberstone - 2016 - College Publications.
  5.  95
    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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  6.  40
    Supervenience, Dependence, Disjunction.Lloyd Humberstone - forthcoming - Logic and Logical Philosophy:1.
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  7. Plural Logic, by Alex Oliver and Timothy Smiley: Oxford: Oxford University Press, 2013, Pp. Xiv + 336, £40. [REVIEW]Lloyd Humberstone - 2015 - Australasian Journal of Philosophy 93 (1):192-195.
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  8.  5
    Power Matrices and Dunn--Belnap Semantics: Reflections on a Remark of Graham Priest.Lloyd Humberstone - 2014 - Australasian Journal of Logic 11 (1).
    The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices whose underlying algebras are power algebras, where the power algebra of a given algebra has as elements textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis of (...)
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  9. 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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  10.  54
    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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  11. 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.  21
    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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  13. Modality.Lloyd Humberstone - 2005 - In Frank Jackson & Michael Smith (eds.), The Oxford Handbook of Contemporary Philosophy. Oxford University Press.
  14. A Perspective on Modal Sequent Logic.Stephen Blamey & Lloyd Humberstone - 1991 - Publications of the Research Institute for Mathematical Sciences 27 (5):763-782.
  15. Sentence Connectives in Formal Logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
  16.  70
    Logical Relations.Lloyd Humberstone - 2013 - Philosophical Perspectives 27 (1):175-230.
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  17.  38
    Extensionality in Sentence Position.Lloyd Humberstone - 1986 - Journal of Philosophical Logic 15 (1):27 - 54.
  18.  77
    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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  19. 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.
     
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  20.  14
    Classically Archetypal Rules.Tomasz Połacik & Lloyd Humberstone - 2018 - Review of Symbolic Logic 11 (2):279-294.
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  21.  44
    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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  22. 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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  23. 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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  24.  72
    Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness.Lloyd Humberstone - 2007 - 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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  25.  39
    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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  26.  74
    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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  27.  33
    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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  28.  67
    Can Every Modifier Be Treated as a Sentence Modifier?Lloyd Humberstone - 2008 - Philosophical Perspectives 22 (1):241-275.
  29.  31
    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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  30.  79
    Lloyd Humberstone.Lloyd Humberstone - 2006 - Aristotelian Society Supplementary Volume 80 (1):265–320.
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  31.  44
    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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  32.  31
    Aggregation and Idempotence.Lloyd Humberstone - 2013 - Review of Symbolic Logic 6 (4):680-708.
    A 1-ary sentential context is aggregative (according to a consequence relation) if the result of putting the conjunction of two formulas into the context is a consequence (by that relation) of the results of putting first the one formula and then the other into that context. All 1-ary contexts are aggregative according to the consequence relation of classical propositional logic (though not, for example, according to the consequence relation of intuitionistic propositional logic), and here we explore the extent of this (...)
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  33.  32
    Zolin and Pizzi: Defining Necessity From Noncontingency.Lloyd Humberstone - 2013 - Erkenntnis 78 (6):1275-1302.
    The point of the present paper is to draw attention to some interesting similarities, as well as differences, between the approaches to the logic of noncontingency of Evgeni Zolin and of Claudio Pizzi. Though neither of them refers to the work of the other, each is concerned with the definability of a (normally behaving, though not in general truth-implying) notion of necessity in terms of noncontingency, standard boolean connectives and additional but non-modal expressive resources. The notion of definability involved is (...)
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  34.  27
    Explicating Logical Independence.Lloyd Humberstone - 2020 - Journal of Philosophical Logic 49 (1):135-218.
    Accounts of logical independence which coincide when applied in the case of classical logic diverge elsewhere, raising the question of what a satisfactory all-purpose account of logical independence might look like. ‘All-purpose’ here means: working satisfactorily as applied across different logics, taken as consequence relations. Principal candidate characterizations of independence relative to a consequence relation are that there the consequence relation concerned is determined by only by classes of valuations providing for all possible truth-value combinations for the formulas whose independence (...)
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  35.  25
    Note on Extending Congruential Modal Logics.Lloyd Humberstone - 2016 - Notre Dame Journal of Formal Logic 57 (1):95-103.
    It is observed that a consistent congruential modal logic is not guaranteed to have a consistent extension in which the Box operator becomes a truth-functional connective for one of the four one-place truth functions.
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  36.  30
    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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  37.  38
    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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  38. Logical Discrimination.Lloyd Humberstone - unknown
     
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  39.  5
    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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  40.  56
    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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  41. The Background of Circumstances.Lloyd Humberstone - 1983 - Pacific Philosophical Quarterly 64:19-34.
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  42.  38
    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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  43.  11
    I—Lloyd Humberstone.Lloyd Humberstone - 2006 - Aristotelian Society Supplementary Volume 80 (1):265-320.
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  44.  44
    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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  45.  43
    Note on Supervenience and Definability.Lloyd Humberstone - 1998 - Notre Dame Journal of Formal Logic 39 (2):243-252.
    The idea of a property's being supervenient on a class of properties is familiar from much philosophical literature. We give this idea a linguistic turn by converting it into the idea of a predicate symbol's being supervenient on a set of predicate symbols relative to a (first order) theory. What this means is that according to the theory, any individuals differing in respect to whether the given predicate applies to them also differ in respect to the application of at least (...)
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  46.  87
    Intuitionistic Logic and Elementary Rules.Lloyd Humberstone & David Makinson - 2011 - Mind 120 (480):1035-1051.
    The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and intuitionistic consequence satisfy exactly the (...)
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  47.  51
    Note on Contraries and Subcontraries.Lloyd Humberstone - 2003 - Noûs 37 (4):690–705.
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  48. Yet Another "Choice of Primitives" Warning: Normal Modal Logics.Lloyd Humberstone - 2004 - Logique Et Analyse 47.
  49.  63
    Co-Instantiation and Identity.Lloyd Humberstone & Aubrey Townsend - 1994 - Philosophical Studies 74 (2):243 - 272.
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  50.  58
    Replacement in Logic.Lloyd Humberstone - 2013 - Journal of Philosophical Logic 42 (1):49-89.
    We study a range of issues connected with the idea of replacing one formula by another in a fixed context. The replacement core of a consequence relation ⊢ is the relation holding between a set of formulas {A1,..., Am,...} and a formula B when for every context C, we have C,..., C,... ⊢ C. Section 1 looks at some differences between which inferences are lost on passing to the replacement cores of the classical and intuitionistic consequence relations. For example, we (...)
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