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Lloyd Humberstone [78]L. Humberstone [7]
  1.  266 DLs
    Martin Davies & Lloyd Humberstone (1980). Two Notions of Necessity. Philosophical Studies 38 (1):1-31.
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  2.  109 DLs
    Lloyd Humberstone (2009). Logical Pluralism. Australasian Journal of Philosophy 87 (1):162 – 168.
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  3.  74 DLs
    Lloyd Humberstone (2004). Two-Dimensional Adventures. 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.  56 DLs
    Lloyd Humberstone (2008). Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau). 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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  5.  53 DLs
    L. Humberstone & D. Makinson (2012). Intuitionistic Logic and Elementary Rules. 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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  6.  51 DLs
    Lloyd Humberstone (2014). Plural Logic, by Alex Oliver and Timothy Smiley. Australasian Journal of Philosophy 93 (1):192-195.
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  7.  44 DLs
    Lloyd Humberstone (2000). The Revival of Rejective Negation. 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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  8.  43 DLs
    Lloyd Humberstone (2013). Replacement in Logic. Journal of Philosophical Logic 42 (1):49-89.
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  9.  43 DLs
    A. P. Hazen & Lloyd Humberstone (2004). Similarity Relations and the Preservation of Solidity. 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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  10.  41 DLs
    Lloyd Humberstone (2011). Variation on a Trivialist Argument of Paul Kabay. 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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  11.  41 DLs
    Lloyd Humberstone (2008). Parts and Partitions. 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 (...)
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  12.  36 DLs
    Frank Jackson & Lloyd Humberstone (1982). On a Challenge by Anderson and Belnap. Analysis 42 (4):179 - 181.
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  13.  34 DLs
    Lloyd Humberstone (2006). Lloyd Humberstone. Aristotelian Society Supplementary Volume 80 (1):265–320.
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  14.  32 DLs
    Lloyd Humberstone (2008). Can Every Modifier Be Treated as a Sentence Modifier? Philosophical Perspectives 22 (1):241-275.
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  15.  32 DLs
    Lloyd Humberstone (2013). Logical Relations. Philosophical Perspectives 27 (1):175-230.
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  16.  29 DLs
    John N. Crossley & Lloyd Humberstone (1981). Meeting of the Association for Symbolic Logic: Melbourne, Australia 1979. Journal of Symbolic Logic 46 (2):424-426.
  17.  27 DLs
    Lloyd Humberstone & Aubrey Townsend (1994). Co-Instantiation and Identity. Philosophical Studies 74 (2):243 - 272.
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  18.  26 DLs
    Lloyd Humberstone (2007). Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness. [REVIEW] 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 (explaining the use of the word 'elsewhere'), as well as in the case in which they represent moments of time. This logic is applied here (...)
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  19.  26 DLs
    Lloyd Humberstone (2011). The Connectives. 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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  20.  25 DLs
    Lloyd Humberstone & Timothy Williamson (1997). Inverses for Normal Modal Operators. 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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  21.  23 DLs
    Lloyd Humberstone (1998). Note on Supervenience and Definability. 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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  22.  21 DLs
    Lloyd Humberstone (2005). Geach's Categorial Grammar. Linguistics and Philosophy 28 (3):281 - 317.
    Geach’s rich paper ‘A Program for Syntax’ introduced many ideas into the arena of categorial grammar, not all of which have been given the attention they warrant in the thirty years since its first publication. Rather surprisingly, one of our findings (Section 3 below) is that the paper not only does not contain a statement of what has widely come to be known as “Geach’s Rule”, but in fact presents considerations which are inimical to the adoption of the rule in (...)
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  23.  21 DLs
    Lloyd Humberstone (2008). Béziau's Translation Paradox. 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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  24.  20 DLs
    Lloyd Humberstone & Herman Cappelen (2006). Sufficiency and Excess. 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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  25.  20 DLs
    Lloyd Humberstone (2003). Note on Contraries and Subcontraries. Noûs 37 (4):690–705.
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  26.  20 DLs
    Lloyd Humberstone (2013). Inverse Images of Box Formulas in Modal Logic. Studia Logica 101 (5):1031-1060.
    We investigate, for several modal logics but concentrating on KT, KD45, S4 and S5, the set of formulas B for which ${\square B}$ is provably equivalent to ${\square A}$ for a selected formula A (such as p, a sentence letter). In the exceptional case in which a modal logic is closed under the (‘cancellation’) rule taking us from ${\square C \leftrightarrow \square D}$ to ${C \leftrightarrow D}$ , there is only one formula B, to within equivalence, in this inverse image, (...)
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  27.  20 DLs
    Lloyd Humberstone (2013). Zolin and Pizzi: Defining Necessity From Noncontingency. 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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  28.  18 DLs
    Lloyd Humberstone (2001). The Pleasures of Anticipation: Enriching Intuitionistic Logic. [REVIEW] 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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  29.  16 DLs
    Lloyd Humberstone (2000). Contra-Classical Logics. 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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  30.  16 DLs
    Lloyd Humberstone (1995). Names and Pseudonyms. 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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  31.  16 DLs
    Lloyd Humberstone (1988). The Lattice of Extensional Connectives: A Correction. [REVIEW] Journal of Philosophical Logic 17 (3):221 - 223.
  32.  16 DLs
    Lloyd Humberstone (2007). Investigations Into a Left-Structural Right-Substructural Sequent Calculus. 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 (fission, ‘cotensor’, par) 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 (...)
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  33.  16 DLs
    Lloyd Humberstone (2004). Archetypal Forms of Inference. Synthese 141 (1):45 - 76.
    A form (or pattern) of inference, let us say, explicitlysubsumes just such particular inferences as are instances of the form, and implicitly subsumes thoseinferences with a premiss and conclusion logically equivalent to the premiss and conclusion of an instanceof the form in question. (For simplicity we restrict attention to one-premiss inferences.) A form ofinference is archetypal if it implicitly subsumes every correct inference. A precise definition (Section 1)of these concepts relativizes them to logics, since different logics classify different inferences ascorrect, (...)
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  34.  16 DLs
    Lloyd Humberstone (2007). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] 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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  35.  15 DLs
    Lloyd Humberstone (1986). Extensionality in Sentence Position. Journal of Philosophical Logic 15 (1):27 - 54.
  36.  15 DLs
    Lloyd Humberstone (2008). Invitation to Autoepistemology. 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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  37.  15 DLs
    Lloyd Humberstone (2000). What Fa Says About A. 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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  38.  15 DLs
    Lloyd Humberstone & J. M. Bell (1977). Two Systems of Presupposition Logic. Notre Dame Journal of Formal Logic 18 (3):321-339.
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  39.  15 DLs
    Lloyd Humberstone (2006). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] 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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  40.  15 DLs
    Lloyd Humberstone (1996). Valuational Semantics of Rule Derivability. 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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  41.  14 DLs
    Rohan French & Lloyd Humberstone (2009). Partial Confirmation of a Conjecture on the Boxdot Translation in Modal Logic. 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.  14 DLs
    Lloyd Humberstone, Weaker-to-Stronger Translational Embeddings in Modal Logic.
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  43.  13 DLs
    Lloyd Humberstone (2003). False Though Partly True – an Experiment in Logic. 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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  44.  13 DLs
    Lloyd Humberstone (2000). An Intriguing Logic with Two Implicational Connectives. 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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  45.  11 DLs
    Lloyd Humberstone (2003). A Strange Remark Attributed to Gödel. History and Philosophy of Logic 24 (1):39-44.
    We assemble material from the literature on matrix methodology for sentential logic?without claiming to present any new logical results?in order to show that Gödel once made (or at least, is quoted as having made) an uncharacteristically ill-considered remark in this area.
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  46.  10 DLs
    Lloyd Humberstone (2004). Yet Another "Choice of Primitives" Warning: Normal Modal Logics. Logique Et Analyse 47.
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  47.  9 DLs
    Lloyd Humberstone, How Not to Think About Modal Definability: A Modal Axiom From G. E. Hughes.
    In a 1990 paper, George Hughes axiomatized the logic determined by the class of all frames in which each point has a reflexive successor, and raised various questions along the way, one of which is answered incorrectly here by means of an interestingly fallacious argument.
     
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  48.  8 DLs
    Lloyd Humberstone (2005). For Want of an 'And': A Puzzle About Non-Conservative Extension. 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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  49.  7 DLs
    Lloyd Humberstone (2006). Variations on a Theme of Curry. 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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  50.  7 DLs
    Lloyd Humberstone (2002). The Modal Logic of Agreement and Noncontingency. 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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