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Summary "Disjunction" is the technical term for the English connective "or."  As many of the entries in this leaf node attest, "or" in English means "inclusive or," i.e., "and/or."  The so-called "exclusive or," while one of the sixteen combinatorially possible binary connectives in the propositional calculus, is merely an implicature from a mutually exhaustive context or cue words whose own semantics indicate exclusivity, e.g. "else" as in "or else."  There is a "menu or" in English, but this is an n-ary connective with n not necessarily 2, and does not normally appear in ordinary declarative contexts.
Key works Aside from the book cited below, the article Barrett & Stenner 1971 is key, as are the various works by Crain and his colleagues.  I particularly recommend Crain & Khlentzos 2010.
Introductions The book  Jennings 1994, while not particularly easy reading for the neophyte, is indispensable.  It is to "Disjunction" what Horn 1989 is to "Negation."
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  1. Diederik Aerts, Ellie D'Hondt & Liane Gabora (2000). Why the Disjunction in Quantum Logic is Not Classical. Foundations of Physics 30 (9):1473-1480.
    The quantum logical `or' is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation. Specifically, the presence of potentiality in these correlation states gives rise to the quantum deviation from the classical logical `or'. We show how this arises not only in the microworld, but also in macroscopic situations where EPR-like correlation states are present. We investigate how application (...)
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  2. Scott AnderBois (2012). Focus and Uninformativity in Yucatec Maya Questions. Natural Language Semantics 20 (4):349-390.
    Crosslinguistically, questions frequently make crucial use of morphosyntactic elements which also occur outside of questions. Chief among these are focus, disjunctions, and wh-words with indefinite semantics. This paper provides a compositional account of the semantics of wh-, alternative, and polar questions in Yucatec Maya (YM), which are composed primarily of these elements. Key to the account is a theory of disjunctions and indefinites (extending work by others) which recognizes the inherently inquisitive nature of these elements. While disjunctions and indefinites are (...)
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  3. Robert B. Barrett & Alfred J. Stenner (1971). The Myth of the Exclusive `Or'. Mind 80 (317):116-121.
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  4. Jean-Yves Beziau, Combining Conjunction with Disjunction.
    In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. (...)
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  5. Stephen Crain, Acquisition of Disjunction in Conditional Sentences.
    This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. Previous research has concluded that adult truth conditions for logical connectives are acquired relatively late in the course of language development. With particular reference to disjunction, the results of several studies have led to two claims. First, it has been argued that the full range of truth-conditions associated with inclusive-or is not initially available to children; instead, children are supposed (...)
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  6. Stephen Crain, At the Semantics/Pragmatics Interface in Child Language.
    This paper investigates scalar implicatures and downward entailment in child English. In previous experimental work we have shown that adults’ computation of scalar implicatures is sensitive to entailment relations. For instance, when the disjunction operator or occurs in positive contexts, an implicature of exclusivity arises. By contrast when the disjunction operator occurs within the scope of a downward entailing linguistic expression, no implicature of exclusivity is computed. Investigations on children’s computation of scalar implicatures in the same contexts have led to (...)
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  7. Stephen Crain, Children's Command of Negation.
    Poverty -of-stimulus arguments have taken new ground recently, augmented by experimental findings from th e study of child language. In this paper, we briefly review two variants of the poverty-of-stimulus argument that have received empirical support from studies of child language; then we examine a third argument of this kind in more detail. The case under discussion involves the structural notion of c-command as it pertains to children’s interpretation of disjunction in the scope of negation.
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  8. Stephen Crain, The Acquisition of Disjunction: Evidence for a Grammatical View of Scalar Implicatures.
    This paper investigates young children's knowledge of scalar implicatures and downward entailment. In previous experimental work, we have shown that young children access the full range of truth-conditions associated with logical words in classical logic, including the disjunction operator, as well as the indefinite article. The present study extends this research in three ways, taking disjunction as a case study. Experiment 1 draws upon the observation that scalar implicatures (SIs) are cancelled (or reversed) in downward entailing (DE) linguistic environments, e.g., (...)
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  9. Stephen Crain, The Inclusion of Disjunction in Child Grammar: Evidence From Modal Verbs.
    This study is concerned with the acquisition of the disjunction operator, or, in English. Two mutually inconsistent claims have been made about the acquisition of disjunction. One claim is that the acquisition of the adult truth conditions for logical connectives, including disjunction, is a late and not fully universal, achievement. With particular reference to disjunction, the findings from several studies are interpreted as showing that only the truth conditions associated with exclusive-or are available to young children (e.g., Beilin and Lust (...)
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  10. Stephen Crain & Drew Khlentzos (2010). The Logic Instinct. Mind and Language 25 (1):30-65.
    We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by observing how adults use (...)
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  11. Charles B. Daniels (1997). The Genealogy of Disjunction R. E. Jennings New York and Oxford: Oxford University Press, 1994, X + 344 Pp., $66.95. [REVIEW] Dialogue 36 (1):208-210.
  12. J. M. Font & V. Verdú (1993). Algebraic Logic for Classical Conjunction and Disjunction. Studia Logica 52 (1):181.
    In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...)
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  13. Josep M. Font & Ventura Verdú (1991). Algebraic Logic for Classical Conjunction and Disjunction. Studia Logica 50 (3-4):391 - 419.
    In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. (...)
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  14. Joseph S. Fulda (1993). Exclusive Disjunction and the Biconditional: An Even-Odd Relationship. Mathematics Magazine 66 (2):124.
    Proves two simple identities relating the biconditional and exclusive disjunction. -/- The PDF has been made available gratis by the publisher.
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  15. L. Goddard (1960). The Exclusive 'Or'. Analysis 20 (5):97 - 105.
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  16. Andrea Gualmini, Acquisition of Disjunction in Conditional Sentences.
    This study is concerned with the properties of the disjunction operator, or, and the acquisition of these properties by English-speaking children. Previous research has concluded that adult truth conditions for logical connectives are acquired relatively late in the course of language development. With particular reference to disjunction, the results of several studies have led to two claims. First, it has been argued that the full range of truth-conditions associated with inclusive-or is not initially available to children; instead, children are supposed (...)
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  17. Andrea Gualmini, The Inclusion of Disjunction in Child Grammar: Evidence From Modal Verbs.
    This study is concerned with the acquisition of the disjunction operator, or, in English. Two mutually inconsistent claims have been made about the acquisition of disjunction. One claim is that the acquisition of the adult truth conditions for logical connectives, including disjunction, is a late and not fully universal, achievement. With particular reference to disjunction, the findings from several studies are interpreted as showing that only the truth conditions associated with exclusive-or are available to young children (e.g., Beilin and Lust (...)
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  18. R. E. Jennings (1994). The Genealogy of Disjunction. Oxford University Press.
    This is a comprehensive study of the English word 'or', and the logical operators variously proposed to present its meaning. Although there are indisputably disjunctive uses of or in English, it is a mistake to suppose that logical disjunction represents its core meaning. 'Or' is descended from the Anglo-Saxon word meaning second, a form which survives in such expressions as "every other day." Its disjunctive uses arise through metalinguistic applications of an intermediate adverbial meaning which is conjunctive rather than disjunctive (...)
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  19. R. E. Jennings (1994). The or of Free Choice Permission. Topoi 13 (1):3-10.
    I argue that the conjunctive distribution of permissibility over or, which is a puzzling feature of free-choice permission is just one instance of a more general class of conjunctive occurrences of the word, and that these conjunctive uses are more directly explicable by the consideration that or is a descendant of oper than by reference to the disjunctive occurrences which logicalist prejudices may tempt us to regard as semantically more fundamental. I offer an account of how the disjunctive uses of (...)
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  20. R. E. Jennings (1986). The Punctuational Sources of the Truth-Functional 'Or'. Philosophical Studies 50 (2):237-259.
  21. Ray Jennings, Disjunction. Stanford Encyclopedia of Philosophy.
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  22. Nathan Klinedinst & Daniel Rothschild (2012). Connectives Without Truth Tables. Natural Language Semantics 20 (2):137-175.
    There are certain uses of and and or that cannot be explained by their normal meanings as truth-functional connectives, even with sophisticated pragmatic resources. These include examples such as The cops show up, and a fight will break out (‘If the cops show up, a fight will break out’), and I have no friends, or I would throw a party (‘I have no friends. If I did have friends, I would throw a party.’). We argue that these uses are indeed (...)
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  23. Luisa Meronia, At the Semantics/Pragmatics Interface in Child Language.
    This paper investigates scalar implicatures and downward entailment in child English. In previous experimental work we have shown that adults’ computation of scalar implicatures is sensitive to entailment relations. For instance, when the disjunction operator or occurs in positive contexts, an implicature of exclusivity arises. By contrast when the disjunction operator occurs within the scope of a downward entailing linguistic expression, no implicature of exclusivity is computed. Investigations on children’s computation of scalar implicatures in the same contexts have led to (...)
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  24. Luisa Meronib, The Acquisition of Disjunction: Evidence for a Grammatical View of Scalar Implicatures.
    This paper investigates young children's knowledge of scalar implicatures and downward entailment. In previous experimental work, we have shown that young children access the full range of truth-conditions associated with logical words in classical logic, including the disjunction operator, as well as the indefinite article. The present study extends this research in three ways, taking disjunction as a case study. Experiment 1 draws upon the observation that scalar implicatures (SIs) are cancelled (or reversed) in downward entailing (DE) linguistic environments, e.g., (...)
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  25. Friederike Moltmann (1992). Coordination and Comparatives. Dissertation, MIT
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  26. Ira A. Noveck, Gennaro Chierchia, Florelle Chevaux, Raphaelle Guelminger & Emmanuel Sylvestre (2002). Linguistic-Pragmatic Factors in Interpreting Disjunctions. Thinking and Reasoning 8 (4):297 – 326.
    The connective or can be treated as an inclusive disjunction or else as an exclusive disjunction. Although researchers are aware of this distinction, few have examined the conditions under which each interpretation should be anticipated. Based on linguistic-pragmatic analyses, we assume that interpretations are initially inclusive before either (a) remaining so, or (b) becoming exclusive by way of an implicature ( but not both ). We point to a class of situations that ought to predispose disjunctions to inclusive interpretations and (...)
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  27. Francesco Paoli (2005). The Ambiguity of Quantifiers. Philosophical Studies 124 (3):313 - 330.
    In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.
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  28. Vera Peetz (1978). Disjunctions and Questions. Philosophy 53 (204):264 - 269.
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  29. Scott L. Pratt (2010). The Politics of Disjunction. Transactions of the Charles S. Peirce Society 46 (2):202-220.
    In his 1905 work on the logical foundations of geometry, Royce proposed a logic based on the “obverse” or O-relation that could provide a means of understanding any system of order. Royce explains that this relation, which he calls the O-relation, “in logical terms, . . . is the relation in which (if we were talking of the possible chances [choices] open to one who had to decide upon a course of action) any set of exhaustive but, in their entirety, (...)
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  30. Stephen Read (1982). Disjunction. Journal of Semantics 1 (3-4):275-285.
    In relevant logics one can formally distinguish two logical operators, symbolised as ┌A ∨ B┐ and ┌A + B┐. Addition holds for ‘ ∨ ’ and Disjunctive Syllogism for ‘ + ’, but not vice versa. The question arises, whether this distinction between two different formal notions of disjunction can be found in natural reasoning. First it is necessary to rebut Quinean objections to any rival to classical logic, Crice's claim that an intensional disjunction is not needed to explain the (...)
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  31. Thomas J. Richards & Roderic A. Girle (1989). 'Or' and 'And/Or':A Discussion. History and Philosophy of Logic 10 (1):29-45.
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  32. G. R. T. Ross (1903). The Disjunctive Judgment. Mind 12 (48):489-501.
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  33. Mandy Simons (2001). Disjunction and Alternativeness. Linguistics and Philosophy 24 (5):597-619.
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  34. Mandy Simons, On The Felicity Conditions of Disjunctive Sentences.
    Mandy Simons. On The Felicity Conditions of Disjunctive Sentences.
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  35. Raj Singh (2008). On the Interpretation of Disjunction: Asymmetric, Incremental, and Eager for Inconsistency. [REVIEW] Linguistics and Philosophy 31 (2):245-260.
    Hurford’s Constraint (Hurford, Foundations of Language, 11, 409–411, 1974) states that a disjunction is infelicitous if its disjuncts stand in an entailment relation: #John was born in Paris or in France. Gazdar (Pragmatics, Academic Press, NY, 1979) observed that scalar implicatures can obviate the constraint. For instance, sentences of the form (A or B) or (Both Aand B) are felicitous due to the exclusivity implicature of the first disjunct: A or B implicates ‘not (A and B)’. Chierchia, Fox, and Spector (...)
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  36. B. H. Slater (1976). A Grammatical Point About Disjunction. Philosophy 51 (196):226 - 228.
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  37. Tony Street (1995). Tūsī on Avicenna's Logical Connectives∗. History and Philosophy of Logic 16 (2):257-268.
    T?s?, a thirteenth century logician writing in Arabic, uses two logical connectives to build up molecular propositions: ?if-then?, and ?either-or?. By referring to a dichotomous Tree, T?s? shows how to choose the proper disjunction relative to the terms in the disjuncts. He also discusses the disjunctive propositions which follow from a conditional proposition.
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  38. Liza Verhoeven (2007). The Relevance of a Relevantly Assertable Disjunction for Material Implication. Journal of Philosophical Logic 36 (3):339-366.
    In this paper Grice's requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz's conclusion-relevant consequence relation.
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  39. Liza Verhoeven & Leon Horsten (2005). On the Exclusivity Implicature of 'Or' or on the Meaning of Eating Strawberries. Studia Logica 81 (1):19-24.
    This paper is a contribution to the program of constructing formal representations of pragmatic aspects of human reasoning. We propose a formalization within the framework of Adaptive Logics of the exclusivity implicature governing the connective ‘or’.Keywords: exclusivity implicature, Adaptive Logics.
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  40. Jack Woods (2012). Failures of Categoricity and Compositionality for Intuitionistic Disjunction. Thought 1 (4):281-291.
    I show that the model-theoretic meaning that can be read off the natural deduction rules for disjunction fails to have certain desirable properties. I use this result to argue against a modest form of inferentialism which uses natural deduction rules to fix model-theoretic truth-conditions for logical connectives.
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