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  1. E. J. Ashworth (1968). Propositional Logic in the Sixteenth and Early Seventeenth Centuries. Notre Dame Journal of Formal Logic 9 (2):179-192.
  2. Ivan Boh (1966). Propositional Connectives, Supposition, and Consequence in Paul of Pergola. Notre Dame Journal of Formal Logic 7 (1):109-128.
  3. Robert B. Brandom (1979). A Binary Sheffer Operator Which Does the Work of Quantifiers and Sentential Connectives. Notre Dame Journal of Formal Logic 20 (2):262-264.
  4. Jean Mark Gawron & Andrew Kehler (2004). The Semantics of Respective Readings, Conjunction, and Filler-Gap Dependencies. Linguistics and Philosophy 27 (2):169-207.
    We provide a semantic analysis of respective readings, including butnot limited to the interpretation of examples containing the adverbrespectively, which accounts for a number of facts that haveeither proven difficult for previous studies or heretofore goneunnoticed in the literature. The analysis introduces the new notionsof property sum and proposition sum which integrate smoothly with existing analyses of plurals and distributivity. The analysis also admits of a straightforward account of previouslyunacknowledged examples involving filler-gap dependencies that areproblematic for contemporary syntactic theories. Ramifications (...)
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  5. Marco Hollenberg & Albert Visser (1999). Dynamic Negation, the One and Only. Journal of Logic, Language and Information 8 (2):137-141.
    We consider the variety of Dynamic Relation Algebras V(DRA). We show that the monoid of an algebra in this variety determines dynamic negation uniquely.
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  6. 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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  7. Lucja Iwańska (1993). Logical Reasoning in Natural Language: It is All About Knowledge. [REVIEW] Minds and Machines 3 (4):475-510.
    A formal, computational, semantically clean representation of natural language is presented. This representation captures the fact that logical inferences in natural language crucially depend on the semantic relation of entailment between sentential constituents such as determiner, noun, adjective, adverb, preposition, and verb phrases.The representation parallels natural language in that it accounts for human intuition about entailment of sentences, it preserves its structure, it reflects the semantics of different syntactic categories, it simulates conjunction, disjunction, and negation in natural language by computable (...)
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  8. Manfred Krifka, How to Interpret “Expletive” Negation Under Bevor in German.
    (2) Peter wollte Potsdam nicht verlassen bevor das Projekt in ruhigem Fahrwasser war. There are other well-known examples of non-interpreted negation, viz. cases of so-called negative concord in Slavic and Romance languages, but also in dialects of German and English. But arguably, in those cases the “superfluous” negation has to be present for grammatical reasons, which is not the case here. I will show that the negation is in fact interpreted, and that, due to a complex interplay of semantic and (...)
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  9. Alex Lascarides & Emily M. Bender, On Modeling Scope of Inflectional Negation.
    In this paper, we investigate the representation of negated sentences in Minimal Recursion Semantics (Copestake, Flickinger, Pollard, & Sag, 2005). We begin with its treatment in the English Resource Grammar (Flickinger, 2000, 2011), a broad-coverage implemented HPSG (Pollard & Sag, 1994), and argue that it is largely a suitable representation for English, despite possible objections. We then explore whether it is suitable for typologically different languages: namely, those that express sentential negation via inflection on the verb, particularly Turkish and Inuktitut. (...)
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  10. Chungmin Lee (2009). Information Structure in Pa/Sn or Descriptive/Metalinguistic Negation: With Reference to Scalar Implicatures. In Dingfang Shu & Ken Turner (eds.), Contrasting Meanings in Languages of the East and West. Peter Lang.
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  11. Witold A. Pogorzelski & Piotr Wojtylak (2001). Cn-Definitions of Propositional Connectives. Studia Logica 67 (1):1-26.
    We attempt to define the classical propositional logic by use of appropriate derivability conditions called Cn-definitions. The conditions characterize basic properties of propositional connectives.
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  12. Timothy Smiley (1962). The Independence of Connectives. Journal of Symbolic Logic 27 (4):426-436.
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  13. D. C. Stove (1972). Misconditionalisation. Australasian Journal of Philosophy 50 (2):173 – 183.
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  14. Henriëtte De Swart & Ivan A. Sag (2002). Negation and Negative Concord in Romance. Linguistics and Philosophy 25 (4):373 - 417.
    This paper addresses the two interpretations that a combination of negative indefinites can get in concord languages like French: a concord reading, which amounts to a single negation, and a double negation reading. We develop an analysis within a polyadic framework, where a sequence of negative indefinites can be interpreted as an iteration of quantifiers or via resumption. The first option leads to a scopal relation, interpreted as double negation. The second option leads to the construction of a polyadic negative (...)
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  15. Jamie Tappenden, Negation, Denial and Language Change in Philosophical Logic.
    This paper uses the strengthened liar paradox as a springboard to illuminate two more general topics: i) the negation operator and the speech act of denial among speakers of English and ii) some ways the potential for acceptable language change is constrained by linguistic meaning. The general and special problems interact in reciprocally illuminating ways. The ultimate objective of the paper is, however, less to solve certain problems than to create others, by illustrating how the issues that form the topic (...)
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  16. Assimakis Tseronis (2011). From Connectives to Argumentative Markers: A Quest for Markers of Argumentative Moves and of Related Aspects of Argumentative Discourse. [REVIEW] Argumentation 25 (4):427-447.
    In this paper, I explore the potential of systematically studying the linguistic surface of discourse for the purposes of identifying markers of argumentative moves and other related categories, such as types of arguments and argumentative strategies. Such a list of argumentative markers can prove useful for the (semi)automatic treatment of a large corpus of texts. After reviewing literature on the linguistic realization of argumentative moves as well as literature on the subject of discourse markers, it becomes clear that the search (...)
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  17. Thomas Ede Zimmermann (2000). Free Choice Disjunction and Epistemic Possibility. Natural Language Semantics 8 (4):255-290.
    This paper offers an explanation of the fact that sentences of the form (1) ‘X may A or B’ may be construed as implying (2) ‘X may A and X may B’, especially if they are used to grant permission. It is suggested that the effect arises because disjunctions are conjunctive lists of epistemic possibilities. Consequently, if the modal may is itself epistemic, (1) comes out as equivalent to (2), due to general laws of epistemic logic. On the other hand, (...)
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Conjunction
  1. Axel Arturo Barceló Aspeitia (2007). What Does '&' Mean? The Proceedings of the Twenty-First World Congress of Philosophy 5:45-50.
    Using conjunction as an example, I show a technical and philosophical problem when trying to conciliate the currently prevailing views on the meaning of logical connectives: the inferientialist (also called 'syntactic') one based on introduction and elimination rules, and the representationalist (also called 'semantic') one given through truth tables. Mostly I show that the widespread strategy of using the truth theoretical definition of logical consequence to collapse both definitions must be rejected by inferentialists. An important consequence of my argument is (...)
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  2. 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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  3. Diane Blakemore (1989). Denial and Contrast: A Relevance Theoretic Analysis of But. [REVIEW] Linguistics and Philosophy 12 (1):15 - 37.
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  4. Susanne Bobzien (2011). The Combinatorics of Stoic Conjunction. Oxford Studies in Ancient Philosophy 40 (1):157-188.
    ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is why Hipparchus’ (...)
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  5. Joseph T. Clark (1952). Truth-Functional Conjunction. Philosophical Studies of the American Catholic Philosophical Association 3:24-25.
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  6. 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.
  7. 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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  8. 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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  9. 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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  10. 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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  11. R. E. Jennings (1986). The Punctuational Sources of the Truth-Functional 'Or'. Philosophical Studies 50 (2):237-259.
  12. E. Keshet (2013). Focus on Conditional Conjunction. Journal of Semantics 30 (2):211-256.
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  13. 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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  14. Peter Lasersohn (1992). Generalized Conjunction and Temporal Modification. Linguistics and Philosophy 15 (4):381 - 410.
    Argues for an assimilation of sentential and predicate conjunction to collective conjunction, based on modification of predicates by adverbs such as 'alternately'.
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  15. Friederike Moltmann (1992). Coordination and Comparatives. Dissertation, MIT
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  16. Friederike Moltmann (1992). On the Interpretation of Three-Dimensional Syntactic Trees. In Chris Barker & David Dowty (eds.), Proceedings of Sinn und Bedeutung 2, Ohio State University.
    Syntacticians have proposed three-dimensional syntactic structures to account for the peculiarities of coordination. This paper proposes a way of interpreting such structures and gives an account of sentences of the sort 'John bought and Mary sold a total of ten cars' based on a notion of 'implicit' coordination.
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  17. Anna Szabolcsi & Bill Haddican (2004). Conjunction Meets Negation: A Study in Cross-Linguistic Variation. Journal of Semantics 21 (3):219-249.
    The central topic of this inquiry is a cross-linguistic contrast in the interaction of conjunction and negation. In Hungarian (Russian, Serbian, Italian, Japanese), in contrast to English (German), negated definite conjunctions are naturally and exclusively interpreted as `neither’. It is proposed that Hungarian-type languages conjunctions simply replicate the behavior of plurals, their closest semantic relatives. More puzzling is why English-type languages present a different range of interpretations. By teasing out finer distinctions in focus on connectives, syntactic structure, and context, the (...)
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  18. Isabel Gómez Txurruka (2003). The Natural Language Conjunction And. Linguistics and Philosophy 26 (3):255-285.
    In the first part of this article, we show that, contrary to the Gricean tradition, inter-clausal and is not semantically equivalent to logical conjunction and, contrary to temporal approaches such as Bar-Levand Palacas 1980, it is not temporallyloaded. We then explore a commonsenseidea – namely that while sentence juxtaposition might be interpreted either as discourse coordination or subordination, and indicates coordination. SDRT already includes notions of coordinating and subordinating discourse relations (cf. Lascarides and Asher 1993, Asher 1993), and the meaning (...)
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  19. Yoad Winter (1994). Contrast and Implication in Natural Language. Journal of Semantics 11 (4):365-406.
    In this paper we introduce a theoretical framework and a logical application for analysing the semantics and pragmatics of contrastive conjunctions in natural language. It is shown how expressions like although, nevertheless, yet, and but are semantically definable as connectives using an operator for implication in natural language and how similar pragmatic principles affect the behaviour of both contrastive conjunctions and indicative conditionals. Following previous proposals, conditions on contrast in a conjunction are analysed as presuppositions of die conjunction. Further linguistic (...)
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Disjunction
  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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