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  1. Stål O. Aanderaa, Egon Börger & Harry R. Lewis (1982). Conservative Reduction Classes of Krom Formulas. Journal of Symbolic Logic 47 (1):110-130.
    A Krom formula of pure quantification theory is a formula in conjunctive normal form such that each conjunct is a disjunction of at most two atomic formulas or negations of atomic formulas. Every class of Krom formulas that is determined by the form of their quantifier prefixes and which is known to have an unsolvable decision problem for satisfiability is here shown to be a conservative reduction class. Therefore both the general satisfiability problem, and the problem of satisfiability in finite (...)
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  2. Stal O. Aanderaa & Harry R. Lewis (1974). Linear Sampling and the |Forall |Exists |Forall Case of the Decision Problem. Journal of Symbolic Logic 39 (3):519 - 548.
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  3. Stål O. Aanderaa & Harry R. Lewis (1973). Prefix Classes of Krom Formulas. Journal of Symbolic Logic 38 (4):628-642.
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  4. M. Abad, J. P. Díaz Varela, L. A. Rueda & A. M. Suardíaz (2000). Varieties of Three-Valued Heyting Algebras with a Quantifier. Studia Logica 65 (2):181-198.
    This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties (...)
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  5. Barbara Abbott, Reference and Quantification: The Partee Effect.
    Partee (1973) discussed quotation from the perspective of the then relatively new theory of transformational grammar.2 As she pointed out, the phenomenon presents many curious puzzles. In some ways quotes seem quite separate from their surrounding text; they may be in a different dialect, as in her example in (1), (1) ‘I talk better English than the both of youse!’ shouted Charles, thereby convincing me that he didn’t. [Partee (1973):ex. 20] or even in a different language, as in (2): (2) (...)
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  6. Klaus Abels & Luisa Martí (2010). A Unified Approach to Split Scope. Natural Language Semantics 18 (4):435-470.
    The goal of this paper is to propose a unified approach to the split scope readings of negative indefinites, comparative quantifiers, and numerals. There are two main observations that justify this approach. First, split scope shows the same kinds of restrictions across these different quantifiers. Second, split scope always involves low existential force. In our approach, following Sauerland, natural language determiner quantifiers are quantifiers over choice functions, of type <<,t>,t>. In split readings, the quantifier over choice functions scopes above other (...)
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  7. Dorit Abusch (1993). The Scope of Indefinites. Natural Language Semantics 2 (2):83-135.
    This paper claims that indefinite descriptions, singular and plural, have different scope properties than genuine quantifiers. This claim is based on their distinct behavior in island constructions: while indefinites in islands can have intermediate (and maximal) scope readings, quantifiers cannot. Further, the simplest in situ interpretation strategy for indefinites results in incorrect truth conditions for intermediate (and maximal) scope readings. I introduce a mechanism which “auto-matically” preserves the restriction on free variables corresponding to indefinites, in a way which allows the (...)
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  8. Ken Akiba (2009). A New Theory of Quantifiers and Term Connectives. Journal of Logic, Language and Information 18 (3):403-431.
    This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , and the boys (...)
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  9. Natasha Alechina (2000). Functional Dependencies Between Variables. Studia Logica 66 (2):273-283.
    We consider a predicate logic Lfd where not all assignments of values to individual variables are possible. Some variables are functionally dependent on other variables. This makes sense if the models of logic are assumed to correspond to databases or states. We show that Lfd is undecidable but has a complete and sound sequent calculus formalisation.
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  10. Peter Alrenga & Christopher Kennedy (2014). No More Shall We Part: Quantifiers in English Comparatives. Natural Language Semantics 22 (1):1-53.
    It is well known that the interpretation of quantificational expressions in the comparative clause poses a serious challenge for semantic analyses of the English comparative. In this paper, we develop a new analysis of the comparative clause designed to meet this challenge, in which a silent occurrence of the negative degree quantifier no (observed overtly in collocations like no more, no greater, etc.) interacts with other quantificational expressions to derive the observed range of interpretations. Although our analysis incorporates ideas from (...)
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  11. Daniel Altshuler (2007). WCO, ACD and What They Reveal About Complex Demonstratives. Natural Language Semantics 15 (3):265-277.
    This squib presents a rebuttal to two of King’s (Complex demonstratives: A quantificational account. Cambridge, Mass.: MIT Press, 2001) arguments that complex demonstratives are quantifier phrases like every man. The first is in response to King’s argument that because complex demonstratives induce weak crossover effects, they are quantifier phrases. I argue that unlike quantifier phrases and like other definite determiner phrases, complex demonstratives in object position can corefer with singular pronouns contained in the subject DP. Although complex demonstratives could undergo (...)
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  12. Ignacio Angelelli & María Cerezo (eds.) (1996). Studies on the History of Logic: Proceedings of the Iii. Symposium on the History of Logic. Walter De Gruyter.
  13. G. Aldo Antonelli, First-Order Quantifiers.
    In §21 of Grundgesetze der Arithmetik asks us to consider the forms: a a2 = 4 and a a > 0 and notices that they can be obtained from a φ(a) by replacing the function-name placeholder φ(ξ) by names for the functions ξ2 = 4 and ξ > 0 (and the placeholder cannot be replaced by names of objects or of functions of 2 arguments).
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  14. G. Aldo Antonelli (2010). Numerical Abstraction Via the Frege Quantifier. Notre Dame Journal of Formal Logic 51 (2):161-179.
    This paper presents a formalization of first-order arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a nonstandard (but still first-order) cardinality quantifier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a nonreductionist conception of logicism, a deflationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the natural numbers over the structural ones.
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  15. G. Aldo Antonelli (2007). Free Quantification and Logical Invariance. Rivista di Estetica 33 (1):61-73.
    Henry Leonard and Karel Lambert first introduced so-called presupposition-free (or just simply: free) logics in the 1950’s in order to provide a logical framework allowing for non-denoting singular terms (be they descriptions or constants) such as “the largest prime” or “Pegasus” (see Leonard [1956] and Lambert [1960]). Of course, ever since Russell’s paradigmatic treatment of definite descriptions (Russell [1905]), philosophers have had a way to deal with such terms. A sentence such as “the..
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  16. Sergei N. Artemov & Lev D. Beklemishev (1993). On Propositional Quantifiers in Provability Logic. Notre Dame Journal of Formal Logic 34 (3):401-419.
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  17. E. J. Ashworth (1978). Multiple Quantification and the Use of Special Quantifiers in Early Sixteenth Century Logic. Notre Dame Journal of Formal Logic 19 (4):599-613.
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  18. Kent Bach (2000). Quantification, Qualification and Context a Reply to Stanley and Szabó. Mind and Language 15 (2&3):262–283.
    We hardly ever mean exactly what we say. I don’t mean that we generally speak figuratively or that we’re generally insincere. Rather, I mean that we generally speak loosely, omitting words that could have made what we meant more explicit and letting our audience fill in the gaps. Language works far more efficiently when we do that. Literalism can have its virtues, as when we’re drawing up a contract, programming a computer, or writing a philosophy paper, but we generally opt (...)
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  19. Kent Bach (1982). Semantic Nonspecificity and Mixed Quantifiers. Linguistics and Philosophy 4 (4):593 - 605.
  20. Mark Baker & Lisa Travis (1997). Mood as Verbal Definiteness in a" Tenseless" Language. Natural Language Semantics 5 (3):213-269.
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  21. Chris Barker (2002). Continuations and the Nature of Quantification. Natural Language Semantics 10 (3):211-242.
    This paper proposes that the meanings of some natural language expressions should be thought of as functions on their own continuations. Continuations are a well-established analytic tool in the theory of programming language semantics; in brief, a continuation is the entire default future of a computation. I show how a continuation-based grammar can unify several aspects of natural language quantification in a new way: merely stating the truth conditions for quantificational expressions in terms of continuations automatically accounts for scope displacement (...)
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  22. Chris Barker (1996). Presuppositions for Proportional Quantifiers. Natural Language Semantics 4 (3):237-259.
    Most studies of the so-called proportion problem seek to understand how lexical and structural properties of sentences containing adverbial quantifiers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sentences allow an asymmetric reading when other, structurally similar sentences seem to require a symmetric reading? Potential factors suggested in (...)
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  23. S. J. Barker (1997). E-Type Pronouns, DRT, Dynamic Semantics and the Quantifier/Variable-Binding Model. Linguistics and Philosophy 20 (2):195-228.
  24. John A. Barnden & Kankanahalli Srinivas (1996). Quantification Without Variables in Connectionism. Minds and Machines 6 (2):173-201.
    Connectionist attention to variables has been too restricted in two ways. First, it has not exploited certain ways of doing without variables in the symbolic arena. One variable-avoidance method, that of logical combinators, is particularly well established there. Secondly, the attention has been largely restricted to variables in long-term rules embodied in connection weight patterns. However, short-lived bodies of information, such as sentence interpretations or inference products, may involve quantification. Therefore short-lived activation patterns may need to achieve the effect of (...)
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  25. Jon Barwise (1979). On Branching Quantifiers in English. Journal of Philosophical Logic 8 (1):47 - 80.
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  26. JC Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall (2006). Relevant Restricted Quantification. Journal of Philosophical Logic 35 (6):587 - 598.
    The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.
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  27. Richard Beatty (1969). Peirce's Development of Quantifiers and of Predicate Logic. Notre Dame Journal of Formal Logic 10 (1):64-76.
  28. Sigrid Beck (1996). Quantified Structures as Barriers for LF Movement. Natural Language Semantics 4 (1):1-56.
    In this paper I argue for a restriction on certain types of LF movement, which I call ‘wh-related LF movement’. Evidence comes from a number of wh-in-situ constructions in German, such as the scope-marking construction and multiple questions. For semantic reasons, the in situ element in those constructions has to move at LF to either a position reserved for wh-phrases, or even higher up in the structure. The restriction (the Minimal Quantified Structure Constraint, MQSC) is that an intervening quantified expression (...)
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  29. Sigrid Beck & Uli Sauerland (2000). Cumulation is Needed: A Reply to Winter (2000). [REVIEW] Natural Language Semantics 8 (4):349-371.
    Winter (2000) argues that so-called co-distributive or cumulative readings do not involve polyadic quantification (contra proposals by Krifka, Schwarzschild, Sternefeld, and others). Instead, he proposes that all such readings involve a hidden anaphoric dependency or a lexical mechanism. We show that Winter's proposal is insufficient for a number of cases of cumulative readings, and that Krifka's and Sternefeld's polyadic **-operator is needed in addition to dependent definites. Our arguments come from new observations concerning dependent plurals and clause-boundedness effects with cumulative (...)
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  30. Luc Bélair & Françoise Point (2010). Quantifier Elimination in Valued Ore Modules. Journal of Symbolic Logic 75 (3):1007-1034.
    We consider valued fields with a distinguished isometry or contractive derivation as valued modules over the Ore ring of difference operators. Under certain assumptions on the residue field, we prove quantifier elimination first in the pure module language, then in that language augmented with a chain of additive subgroups, and finally in a two-sorted language with a valuation map. We apply quantifier elimination to prove that these structures do not have the independence property.
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  31. Nuel D. Belnap Jr (1970). Conditional Assertion and Restricted Quantification. Noûs 4 (1):1-12.
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  32. Johan Benthem (1989). Polyadic Quantifiers. Linguistics and Philosophy 12 (4):437 - 464.
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  33. Claudia Bianchi (2006). 'Nobody Loves Me': Quantification and Context. Philosophical Studies 130 (2):377 - 397.
    In my paper, I present two competing perspectives on the foundational problem (as opposed to the descriptive problem) of quantifier domain restriction: the objective perspective on context (OPC) and the intentional perspective on context (IPC). According to OPC, the relevant domain for a quantified sentence is determined by objective facts of the context of utterance. In contrast, according to IPC, we must consider certain features of the speaker’s intention in order to determine the proposition expressed. My goal is to offer (...)
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  34. Robert Binkley (1970). Quantifying, Quotation, and a Paradox. Noûs 4 (3):271-277.
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  35. Maria Bittner, Nominal Quantification as Top-Level Anaphora.
    So far, we have focused on discourse reference to atomic individuals and specific times, events, and states. The basic point of the argument was that all types of discourse reference involve attention-guided anaphora (in the sense of Bittner 2012: Ch. 2). We now turn to discourses involving anaphora to and by quantificational expressions. Today, we focus on quantification over individuals but the analysis we develop will directly generalize to other semantic types. The basic idea is that quantification is one more (...)
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  36. Maria Bittner & Naja Trondhjem (2008). Quantification as Reference: Evidence From Q-Verbs. In Lisa Matthewson (ed.), Quantification: A Cross-Linguistic Perspective. Emerald. 2--7.
    Formal semantics has so far focused on three categories of quantifiers, to wit, Q-determiners (e.g. 'every'), Q-adverbs (e.g. 'always'), and Q-auxiliaries (e.g. 'would'). All three can be analyzed in terms of tripartite logical forms (LF). This paper presents evidence from verbs with distributive affixes (Q-verbs), in Kalaallisut, Polish, and Bininj Gun-wok, which cannot be analyzed in terms of tripartite LFs. It is argued that a Q-verb involves discourse reference to a distributive verbal dependency, i.e. an episode-valued function that sends different (...)
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  37. Andrea Bonomi (1997). Aspect, Quantification and When-Clauses in Italian. Linguistics and Philosophy 20 (5):469-514.
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  38. 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.
  39. E. P. Brandon (1982). Quantifiers and the Pursuit of Truth. Educational Philosophy and Theory 14 (1):51–58.
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  40. Adrian Brasoveanu, Structured Anaphora to Quantifier Domains: A Unified Account of Quantificational and Modal Subordination.
    The paper proposes an account of the contrast (noticed in Karttunen 1976) between the interpretations of the following two discourses: Harvey courts a girl at every convention. {She is very pretty. vs. She always comes to the banquet with him.}. The initial sentence is ambiguous between two quantifier scopings, but the first discourse as a whole allows only for the wide-scope indefinite reading, while the second allows for both. This cross-sentential interaction between quantifier scope and anaphora is captured by means (...)
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  41. Adrian Brasoveanu (2013). The Grammar of Quantification and the Fine Structure of Interpretation Contexts. Synthese 190 (15):3001-3051.
    Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that to account for these phenomena, we need richly structured contexts of interpretation that are passed on between different parts of the same sentence and also across sentential boundaries. The main contribution of the paper is showing how we can add structure to (...)
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  42. Adrian Brasoveanu (2011). Sentence-Internal Different as Quantifier-Internal Anaphora. Linguistics and Philosophy 34 (2):93-168.
    The paper proposes the first unified account of deictic/sentence-external and sentence-internal readings of singular different . The empirical motivation for such an account is provided by a cross-linguistic survey and an analysis of the differences in distribution and interpretation between singular different , plural different and same (singular or plural) in English. The main proposal is that distributive quantification temporarily makes available two discourse referents within its nuclear scope, the values of which are required by sentence-internal uses of singular different (...)
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  43. Adrian Brasoveanu (2008). Donkey Pluralities: Plural Information States Versus Non-Atomic Individuals. [REVIEW] Linguistics and Philosophy 31 (2):129 - 209.
    The paper argues that two distinct and independent notions of plurality are involved in natural language anaphora and quantification: plural reference (the usual non-atomic individuals) and plural discourse reference, i.e., reference to a quantificational dependency between sets of objects (e.g., atomic/non-atomic individuals) that is established and subsequently elaborated upon in discourse. Following van den Berg (PhD dissertation, University of Amsterdam, 1996), plural discourse reference is modeled as plural information states (i.e., as sets of variable assignments) in a new dynamic system (...)
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  44. Adrian Brasoveanu & Donka F. Farkas (2011). How Indefinites Choose Their Scope. Linguistics and Philosophy 34 (1):1-55.
    The paper proposes a novel solution to the problem of scope posed by natural language indefinites that captures both the difference in scopal freedom between indefinites and bona fide quantifiers and the syntactic sensitivity that the scope of indefinites does nevertheless exhibit. Following the main insight of choice functional approaches, we connect the special scopal properties of indefinites to the fact that their semantics can be stated in terms of choosing a suitable witness. This is in contrast to bona fide (...)
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  45. Wylie Breckenridge & Ofra Magidor (2012). Arbitrary Reference. Philosophical Studies 158 (3):377-400.
    Two fundamental rules of reasoning are Universal Generalisation and Existential Instantiation. Applications of these rules involve stipulations (even if only implicitly) such as ‘Let n be an arbitrary number’ or ‘Let John be an arbitrary Frenchman’. Yet the semantics underlying such stipulations are far from clear. What, for example, does ‘n’ refer to following the stipulation that n be an arbitrary number? In this paper, we argue that ‘n’ refers to a number—an ordinary, particular number such as 58 or 2,345,043. (...)
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  46. Berit Brogaard, Donkey Sentences and Quantifier Variability.
    the Central Division of the APA in Chicago, April 19-21 2007. The paper proposes an account of conditional donkey sentences, such as ‘if a farmer buys a donkey, he usually vaccinates it’, which accommodates the fact that the adverb of quantification seems to affect the interpretation of pronouns that are not within its syntactic scope. The analysis defended takes donkey pronouns to go proxy for partitive noun phrases with varying quantificational force. The variation in the interpretation of donkey pronouns, it (...)
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  47. Ian F. Carlstrom (1975). Truth and Entailment for a Vague Quantifier. Synthese 30 (3-4):461 - 495.
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  48. Rudolf Carnap (1946). Modalities and Quantification. Journal of Symbolic Logic 11 (2):33-64.
  49. Emmanuel Chemla (2009). Presuppositions of Quantified Sentences: Experimental Data. [REVIEW] Natural Language Semantics 17 (4):299-340.
    Some theories assume that sentences like (i) with a presupposition trigger in the scope of a quantifier carry an existential presupposition, as in (ii); others assume that they carry a universal presupposition, as in (iii). No student knows that he is lucky. Existential presupposition: At least one student is lucky.Universal presupposition: Every student is lucky. This work is an experimental investigation of this issue in French. Native speakers were recruited to evaluate the robustness of the inference from (i) to (iii). (...)
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  50. Gennaro Chierchia (1993). Questions with Quantifiers. Natural Language Semantics 1 (2):181-234.
    This paper studies the distribution of ‘list readings’ in questions like who does everyone like? vs. who likes everyone?. More generally, it focuses on the interaction between wh-words and quantified NPs. It is argued that, contrary to widespread belief, the pattern of available readings of constituent questions can be explained as a consequence of Weak Crossover, a well-known property of grammar. In particular, list readings are claimed to be a special case of ‘functional readings’, rather than arising from quantifying into (...)
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