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Summary This category can be used for any consideration of quantifiers collectively or, perhaps more appropriately, specific quantifiers (other than existential and universal), such as are present in natural language but not present in another category under Quantifiers.  (I would use the top category for a consideration of quantifiers collectively.)  It can also be used for a consideration of, say, both restricted and unrestricted quantification, or both objectual and substitutional quantification.
Key works An excellent example of a quantifier ever-present in natural language, which is one way to explain the ubiquity of vagueness in natural language (and in our thinking) is Grim 2005.  There really aren't key works, though, given how many topics are covered in a miscellaneous category.
Introductions Likewise, and most certainly, there are no introductory works for any specific quantifier, although some works, such as the one cited above, do not need a great deal of technical sophistication to appreciate (in both senses of that word). Standard logic textbooks are the best introductions to the existential and universal quantifiers, which is why most discussions of these really do not fit here.
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  1. Michele Abrusci & Christian Retoré, Some Proof Theoretical Remarks on Quantification in Ordinary Language.
    This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for a different view based on proof theory, which on many aspects gets closer to the language itself. We stress the importance of Hilbert's oper- ator epsilon and tau for, respectively, existential and universal quantifications. Indeed, these operators help a lot to construct semantic representation close to (...)
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  2. Ernest W. Adams (1974). The Logic of 'Almost All'. Journal of Philosophical Logic 3 (1/2):3 - 17.
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  3. John Bacon (1973). The Semantics of Generic The. Journal of Philosophical Logic 2 (3):323 - 339.
  4. Tista Bagchi, Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface.
    Quantification, Negation, and Focus: Challenges at the Conceptual-Intentional Semantic Interface Tista Bagchi National Institute of Science, Technology, and Development Studies (NISTADS) and the University of Delhi Since the proposal of Logical Form (LF) was put forward by Robert May in his 1977 MIT doctoral dissertation and was subsequently adopted into the overall architecture of language as conceived under Government-Binding Theory (Chomsky 1981), there has been a steady research effort to determine the nature of LF in language in light of structurally (...)
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  5. Pierre Baumann (2013). Are Quantifier Phrases Always Quantificational? The Case of 'Every F'. Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 (2):143-172.
    This paper argues that English quantifier phrases of the form ‘every F’ admit of a literal referential interpretation, contrary to the standard semantic account of this expression, according to which it denotes a set and a second-order relation. Various arguments are offered in favor of the referential interpretation, and two likely objections to it are forestalled.
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  6. Arvid Båve (2011). How To Precisify Quantifiers. Journal of Philosophical Logic 40 (1):103-111.
    I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the (...)
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  7. André Bazzoni (forthcoming). Hintikka on the Foundations of Mathematics: IF Logic and Uniformity Concepts. Journal of Philosophical Logic:1-10.
    The initial goal of the present paper is to reveal a mistake committed by Hintikka in a recent paper on the foundations of mathematics. His claim that independence-friendly logic (IFL) is the real logic of mathematics is supported in that article by an argument relying on uniformity concepts taken from real analysis. I show that the central point of his argument is a simple logical mistake. Second and more generally, I conclude, based on the previous remarks and on another standard (...)
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  8. David Bell (1971). Fallacies in Predicate Logic? Mind 80 (317):145-147.
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  9. Hanoch Ben-Yami (2014). The Quantified Argument Calculus. Review of Symbolic Logic 7 (1):120-146.
    I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on (...)
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  10. Maria Bittner, Temporal Quantification as Top-Level Anaphora.
    This is part two of our discussion of discourses involving anaphora to and by quantificational expressions of various types. In part one (March 8), we focused on quantification over individuals ("Nominal quantification as top-level anaphora"). In part two (March 22-29), we show that the proposed analysis of quantification, as anaphoric discourse reference to top-ranked sets, automatically generalizes to temporal quantifiers (over times, events, or states).
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  11. Maria Bittner (1995). Quantification in Eskimo: A Challenge for Compositional Semantics. In E. Bach, E. Jelinek, A. Kratzer & B. Partee (eds.), Quantification in Natural Languages. Kluwer. 59--80.
    This paper describes quantificational structures in Greenlandic Eskimo (Kalaallisut), a language where familiar quantificational meanings are expressed in ways that are quite different from English. Evidence from this language thus poses some formidable challenges for cross-linguistic theories of compositional semantics.
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  12. Maria Bittner (1987). On the Semantics of the Greenlandic Antipassive and Related Constructions. International Journal of American Linguistics 53:194–231.
    : This study describes a new field method, suited for investigating scope relations — and other aspects of truth conditional meaning — with native speaker consultants who may speak no other language and have no background in linguistics or logic. This method revealed a surprising scope contrast between the antipassive and the ergative construction in Greenlandic Eskimo. The results of this field work are described in detail and a crosslinguistic scope generalization is proposed based on Greenlandic Eskimo, Basque, Polish, Russian, (...)
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  13. Adrian Brasoveanu & Donka F. Farkas, Exceptional Wide Scope as Anaphora to Quantificational Dependencies.
    The paper proposes a novel account to the problem of exceptional scope (ES) of (in)definites, e.g. the widest and intermediate scope readings of the sentence Every student of mine read every poem that a famous Romanian poet wrote before World War II. We propose that ES readings are available when the sentence is interpreted as anaphoric to quantificational domains and quantificational dependencies introduced in the previous discourse. For example, the two every quantifiers and the indefinite elaborate on the sets of (...)
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  14. Adam Cuevas, Unrestricted Exportation: No Toying with Pragmatic English as English Itself.
  15. Martin Davies (1989). 'Two Examiners Marked Six Scripts.' Interpretations of Numerically Quantified Sentences. Linguistics and Philosophy 12 (3):293 - 323.
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  16. Alice Drewery (2005). The Logical Form of Universal Generalizations. Australasian Journal of Philosophy 83 (3):373 – 393.
    First order logic does not distinguish between different forms of universal generalization; in this paper I argue that lawlike and accidental generalizations (broadly construed) have a different logical form, and that this distinction is syntactically marked in English. I then consider the relevance of this broader conception of lawlikeness to the philosophy of science.
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  17. Paulo Faria (2010). Existence as a Real Predicate. Veritas: Revista de Filosofia da PUCRS 55 (2):33-41.
  18. Ilaria Frana (2013). Quantified Concealed Questions. Natural Language Semantics 21 (2):179-218.
    This paper presents a novel treatment of quantified concealed questions , examining different types of NP predicates and deriving the truth conditions for pair-list and set readings. A generalization is proposed regarding the distribution of the two readings, namely that pair-list readings arise from CQs with relational head nouns, whereas set readings arise from CQs whose head nouns are not relational. It is shown that set readings cannot be derived under the ‘individual concept’ approach, one of the most influential analyses (...)
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  19. Danny Frederick, Flaws in Dummett’s Syntactical Account of Singular Terms.
    Dummett defines a ‘predicate’ as that which combines with one or more singular terms to form a sentence. His account of ‘singular term’ is syntactical, involving three necessary conditions. He discusses a fourth, ‘Aristotelian’, criterion before propounding a criterion of predicate quantification which he claims to be superior to it. He tentatively proposes that the three necessary conditions plus the criterion of predicate quantification yield sufficient conditions for being a singular term. I show that Dummett’s necessary conditions fail with regard (...)
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  20. Joseph Fulda (1996). Counterfactuals Revisited. Sorites 5:35-38.
    This paper presents an ontologically leaner, mathematically cleaner, and logically keener explication of counterfactuals and possible worlds than the standard Lewis-Stalnaker account.
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  21. Joseph Fulda (1995). Denied Conditionals Are Not Negated Conditionals. Sorites 2:45-45.
    This note addresses the problems that arise from denying conditionals in classical logic and concludes that such problems result from using propositional logic where predicate logic with quantification over cases is indicated.
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  22. Joseph S. Fulda (2013). The Logic of Failures of the Cinematic Imagination: Two Case Studies and a Logical Puzzle and Solution in Just One. Pragmatics and Society 4 (1):105-111.
    This piece is intended to explicate - by providing a precising definition of - the common cinematic figure which I term “the failure of the cinematic imagination,“ while presenting a logical puzzle and its solution within a simple Gricean framework. -/- It should be noted that this is neither fully accurate nor fully precise, because of the audience; one should examine the remaining articles in the issue to understand what I mean.
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  23. Joseph S. Fulda (2005). A Pragmatic, Truth-Functional Solution to a Logical Difficulty with Biconditionals Absent in Conditionals. Journal of Pragmatics 37 (9/12):1419-1425/2120.
    Solves what is sometimes, but not always, referred to as the third paradox of material implication. Readers downloading this piece should please also download the corrigendum. Note that "pragmatic" is here used in its original sense of context-sensitive, that is, adjacency. (This comment is made in response to an article in a student journal published in the western U.S. which claimed that I said that because something involves translation it must be pragmatic; that is so, in the original sense; only (...)
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  24. Joseph S. Fulda (1992). Material Implications. American Mathematical Monthly 99 (5):480.
  25. Pietro Galliani (2013). Epistemic Operators in Dependence Logic. Studia Logica 101 (2):367-397.
    The properties of the ${\forall^{1}}$ quantifier defined by Kontinen and Väänänen in [13] are studied, and its definition is generalized to that of a family of quantifiers ${\forall^{n}}$ . Furthermore, some epistemic operators δ n for Dependence Logic are also introduced, and the relationship between these ${\forall^{n}}$ quantifiers and the δ n operators are investigated.The Game Theoretic Semantics for Dependence Logic and the corresponding Ehrenfeucht- Fraissé game are then adapted to these new connectives.Finally, it is proved that the ${\forall^{1}}$ quantifier (...)
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  26. Christopher Gauker (2010). Global Domains Versus Hidden Indexicals. Journal of Semantics 27 (2):243-270.
    Jason Stanley has argued that in order to obtain the desired readings of certain sentences, such as “In most of John’s classes, he fails exactly three Frenchmen”, we must suppose that each common noun is associated with a hidden indexical that may be either bound by a higher quantifier phrase or interpreted by the context. This paper shows that the desired readings can be obtained as well by interpreting nouns as expressing relations and without supposing that nouns are associated with (...)
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  27. Anastasia Giannakidou (2001). The Meaning of Free Choice. Linguistics and Philosophy 24 (6):659-735.
    In this paper, I discuss the distribution and interpretation of free choice items (FCIs) in Greek, a language exhibiting a lexical paradigm of such items distinct from that of negative polarity items. Greek differs in this respect from English, which uniformly employs any. FCIs are grammatical only in certain contexts that can be characterized as nonveridical (Giannakidou 1998, 1999), and although they yield universal-like interpretations in certain structures, they are not, I argue, universal quantifiers. Evidence will be provided that FCIsare (...)
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  28. Nina Gierasimczuk & Jakub Szymanik (2009). Branching Quantification V. Two-Way Quantification. Journal of Semantics 26 (4):329-366.
    Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.
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  29. Michael Glanzberg (2007). Definite Descriptions and Quantifier Scope: Some Mates Cases Reconsidered. European Journal of Analytic Philosophy 3 (2):133-158.
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  30. Michael Glanzberg (2004). Quantification and Realism. Philosophy and Phenomenological Research 69 (3):541–572.
    This paper argues for the thesis that, roughly put, it is impossible to talk about absolutely everything. To put the thesis more precisely, there is a particular sense in which, as a matter of semantics, quantifiers always range over domains that are in principle extensible, and so cannot count as really being ‘absolutely everything’. The paper presents an argument for this thesis, and considers some important objections to the argument and to the formulation of the thesis. The paper also offers (...)
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  31. Michael Glanzberg, Quantifiers.
    Quantified terms are terms of generality. They are also provide some of our prime examples of the phenomenon of scope. The distinction between singular and general terms, as well as the ways that general terms enter into scope relations, are certainly fundamental to our understanding of language. Yet when we turn to natural language, we encounter a huge and apparently messy collection of general terms; not just every and some, but most, few, between five and ten, and many others. Natural-language (...)
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  32. Joanna Golinska-Pilarek & Konrad Zdanowski (2003). Spectra of Formulae with Henkin Quantifiers. In A. Rojszczak, J. Cachro & G. Kurczewski (eds.), Philosophical Dimensions of Logic and Science. Kluwer Academic Publishers.
    It is known that various complexity-theoretical problems can be translated into some special spectra problems. Thus, questions about complexity classes are translated into questions about the expressive power of some languages. In this paper we investigate the spectra of some logics with Henkin quantifiers in the empty vocabulary.
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  33. Patrick Grim (2005). The Buried Quantifier: An Account of Vagueness and the Sorites. Analysis 65 (286):95–104.
  34. J. H. Harris (1982). What's So Logical About the “Logical” Axioms? Studia Logica 41 (2-3):159 - 171.
    Intuitionists and classical logicians use in common a large number of the logical axioms, even though they supposedly mean different things by the logical connectives and quantifiers — conquans for short. But Wittgenstein says The meaning of a word is its use in the language. We prove that in a definite sense the intuitionistic axioms do indeed characterize the logical conquans, both for the intuitionist and the classical logician.
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  35. Jim Higginbotham (1994). Mass and Count Quantifiers. Linguistics and Philosophy 17 (5):447 - 480.
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  36. Philip Hugly & Charles Sayward (1984). Do We Need Quantification? Notre Dame Journal of Formal Logic 25 (4):289-302.
    The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can (...)
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  37. Andrea Iacona (forthcoming). Quantification and Logical Form. In Alessandro Torza (ed.), Quantifiers, Quantifiers, and Quantifiers. Springer.
    This paper deals with the logical form of quantified sentences. Its purpose is to elucidate one plausible sense in which quantified sentences can adequately be represented in the language of first-order logic. Section 1 introduces some basic notions drawn from general quantification theory. Section 2 outlines a crucial assumption, namely, that logical form is a matter of truth-conditions. Section 3 shows how the truth-conditions of quantified sentences can be represented in the language of first-order logic consistently with some established undefinability (...)
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  38. Fred Johnson (1994). Syllogisms with Fractional Quantifiers. Journal of Philosophical Logic 23 (4):401 - 422.
    Aristotle's syllogistic is extended to include denumerably many quantifiers such as 'more than 2/3' and 'exactly 2/3.' Syntactic and semantic decision procedures determine the validity, or invalidity, of syllogisms with any finite number of premises. One of the syntactic procedures uses a natural deduction account of deducibility, which is sound and complete. The semantics for the system is non-classical since sentences may be assigned a value other than true or false. Results about symmetric systems are given. And reasons are given (...)
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  39. H. Jerome Keisler & Wafik Boulos Lotfallah (2004). First Order Quantifiers in Monadic Second Order Logic. Journal of Symbolic Logic 69 (1):118-136.
    This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01]. We introduce an operation $esists_{n}(S)$ on properties S that says "there are n components having S". We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As a corollary, (...)
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  40. Steven T. Kuhn (1980). Quantifiers as Modal Operators. Studia Logica 39 (2-3):145 - 158.
    Montague, Prior, von Wright and others drew attention to resemblances between modal operators and quantifiers. In this paper we show that classical quantifiers can, in fact, be regarded as S5-like operators in a purely propositional modal logic. This logic is axiomatized and some interesting fragments of it are investigated.
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  41. Shalom Lappin, Intensional First-Order Logic with Types.
    The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. Some extensions to the type theory are discussed, type polymorphism, and enriching the system with sufficient number theory to account for quantifiers of proportion, such as “most.”.
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  42. E. J. Lemmon (1957). Quantifiers and Modal Operators. Proceedings of the Aristotelian Society 58:245 - 268.
  43. Bert Mosselmans (2008). Aristotle's Logic and the Quest for the Quantification of the Predicate. Foundations of Science 13 (3-4):195-198.
    This paper examines the quest for the quantification of the predicate, as discussed by W.S. Jevons, and relates it to the discussion about universals and particulars between Plato and Aristotle. We conclude that the quest for the quantification of the predicate can only be achieved by stripping the syllogism from its metaphysical heritage.
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  44. Kimiko Nakanishi (2012). The Scope of Even and Quantifier Raising. Natural Language Semantics 20 (2):115-136.
    This paper addresses the question of whether the preverbal even (VP-even) embedded in a nonfinite clause can take wide scope (e.g., Bill refused to even drink WATER). The paper presents novel evidence for wide scope VP-even that is independent of the presuppositions of even. The evidence is based on examples of antecedent-contained deletion (ACD), where embedded VP-even associates with a nominal constituent (or part of it) that raises out of the embedded clause via quantifier raising. Assuming that even must c-command (...)
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  45. Paloma Pérez-Ilzarbe (2009). Late Medieval Trinitarian Syllogistics: From the Theological Debates to a Logical Textbook. In A. Schuman (ed.), Logic in Religious Discourse. Ontos Verlag.
    Jerónimo Pardo's analysis of the problems raised by some popular trinitarian paralogisms is studied in this paper. The purpose is to show how the notions employed by the theologians in order to solve theological problems were introduced into a textbook on logic to deal with some genuinely logical problems. First, the problem, common to all logical approaches, of achieving a fine-grained analysis of the logical form of syllogistical inferences. Second, the problem, typical of the terminist approach to logic, of guaranteeing (...)
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  46. Niki Pfeifer & Gernot D. Kleiter, Syllogistic Reasoning with Intermediate Quantifiers.
    n S are P ”) is proposed for evaluating the rationality of human syllogistic reasoning. Some relations between intermediate quantifiers and probabilistic interpretations are discussed. The paper concludes by the generalization of the atmosphere, matching and conversion hypothesis to syllogisms with intermediate quanti- fiers. Since our experiments are currently still running, most of the paper is theoretical and intended to stimulate psychological studies.
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  47. Pierre Pica & William Snyder (1995). Weak Crossover, Scope, and Agreement in a Minimalist Framework. In Susanne Preuss, Martha Senturia, Raul Aranovich & William Byrne (eds.), Proceedings of the 13th West Coast Conference in Linguistics. Cambridge University Press.
    Our paper presents a novel theory of weak crossover effects, based entirely on quantifier scope preferences and their consequences for variable binding. The structural notion of 'crossover' play no role. We develop a theory of scope preferences which ascribes a central role to the AGR-P System.
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  48. Paul M. Pietroski (2003). Quantification and Second Order Monadicity. Philosophical Perspectives 17 (1):259–298.
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  49. Paul Pietroski, Jeffrey Lidz, Tim Hunter & Justin Halberda (2009). The Meaning of 'Most': Semantics, Numerosity and Psychology. Mind and Language 24 (5):554-585.
    The meaning of 'most' can be described in many ways. We offer a framework for distinguishing semantic descriptions, interpreted as psychological hypotheses that go beyond claims about sentential truth conditions, and an experiment that tells against an attractive idea: 'most' is understood in terms of one-to-one correspondence. Adults evaluated 'Most of the dots are yellow', as true or false, on many trials in which yellow dots and blue dots were displayed for 200 ms. Displays manipulated the ease of using a (...)
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  50. Erich Rast (2013). On Contextual Domain Restriction in Categorial Grammar. Synthese 190 (12):2085-2115.
    Abstract -/- Quantifier domain restriction (QDR) and two versions of nominal restriction (NR) are implemented as restrictions that depend on a previously introduced interpreter and interpretation time in a two-dimensional semantic framework on the basis of simple type theory and categorial grammar. Against Stanley (2002) it is argued that a suitable version of QDR can deal with superlatives like tallest. However, it is shown that NR is needed to account for utterances when the speaker intends to convey different restrictions for (...)
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