Search results for 'Polyadic quantification' (try it on Scholar)

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  1.  91
    Ori Simchen (2010). Polyadic Quantification Via Denoting Concepts. Notre Dame Journal of Formal Logic 51 (3):373-381.
    The question of the origin of polyadic expressivity is explored and the results are brought to bear on Bertrand Russell's 1903 theory of denoting concepts, which is the main object of criticism in his 1905 "On Denoting." It is shown that, appearances to the contrary notwithstanding, the background ontology of the earlier theory of denoting enables the full-blown expressive power of first-order polyadic quantification theory without any syntactic accommodation of scopal differences among denoting phrases such as 'all (...)
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  2. Universally Free First Order Quantification (forthcoming). A Note on Universally Free First Order Quantification Theory Ap Rao. Logique Et Analyse.
     
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  3.  33
    Friederike Moltmann (1995). Exception Sentences and Polyadic Quantification. Linguistics and Philosophy 18 (3):223 - 280.
    In this paper, I have proposed a compositional semantic analysis of exception NPs from which three core properties of exception constructions could be derived. I have shown that this analysis overcomes various empirical and conceptual shortcomings of prior proposals of the semantics of exception sentences. The analysis was first formulated for simple exception NPs, where the EP-complement was considered a set-denoting term and the EP-associate was a monadic quantifier. It was then generalized in two steps: first, in order to account (...)
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  4.  68
    Jakub Szymanik (2010). Computational Complexity of Polyadic Lifts of Generalized Quantifiers in Natural Language. Linguistics and Philosophy 33 (3):215-250.
    We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. Next, we focus on a linguistic case study. We use computational complexity results to (...)
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  5.  1
    Yde Venema (1994). A Modal Logic For Quantification And Substitution. Logic Journal of the IGPL 2 (1):31-45.
    The aim of this paper is to study the n-variable fragment of first order logic from a modal perspective. We define a modal formalism called cylindric mirror modal logic, and show how it is a modal version of first order logic with substitution. In this approach, we can define a semantics for the language which is closely related to algebraic logic, as we find Polyadic Equality Algebras as the modal or complex algebras of our system. The main contribution of (...)
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  6.  25
    Nicholas Denyer (1999). Names, Verbs and Quantification Again. Philosophy 74 (3):439-440.
    There are enormous differences between quantifying name-variables only, quantifying verb-variables only, and quantifying both. These differences are found only in the logic of polyadic predication; and this presumably is why Richard Gaskin thinks that they distinguish names from transitive verbs only, and not from verbs generally. But that thought is mistaken: these differences also distinguish names from intransitive verbs. They thus vindicate the common idea that on the difference between names and verbs we may base grandiose metaphysical distinctions, and (...)
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  7.  24
    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 (...)
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  8.  22
    Shane Steinert-Threlkeld & Thomas F. Icard Iii (2013). Iterating Semantic Automata. Linguistics and Philosophy 36 (2):151-173.
    The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic (...)
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  9. Gillian Russell (2005). Review: Warren Goldfarb's Deductive Logic. [REVIEW] Australasian Journal of Logic 3:63-66.
    Deductive Logic is an introductory textbook in formal logic. The book is divided into four parts covering (i) truth-functional logic, (ii) monadic quantifi- cation, (iii) polyadic quantification and (iv) names and identity, and there are exercises for all these topics at the end of the book. In the truth-functional logic part, the reader learns to produce paraphrases of English statements and arguments in logical notation (this subsection is called “analysis”), then about the semantic properties of such paraphrased statements (...)
     
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  10.  17
    Shane Steinert-Threlkeld & I. I. I. Thomas F. Icard (2013). Iterating Semantic Automata. Linguistics and Philosophy 36 (2):151-173.
    The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic (...)
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  11.  29
    Edward L. Keenan, Further Beyond the Frege Boundary.
    avant propos This paper is basically Keenan (1992) augmented by some new types of properly polyadic quantification in natural language drawn from Moltmann (1992), Nam (1991) and Srivastav (1990). In addition I would draw the reader's attention to recent mathematical studies of polyadic quantiicationz Ben-Shalom (1992), Spaan (1992) and Westerstahl (1992). The first and third of these extend and generalize (in some cases considerably) the techniques and results in Keenan (1992). Finally I would like to acknowledge the (...)
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  12.  25
    Jan van Eijck, Types of Relations.
    Many arguments for flexible type assignment to syntactic categories have to do with the need to account for the various scopings resulting from the interaction of quantified DPs with other quantified DPs or with intensional or negated verb contexts. We will define a type for arbitrary arity relations in polymorphic type theory. In terms of this, we develop the Boolean algebra of relations as far as needed for natural language semantics. The type for relations is flexible: it can do duty (...)
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  13.  50
    Maria Bittner, NASSLLI 2016 Dynamic Semantics (5): Quantification.
    Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 5: Quantification. Abstract: In discourse, quantifiers can function as antecedents or anaphors. We analyze a sample discourse in Dynamic Plural Logic (DPlL, van den Berg 1993, 1994), which represents not only current discourse referents, but also current relations by means of plural information states. This makes it possible to analyze quantification as structured discourse reference. Finally, the DPlL analysis is transposed into Update with Centering, to simplify the formalism and (...)
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  14.  46
    Jakub Szymanik (2009). Quantifiers in TIME and SPACE. Computational Complexity of Generalized Quantifiers in Natural Language. Dissertation, University of Amsterdam
    In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in polynomial time. (...)
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  15. Øystein Linnebo (2008). Plural Quantification. Stanford Encyclopedia of Philosophy.
    Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it (...)
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  16. Stephen Barker (2015). Expressivism About Reference and Quantification Over the Non-Existent Without Meinongian Metaphysics. Erkenntnis 80 (S2):215-234.
    Can we believe that there are non-existent entities without commitment to the Meinongian metaphysics? This paper argues we can. What leads us from quantification over non-existent beings to Meinongianism is a general metaphysical assumption about reality at large, and not merely quantification over the non-existent. Broadly speaking, the assumption is that every being we talk about must have a real definition. It’s this assumption that drives us to enquire into the nature of beings like Pegasus, and what our (...)
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  17.  17
    Kai F. Wehmeier (forthcoming). Identity and Quantification. Philosophical Studies:1-12.
    It is a philosophical commonplace that quantification involves, invokes, or presupposes, the relation of identity. There seem to be two major sources for this belief: the conviction that identity is implicated in the phenomenon of bound variable recurrence within the scope of a quantifier; memories of Quine’s insistence that quantification requires absolute identity for the values of variables. With respect to, I show that the only extant argument for a dependence of variable recurrence on identity, due to John (...)
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  18.  30
    Yoad Winter (2000). Distributivity and Dependency. Natural Language Semantics 8 (1):27-69.
    Sentences with multiple occurrences of plural definites give rise to certain effects suggesting that distributivity should be modeled by polyadic operations. Yet in this paper it is argued that the simpler treatment of distributivity using unary universal quantification should be retained. Seemingly polyadic effects are claimed to be restricted to definite NPs. This fact is accounted for by the special anaphoric (dependent) use of definites. Further evidence concerning various plurals, island constraints, and cumulative quantification is shown (...)
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  19.  84
    William Craig (2014). Peter van Inwagen, Substitutional Quantification, and Ontological Commitment. Notre Dame Journal of Formal Logic 55 (4):553-561.
    Peter van Inwagen has long claimed that he doesn’t understand substitutional quantification and that the notion is, in fact, meaningless. Van Inwagen identifies the source of his bewilderment as an inability to understand the proposition expressed by a simple sentence like “,” where “$\Sigma$” is the existential quantifier understood substitutionally. I should think that the proposition expressed by this sentence is the same as that expressed by “.” So what’s the problem? The problem, I suggest, is that van Inwagen (...)
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  20. Andrea Iacona (2015). Quantification and Logical Form. In Alessandro Torza (ed.), Quantifiers, Quantifiers, and Quantifiers. Springer 125-140.
    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 (...)
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  21.  10
    Kristen A. Greer (2014). Extensionality in Natural Language Quantification: The Case of Many and Few. Linguistics and Philosophy 37 (4):315-351.
    This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers :599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen, I assume that the universe consists of the union of alternatives to the (...)
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  22.  39
    J. Landes, J. B. Paris & A. Vencovská (2011). A Survey of Some Recent Results on Spectrum Exchangeability in Polyadic Inductive Logic. Synthese 181 (1):19 - 47.
    We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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  23.  12
    Peter Schroeder-Heister (2014). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica 102 (6):1185-1216.
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational account of proof-theoretic harmony. With every set of introduction rules a canonical (...)
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  24.  83
    Salvatore Florio (2014). Unrestricted Quantification. Philosophy Compass 9 (7):441-454.
    Semantic interpretations of both natural and formal languages are usually taken to involve the specification of a domain of entities with respect to which the sentences of the language are to be evaluated. A question that has received much attention of late is whether there is unrestricted quantification, quantification over a domain comprising absolutely everything there is. Is there a discourse or inquiry that has absolute generality? After framing the debate, this article provides an overview of the main (...)
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  25.  38
    Juha Kontinen & Jakub Szymanik (2008). A Remark on Collective Quantification. Journal of Logic, Language and Information 17 (2):131-140.
    We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize (...)
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  26. Philip Hugly & Charles Sayward (1987). Why Substitutional Quantification Does Not Express Existence. Theory and Decision 50:67-75.
    Fundamental to Quine’s philosophy of logic is the thesis that substitutional quantification does not express existence. This paper considers the content of this claim and the reasons for thinking it is true.
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  27.  62
    Massimiliano Carrara & Enrico Martino (2011). On the Infinite in Mereology with Plural Quantification. Review of Symbolic Logic 4 (1):54-62.
    In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and plural (...)
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  28.  84
    Friederike Moltmann (2015). Quantification with Intentional and with Intensional Verbs. In Alessandro Torza (ed.), Quantifiers, Quantifiers, and Quantifiers. Springer
    The question whether natural language permits quantification over intentional objects as the ‘nonexistent’ objects of thought is the topic of a major philosophical controversy, as is the status of intentional objects as such. This paper will argue that natural language does reflect a particular notion of intentional object and in particular that certain types of natural language constructions (generally disregarded in the philosophical literature) cannot be analysed without positing intentional objects. At the same time, those intentional objects do not (...)
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  29.  7
    Peter Hallman (2009). Proportions in Time: Interactions of Quantification and Aspect. [REVIEW] Natural Language Semantics 17 (1):29-61.
    Proportional quantification and progressive aspect interact in English in revealing ways. This paper investigates these interactions and draws conclusions about the semantics of the progressive and telicity. In the scope of the progressive, the proportion named by a proportionality quantifier (e.g. most in The software was detecting most errors) must hold in every subevent of the event so described, indicating that a predicate in the scope of the progressive is interpreted as an internally homogeneous activity. Such an activity interpretation (...)
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  30.  48
    Geoff Georgi (2015). A Propositional Semantics for Substitutional Quantification. Philosophical Studies 172 (5):1183-1200.
    The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest in substitutional (...), namely, theories of truth and ontological commitment. (shrink)
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  31.  60
    Patrick Dieveney (2014). Quantification and Metaphysical Discourse. Theoria 80 (4):292-318.
    It is common in metaphysical discourse to make claims like “Everything is self-identical” in which “everything” is intended to range over everything. This sort of “unrestricted” generality appears central to metaphysical discourse. But there is debate whether such generality, which appears to involve quantification over an all-inclusive domain, is even meaningful. To address this concern, Shaughan Lavine and Vann McGee supply competing accounts of the generality expressed by this use of “everything.” I argue that, from the perspective of the (...)
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  32.  28
    George Georgescu (2010). States on Polyadic Mv-Algebras. Studia Logica 94 (2):231 - 243.
    This paper is a contribution to the algebraic logic of probabilistic models of Łukasiewicz predicate logic. We study the MV-states defined on polyadic MV-algebras and prove an algebraic many-valued version of Gaifman’s completeness theorem.
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  33.  92
    Philip Hugly & Charles Sayward (2002). There Is A Problem with Substitutional Quantification. Theoria 68 (1):4-12.
    Whereas arithmetical quantification is substitutional in the sense that a some-quantification is true only if some instance of it is true, it does not follow (and, in fact, is not true) that an account of the truth-conditions of the sentences of the language of arithmetic can be given by a substitutional semantics. A substitutional semantics fails in a most fundamental fashion: it fails to articulate the truth-conditions of the quantifications with which it is concerned. This is what is (...)
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  34.  38
    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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  35.  2
    Tarek Sayed Ahmed (2010). The Class of Polyadic Algebras has the Super Amalgamation Property. Mathematical Logic Quarterly 56 (1):103-112.
    We show that for infinite ordinals α the class of polyadic algebras of dimension α has the super amalgamation property.
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  36.  35
    Hellman Geoffrey (1996). Structuralism Without Structures. Philosophia Mathematica 4 (2):100-123.
    Recent technical developments in the logic of nominalism make it possible to improve and extend significantly the approach to mathematics developed in Mathematics without Numbers. After reviewing the intuitive ideas behind structuralism in general, the modal-structuralist approach as potentially class-free is contrasted broadly with other leading approaches. The machinery of nominalistic ordered pairing (Burgess-Hazen-Lewis) and plural quantification (Boolos) can then be utilized to extend the core systems of modal-structural arithmetic and analysis respectively to full, classical, polyadic third- and (...)
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  37.  68
    Philip Percival (2011). Predicate Abstraction, the Limits of Quantification, and the Modality of Existence. Philosophical Studies 156 (3):389-416.
    For various reasons several authors have enriched classical first order syntax by adding a predicate abstraction operator. “Conservatives” have done so without disturbing the syntax of the formal quantifiers but “revisionists” have argued that predicate abstraction motivates the universal quantifier’s re-classification from an expression that combines with a variable to yield a sentence from a sentence, to an expression that combines with a one-place predicate to yield a sentence. My main aim is to advance the cause of predicate abstraction while (...)
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  38. Gregory Lavers (2015). Carnap, Quine, Quantification and Ontology. In Alessandro Torza (ed.), Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language. Springer
    Abstract At the time of The Logical Syntax of Language (Syntax), Quine was, in his own words, a disciple of Carnap’s who read this work page by page as it issued from Ina Carnap’s typewriter. The present paper will show that there were serious problems with how Syntax dealt with ontological claims. These problems were especially pronounced when Carnap attempted to deal with higher order quantification. Carnap, at the time, viewed all talk of reference as being part of the (...)
     
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  39.  2
    Tarek Sayed Ahmed (2006). The Class of Infinite Dimensional Neat Reducts of Quasi‐Polyadic Algebras is Not Axiomatizable. Mathematical Logic Quarterly 52 (1):106-112.
    SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].
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  40.  44
    Takashi Yagisawa (2012). Unrestricted Quantification and Reality: Reply to Kim. [REVIEW] Acta Analytica 27 (1):77-79.
    In my book, Worlds and Individuals, Possible and Otherwise , I use the novel idea of modal tense to respond to a number of arguments against modal realism. Peter van Inwagen’s million-carat-diamond objection is one of them. It targets the version of modal realism by David Lewis and exploits the fact that Lewis accepts absolutely unrestricted quantification. The crux of my response is to use modal tense to neutralize absolutely unrestricted quantification. Seahwa Kim says that even when equipped (...)
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  41.  44
    Mark Textor (2005). Truth Via Sentential Quantification. Dialogue 44 (3):539-550.
    This paper is a critical evaluation of Kuenne's attempt to define truth via quantification into the position of a sentence.
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  42.  37
    Philip Hugly & Charles Sayward (1982). Indenumerability and Substitutional Quantification. Notre Dame Journal of Formal Logic 23 (4):358-366.
    We here establish two theorems which refute a pair of what we believe to be plausible assumptions about differences between objectual and substitutional quantification. The assumptions (roughly stated) are as follows: (1) there is at least one set d and denumerable first order language L such that d is the domain set of no interpretation of L in which objectual and substitutional quantification coincide. (2) There exist interpreted, denumerable, first order languages K with indenumerable domains such that substitutional (...)
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  43.  45
    Stephen Donaho (2002). Standard Quantification Theory in the Analysis of English. Journal of Philosophical Logic 31 (6):499-526.
    Standard first-order logic plus quantifiers of all finite orders ("SFOLω") faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOLω models. The typed structure of SFOLω models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is (...)
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  44.  20
    James Franklin (2007). Accountancy and the Quantification of Rights: Giving Moral Values Legal Teeth. Centre for an Ethical Society Papers.
    If a company’s share price rises when it sacks workers, or when it makes money from polluting the environment, it would seem that the accounting is not being done correctly. Real costs are not being paid. People’s ethical claims, which in a smaller-scale case would be legally enforceable, are not being measured in such circumstances. This results from a mismatch between the applied ethics tradition and the practice of the accounting profession. Applied ethics has mostly avoided quantification of rights, (...)
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  45.  21
    Philip Hugly & Charles Sayward (1991). Prior and Lorenzen on Quantification. Grazer Philosophishe Studien 41:150-173.
    A case against Prior’s theory of propositions goes thus: (1) everyday propositional generalizations are not substitutional; (2) Priorean quantifications are not objectual; (3) quantifications are substitutional if not objectual; (4) thus, Priorean quantifications are substitutional; (5) thus that Priorean quantifications are not ontologically committed to propositions provides no basis for a similar claim about our everyday propositional generalizations. Prior agrees with (1) and (2). He rejects (3), but fails to support that rejection with an account of quantification on which (...)
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  46.  21
    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 (...)
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  47.  7
    Dumitru Daniel Drăgulici (2006). Conservative Extension of Polyadic MV-Algebras to Polyadic Pavelka Algebras. Archive for Mathematical Logic 45 (5):601-613.
    In this paper we prove polyadic counterparts of the Hájek, Paris and Shepherdson's conservative extension theorems of Łukasiewicz predicate logic to rational Pavelka predicate logic. We also discuss the algebraic correspondents of the provability and truth degree for polyadic MV-algebras and prove a representation theorem similar to the one for polyadic Pavelka algebras.
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  48.  21
    Don Pigozzi & Antonino Salibra (1995). The Abstract Variable-Binding Calculus. Studia Logica 55 (1):129 - 179.
    Theabstract variable binding calculus (VB-calculus) provides a formal frame-work encompassing such diverse variable-binding phenomena as lambda abstraction, Riemann integration, existential and universal quantification (in both classical and nonclassical logic), and various notions of generalized quantification that have been studied in abstract model theory. All axioms of the VB-calculus are in the form of equations, but like the lambda calculus it is not a true equational theory since substitution of terms for variables is restricted. A similar problem with the (...)
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  49.  20
    Mireille Staschok (2008). Non-Traditional Squares of Predication and Quantification. Logica Universalis 2 (1):77-85.
    . Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel. The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating (...)
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  50.  3
    Tarek Sayed Ahmed (2011). On the Complexity of Axiomatizations of the Class of Representable Quasi‐Polyadic Equality Algebras. Mathematical Logic Quarterly 57 (4):384-394.
    Using games, as introduced by Hirsch and Hodkinson in algebraic logic, we give a recursive axiomatization of the class RQPEAα of representable quasi-polyadic equality algebras of any dimension α. Following Sain and Thompson in modifying Andréka’s methods of splitting, to adapt the quasi-polyadic equality case, we show that if Σ is a set of equations axiomatizing RPEAn for equation image and equation imageequation image, k′ < ω are natural numbers, then Σ contains infinitely equations in which − occurs, (...)
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