Terms Of Quantifiers Research Articles

Dynamics of quantum correlations in a quantum dot system with intrinsic decoherence effects

In this paper, we explore the dynamics of quantum correlations in an isolated physical quantum dot under the influence of intrinsic decoherence (ID). We characterize quantum correlations in the quantum dot system using Concurrence to capture the amount of entanglement, and we use Trace Distance Discord (TDD) and Local Quantum Uncertainty (LQU) to measure nonclassical correlations. Likewise, we investigate the effect of ID on the temporal evolution of these quantifiers. In particular, the behavior of the two discord-like quantifiers in terms of the system parameters and the ID rate is investigated and analyzed in detail. We found that TDD and LQU behave similarly for different parameters characterizing the considered system and that TDD is more resistant than Concurrence and LQU against the ID effects. Our results also show that the robustness of quantum correlations can be modulated by adjusting the ID rate, quantum dot physical properties and initial conditions.

Entanglement, nonclassical properties and geometric phase of Raman photon pairs in the presence of time-dependent coupling

In this paper, we develop the model of the four-level double Raman pairs by exploiting the required optimal conditions for this system that are feasible with real experimental realization. We investigate qualitatively the entanglement, statistical properties, and geometric phase for the pair of Stokes and anti-Stokes photons in the presence of the time-dependent coupling effect. We show that these quantifiers are very sensitive to the change of the Rabi frequency and time, exhibiting substantial phenomena that are depending on the kind of coupling between the atom and photons. Finally, we explore the relationship between the quantum quantifiers in terms of the physical parameters with and without time-dependent coupling effect.

On the development of binominal quantifiers in Spanish: the notion of lexical persistence revisited

This paper questions the widespread agreement on routinization processes, and ‘desemanticization’ in particular, as a precondition to grammaticalization. In usage-based approaches, increase in (type as well as token) frequency is generally considered both the result of and a primary contributor to the process (Bybee 2003: 605). The reasoning is as follows: since a stimulus loses its impact with repetition (habituation), increasing frequency leads to the gradual weakening of semantic force (also bleaching or generalization of meaning) and eventually to a loss of semantic transparency and compositionality, i.e. to semantic change. However, the corpus-based analysis of nine quantifying nouns in Spanish shows that these constructions not only present an irregular frequency pattern, but also undergo grammaticalization without necessarily engaging in the typical routinization processes. This paper frames the grammaticalization of binominal quantifiers in terms of ‘conceptually-driven analogy’ (Delbecque & Verveckken 2014) and while highlighting the crucial role of semantic persistence as a driving force, it shows that it is encyclopedic in scope (thus amplifying Hopper’s (1991) notion of ‘lexical persistence’).

Incremental quantification and the dynamics of pair-list phenomena

Distributive universals are unique among natural language quantifiers in the following three ways: (i) matrix interrogatives that contain them accept pair-list answers; (ii) indefinites and disjunctions in their scope may assume arbitrary functional readings; and (iii) they permit sentence-internal interpretations of a wide range of comparative adjectives, like "new" and "different". Because other quantifiers in the same environments do not give rise to these interpretations, the constructions provide a window into the semantic processes that underlie quantificational distributivity. In fact, both pair-list and internal readings have been independently argued to expose some of the compositional clockwork behind universal quantification, but the mechanisms they have been taken to reveal are entirely distinct. In contrast, I propose to explain pair-list phenomena, including a class of functional readings not previously recognized as such, and internal readings of comparative adjectives as two sides of the same coin; they are both side effects of incremental quantification. To make this precise, I analyze distributive universal quantifiers in terms of iterated, incremental update, in effect generalizing the sequential conjunction operator of standard dynamic semantics. I argue that this approach captures the tight empirical connection between pair-lists and internal adjectives, and at the same time provides a simpler and more robust account of the data than the specialized alternatives. http://dx.doi.org/10.3765/sp.8.9 BibTeX info

Processing of Numerical and Proportional Quantifiers

Quantifier expressions like "many" and "at least" are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical (at least seven, at least thirteen, at most seven, at most thirteen) or proportional (many, few) quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding the meaning of quantifiers in terms of response times and acceptability judgments. However, a difference emerges in the comparison strategies when a fixed external reference numerosity (seven or thirteen) is used for numerical quantifiers, whereas an internal numerical criterion is invoked for proportional quantifiers. Moreover, for both quantifier types, quantifier semantics and its polarity (positive vs. negative) biased the response direction (accept/reject). Overall, our results indicate that quantifier comprehension involves core numerical and lexical semantic properties, demonstrating integrated processing of language and numbers.

Editors' Introduction

The idea of interpreting quantifiers in terms of a game between two players was first suggested at the end of the 19th century by one of the inventors of quantification theory, C. S. Peirce, but it laid buried in his papers until it was discovered in the 1980s. His idea was independently discovered in the 1950s, when Leon Henkin suggested a game semantics for infinitary languages. Paul Lorenzen introduced his Dialogspiele at the same time, while his student Kuno Lorenz introduced the vocabulary of game theory that led to our modern conception of game semantics shortly after. The idea is to provide an explanation of the meaning of the logical connectives and quantifiers in terms of rules for non-collaborative, zero-sum games between two agents, one of whom argues for the validity of the claim against moves from the other, and to define truth in terms of the existence of a winning strategy for the defender.

Characterizing quantifier extensions of dependence logic

AbstractWe characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.

Naturalness, Vagueness, and Sortals

In the past few years, deflationary positions in the debate on the nature of composite material objects have become prominent. According to Ted Sider these include the thesis of quantifier variance, against which he has defended ontological realism. Recently, Sider has considered the possibility of rejecting his arguments against the vagueness of the unrestricted quantifiers in terms of translation functions. Against this strategy, he has presented an intuitive complaint and has argued that it can only be resisted if quantifier variance is accepted. But this is false. In this paper I argue, against Sider, that there is a coherent way to combine the rejection of quantifier variance with the vagueness of the unrestricted quantifiers. I sketch a model to show this, and then I consider, on the basis of it, several versions of the indeterminacy argument against the vagueness of the unrestricted quantifiers that Sider has formulated over the years.

Definability of second order generalized quantifiers

We study second order generalized quantifiers on finite structures. One starting point of this research has been the notion of definability of Lindström quantifiers. We formulate an analogous notion for second order generalized quantifiers and study definability of second order generalized quantifiers in terms of Lindström quantifiers.

Superlative Quantifiers as Modifiers of Meta-Speech Acts

The superlative quantifiers, at least and at most, are commonly assumed to have the same truth-conditions as the comparative quantifiers more than and fewer than. However, as Geurts & Nouwen (2007) have demonstrated, this is wrong, and several theories have been proposed to account for them. In this paper we propose that superlative quantifiers are illocutionary operators; specifically, they modify meta-speech acts. Meta speech-acts are operators that do not express a speech act, but a willingness to make or refrain from making a certain speech act. The classic example is speech act denegation, e.g. I don't promise to come, where the speaker is explicitly refraining from performing the speech act of promising What denegations do is to delimit the future development of conversation, that is, they delimit future admissible speech acts. Hence we call them meta-speech acts. They are not moves in a game, but rather commitments to behave in certain ways in the future. We formalize the notion of meta speech acts as commitment development spaces, which are rooted graphs: The root of the graph describes the commitment development up to the current point in conversation; the continuations from the root describe the admissible future directions. We define and formalize the meta-speech act GRANT, which indicates that the speaker, while not necessarily subscribing to a proposition, refrains from asserting its negation. We propose that superlative quantifiers are quantifiers over GRANTs. Thus, Mary petted at least three rabbits means that the minimal number n such that the speaker GRANTs that Mary petted n rabbits is n = 3. In other words, the speaker denies that Mary petted two, one, or no rabbits, but GRANTs that she petted more. We formalize this interpretation of superlative quantifiers in terms of commitment development spaces, and show how the truth conditions that are derived from it are partly entailed and partly conversationally implicated. We demonstrates how the theory accounts for a wide variety of phenomena regarding the interpretation of superlative quantifiers, their distribution, and the contexts in which they can be embedded.

QUANTIFICATION AND CONTRIBUTING OBJECTS TO THOUGHTS*

In this paper, I shall explore a determiner in natural language which is ambivalent as to whether it should be classified as quantificational or objectdenoting: the determiner both. Both in many ways appears to be a paradigmatic quantifier; and yet, I shall argue, it can be interpreted as having an individual—an object—as semantic value. To show the significance of this, I shall discuss two ways of thinking about quantifiers. We often think about quantifiers via intuitions about kinds of thoughts. Certain terms are naturally used to express singular thoughts, and appear to do so by contributing objects to the thoughts expressed. Other terms are naturally used to express general thoughts, and appear to do so by contributing higher-order properties to the thoughts expressed. Viewed this way, the main condition on whether a term is a quantifier or not is whether its semantic value is an object or a higher-order property. At least, these provide necessary conditions. Both can be interpreted as contributing objects to thoughts, and in many cases appears to express genuine singular thoughts. Thinking about quantifiers this way, both can appear object-denoting and non-quantificational. We also often think about quantifiers in terms of a range linguistic features, including semantic value, presupposition, scope, binding, syntactic distribution, and many others. Viewed this way, I shall argue, both can appear quantificational. In particular, it displays scope behavior that is one of the hallmarks of quantification. But, I shall show, it can do so even if given a semantics on which it denotes an object. Thus, both appears quantificational by some linguistic standards, and yet appears object-denoting by standards based on intuitions about the kinds of thoughts it expresses. It can appear this way, I shall argue, because the notion of quantification in natural language is in fact the intersection of a number of features, which do not always group together in the same ways, and do not always group together precisely in accord with our intuitions about expressing singular and general thoughts. Both has some important properties related to

Reply to Ostertag

7Jiscussion REPLY TO OSTERTAG ] AN DEJNOZKA Rackham School of Graduate Studies/ U. of Michigan Ann Arbor, MI 48109, USA DEJNOZKA@JUNO.COM Gary Ostertag's reviewof my book, BertrandRussell onModalityand Logical Relevance,'turns everything he discusses upside down. Thus I am glad that he also ignores over nine tenths of my book. Ostertag says, "It appears then, that Russell is, if anything, hostile to the idea that modality plays a fundamental role in logic" (his p. 169). Right. I agree three times (my pp. 1-2, n2-13, 165), and I quote Russell'shostility twice (my pp. 103, 112). But Ostertag bafflingly proclaims, "Dejnozka holds the very opposite. Not only does Russell embrace modality, he espouses a variety of modal logics" (his p. 169). Wrong. I repeatedly proclaim that Russell rejects all modal notions or modal entities, with the sole exception of goodness in his early ethics (my p. 80). And I never say he espouses a modal logic. What then do I find in Russell? Logically implicitmodal logics!I say,"Allseven of the modal logics I find implicit in Russell ... seem closest to S5" (p. 16). I say, "I define seven modal logics which may be implicitly amibuted to Russell" (p. 61). I indicate seven times that I am discussing logically implicit modal logics (my pp. 16, 17,61 twice, 62, 66, 96 quoting Magnell on my views). Even Ostertag unwittingly quotes me as engaged only in formal "paraphrase" (my p. 61, his p. 171). I state the basic message in the Introduction of my book: Russell's idea is simple: co use notions of ordinary quamificarional logic co define and analyze away modal notions. Modal notions are eliminated across rhe board. The individual ("existential") and universal quantifiers are used to simulate and replace modal notions .... Literallyspeaking, Russellhas banished modality from logic. Yerfunctionally speaking, Russell has achieved a modal logic based on a rich and sophisticated theory of modality.... ' Gary Ostertag, "Russell's Modal Logic?", Russeli n.s. 20 (2000): 165-72, reviewing Jan Dejnozka, BertrandRussell on Modalityand L,,gica/ Relevance (Aldershot, U.K.: Ashgate, 1999). russell: theJournalof BertrandRussell Studies The BertrandRussellResearchCentre, McMastcrU. n.s. 2J (summer 20m): 63-7 ISSN 0036--01631 64 Discussion Russell refuses to allow ontological status to modal entities, and refuses to admit modal notions as logicallyprimitive. But if that were the whole story,then there would be no point in writing this book.... But this is only the beginning of the story. (My p. 2, my new emphasis) Thus I scarcely"ignore or glossover ... those contexts in which Russellis critical of modal notions" (Ostertag, p. 169). I quote them (my pp. 103,n2), and I embrace them as half-bur only as half-of my basic message.The messageis that Russell belongs to the crowd of twentieth-century analysts who banish metaphysical necessity, yet who develop sophisticated logical or linguistic eliminative interpretations of necessity to explain away the appearance of necessity.I indicate this messagefiverimes (pp. 1-2, 57-8, 100-1, n2-13, 165). Ostertag says of the three definitions comprising MDL, "This is, of course, nor quite right: we should be defining the first-order quantifiers in terms of modal notions, not the other way around. (Otherwise, we are interpreting the modal operators, not the quantifiers.)" (his p. 169). Wrong. Or else Ostertag is criticizing Russell. Russells definitions are precisely how he interprets-and explains away-modal notions. And strictly speaking, Russell eliminatively defines both the existential quantifier andrhe MDL possibilityoperator as meaning the veridical "F(x) is not always false" (my pp. n2-13). Thus the basic notions ofRussellian quantification are veridical.And even the veridicalnotions are nothing. They are incomplete fi.mctionshaving only veridical meanings-inuse (my pp. 1-2, 23,91,n2-13). Ostertag caJls MDL "trivial" and stipulative (his p. 170), and says it "adds nothing" to the standard understanding of Principia. Wrong. I explain the controversial Parmenidean basis of MDL in Chapters 3-4. Ostertag infers it is trivial to call Principia a modal logic, and goes on to doubt that MDL is S5. Folks, MDL is not the modal logic!I indicate chat eight times (my pp. ix, 3, 16, 62, 80, 96, 194, 196...

A note on the Kolmogorov data complexity and nonuniform logical definitions

We define a new Kolmogorov complexity based measure of complexity of logics. Then we use this new tool to prove a sharp estimate of the length of first order sentences defining nonuniformly more complicated Lindström quantifiers in terms of simpler ones.

Some results on quantifiers.

Introduction We shall study (generalized) quantifiers in the framework introduced by Barwise and Cooper in [ 1 ], the logical investigation of which has been continued in van Ben them [3] and Keenan and Stavi [2]. The present paper, although self-contained, is in the spirit of [3]. Its main characteristic is a systematic use of a method of proof introduced by van Benthem, which is based on a representation of quantifiers as relations on the natural numbers. With this method we give simplified proofs of a number of van Benthem's results and prove some new ones. In particular, the number-theoretic representation proves convenient for studying monotonicity behavior of quantifiers, and our main result is a characterization of the first-order definable quantifiers in terms of monotonicity.

Undefinability of addition from one unary operator

It is the object of this paper to prove that the binary operator of addition of the natural numbers is not arithmetically definable in terms of a single unary operator. An arithmetical (or elementary) definition is one in which no variables ranging over sets of natural numbers are permitted; all variables range over just the natural numbers themselves. It is actually easier to prove something more than this: that a single unary operator will not suffice even when any number of one-place predicates of natural numbers are added. The method of proof is by elimination of quantifiers, originally due to Presburger. A by-product of the method used is the subsidiary result that addition is not definable without quantifiers in terms of any set of unary operators, one-place predicates and two-place predicates. The interpreted well-formed formulas herein considered have the following as symbols: =, identity, interpreted in the usual way; f, a unary functor, interpreted as a unary operator over the natural numbers; truth functions and quantifiers; and predicate letters, each interpreted as a definite property of natural numbers. a, b, c, d, x, y, z are variables. A term will be either a variable x or f'(x), i.e.,f(f (... (x) ... )), in which f occurs i times; thusfo(x) is simply the variable x. t and s, with and without subscripts and superscripts, will be arbitrary terms. The symbols T and I are propositional constants standing, respectively, for truth and falsity. m, n, h, i, j, k are natural numbers. The class of formulas that are allowed can be made precise by the following recursive characterization: (1) if tl, t2, .. are terms and F is an n-ary predicate letter (n > 1) then t1 = t2, Ft, ... tn, T and I are allowed formulas; (2) if 0, and 02 are formulas and x is a variable then -((D), (DI & 02, ( 3x)DI and (x)D I are all formulas; and (3) nothing else is a formula.