This book combines insights from philosophy and linguistics to develop a novel framework for theorizing about linguistic meaning and the role of context in interpretation. A key innovation is to introduce explicit representations of context — assignment variables — in the syntax and semantics of natural language. The proposed theory systematizes a spectrum of “shifting” phenomena in which the context relevant for interpreting certain expressions depends on features of the linguistic environment. Central applications include local and nonlocal contextual dependencies with (...) quantifiers, attitude ascriptions, conditionals, questions, and relativization. The result is an innovative, philosophically informed compositional semantics compatible with the truth-conditional paradigm. (shrink)

In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are constructed out (...) of variable assignments. But this has disquieting consequences, including Fine’s antinomy of the variable and an undue dependence of meanings on language. Here I develop an alternative, Fregean version of predicate logic that uses the traditional quantifier–variable apparatus for the expression of generality, possesses a fully compositional, non-representational semantics, and is not subject to the antinomy of the variable. The advantages of Fregean over Tarskian predicate logic are due to the former’s treating variables not as meaningful lexical items, but as mere marks of punctuation, similar to parentheses. I submit that this is indeed how the variables of predicate logic should be construed. (shrink)

ABSTRACT Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke's ‘objectual’ interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries for epistemic modality. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields (...) the undesirable result that any attempt to ‘quantify in’ to an epistemic environment is blocked. If quantifying into the relevant constructions is vacuous, then such views would seem hopelessly misguided and empirically inadequate. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality. (shrink)

This article takes up a suggestion that the reason we cannot find certain hidden variable theories for quantum mechanics, as in Bell’s theorem, is that we require them to assign joint probability distributions on incompatible observables. These joint distributions are problematic because they are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed getting around this problem by using generalized probability spaces. I present a theorem to show a sense in which generalized probability spaces can’t serve (...) as hidden variable theories for quantum mechanics, so the proposal for getting around Bell’s theorem fails. 1 Introduction2 Bell’s Theorem and Classical Probability Spaces2.1 Bell’s derivation of the Bell inequalities2.2 Pitowsky’s derivation of the Bell inequalities3 Incompatible Observables4 Generalized Probability Spaces5 A ‘No-Go’ Theorem6 Conclusions. (shrink)

The phenomenon of quantification into attitude ascriptions has haunted broadly Fregean views, according to which co-referential proper names are not always substitutable salva veritate in attitude ascriptions. Opponents of Fregeanism argue that a belief ascription containing a proper name such as ‘Michael believes that Lindsay is charitable’ is equivalent to a quantified sentence such as ‘there is someone such that Michael believes that she is charitable, and that person is Lindsay’. They conclude that the semantic contribution of a name such (...) as ‘Lindsay’ is the same as the semantic contribution of a variable under an assignment, which these opponents suggest is merely the object assigned to that variable. However, renewed interest in variables suggests that they make a more complicated contribution to the semantic processing of sentences that contain them. In particular, a variable contributes both an assignment-unsaturated and an assignment-saturated semantic value. I use this dual role of the semantics of variables to develop a response to the argument from quantifying in. I take as my point of departure Cumming's () view that an attitude ascription relates the subject of an attitude to the assignment-unsaturated semantic value of an open sentence. I argue that this approach fails. I propose an alternative, according to which the truth of a belief ascription depends on both the assignment-saturated and the assignment-unsaturated semantic value of the open sentence in its that-clause. This approach reverses standard assumptions concerning the relation between quantification and substitution. (shrink)

Model RB is a model of random constraint satisfaction problems, which exhibits exact satisfiability phase transition and many hard instances, both experimentally and theoretically. Benchmarks based on Model RB have been successfully used by various international algorithm competitions and many research papers. In a previous work, Xu and Li defined two notions called i-constraint assignment tuple and flawed i-constraint assignment tuple to show an exponential resolution complexity of Model RB. These two notions are similar to some kind of consistency in (...) constraint satisfaction problems, but seem different from all kinds of consistency so far known in literatures. In this paper, we explicitly define this kind of consistency, called variable-centered consistency, and show an upper bound on a parameter in Model RB, such that up to this bound the typical instances of Model RB are variable-centered consistent. (shrink)

This paper provides a detailed comparison between discourse representation theory and dependent type semantics, two frameworks for discourse semantics. Although it is often stated that DRT and those frameworks based on dependent types are mutually exchangeable, we argue that they differ with respect to variable handling, more specifically, how substitution and other operations on variables are defined. This manifests itself in two recalcitrant problems posed for DRT; namely, the overwrite problem and the duplication problem. We will see that these (...) problems still pose a challenge for various extended compositional systems based on DRT, while they do not arise in a framework of DTS where substitution and other operations are defined in the standard type-theoretic manner without stipulating any additional constraints. We also compare the notions of contexts underlying these two kinds of frameworks, namely, contexts represented as assignment functions and contexts represented as proof terms, and see what different predictions they make for some linguistic examples. (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give (...) a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

The present studies tested the hypothesis that strong assumptions about within-category homogeneity impede children’s recognition of the inductive value of diverse samples of evidence. In Study 1a, children (7-year-olds) and adults were randomly assigned to receive a prime emphasizing within-category variability, a prime emphasizing within-category similarities, or to not receive a prime. Only following the variability prime, children demonstrated a reliable preference for evaluating diverse over nondiverse samples to determine whether there is support for a category-wide generalization. Adults demonstrated a (...) robust preference for diverse samples in all conditions. These effects extended beyond the specific categories included in the prime, as well as to multiple types of test questions. Study 1b demonstrated that priming variability leads children to select diverse samples only when doing so is informative for induction. Implications for conceptual development are discussed. (shrink)

Noncontextual hidden variables theories, assigning simultaneous values to all quantum mechanical observables, are inconsistent by theorems of Gleason and others. These theorems do not exclude contextual hidden variables theories, in which a complete state assigns values to physical quantities only relative to contexts. However, any contextual theory obeying a certain factorisability conditions implies one of Bell's Inequalities, thereby precluding complete agreement with quantum mechanical predictions. The present paper distinguishes two kinds of contextual theories, ‘algebraic’ and ‘environmental’, and investigates when factorisability (...) is reasonable. Some statements by Fine about the philosophical significance of Bell's Inequalities are then assessed. (shrink)

The Montagovian hypothesis of direct model-theoretic interpretation of syntactic surface structures is supported by an account of the semantics of binding that makes no use of variables, syntactic indices, or assignment functions & shows that the interpretation of a large portion of so-called variable-binding phenomena can dispense with the level of logical form without incurring equivalent complexity elsewhere in the system. Variable-free semantics hypothesizes local interpretation of each surface constituent; binding is formalized as a type-shifting operation on expressions (...) that denote functions, & sentences containing a free pronoun are analyzed as a function from individuals to propositions having a meaning of type (e,t). Standard weak crossover effects & binding patterns in sentences with multiple pronouns are shown to submit to straightforward type-theoretic treatments that do not rely on indexation. The variable-free semantics smoothly implements full surface compositionality & requires less machinery than standard accounts to handle functional questions, their answers, sloppy inferences, & across-the-board binding. 73 References. J. Hitchcock. (shrink)

So-called mass nouns, however precisely they are defined, are in any case a subset of non-count nouns. Count nouns are either singular or plural; to be non-count is hence to be neither singular nor plural. This is not, as such, a metaphysically significant contrast: 'pieces of furniture' is plural whereas 'furniture' itself is non-count. This contrast is simply between 'the many / few' and 'the much / little' - between counting and measuring. However not all non-count nouns are, like 'furniture', (...) semantically atomic - 'wine' and 'water' are not. And here there are serious difficulties in the assignment of a range of values for variables, in a formal representation of quantified sentences involving such non-atomic non-count nouns. (shrink)

The current behavioral consultation case demonstrates how functional behavioral assessment (FBA) data, basic and applied research, teacher preferences, and contextual variables contribute to the decision making process when developing classroom intervention procedures. A male, African-American, fifth-grade general education student was initially referred for his inappropriate vocalizations duringtime designated for independent seatwork. FBA data suggested that this behavior was being reinforced with teacher attention. Additional data showed that he was failing to complete his assignments. An intervention was implemented where the (...) student was given assignments one a time. He was instructed to solicit teacher attention and his next assignment after completing each assignment. Analysis ofteacher ratings for inappropriate vocalizations and assignment performance data suggest that the intervention was effective in increasing assignment completion and decreasing inappropriate verbalizations. Discussion focuses on how the various data playa role in the development and implementation of classroom intervention procedures. (shrink)

How can we find any satisfying assignment for a Boolean formula that has many satisfying assignments? There exists an obvious randomized algorithm for solving this problem: one can just pick an assignment at random and check the truth value of the formula for this assignment, this is iterated until a satisfying assignment occurs. Does there exist a polynomial-time deterministic algorithm that solves the same problem? This paper presents such an algorithm and shows that its worst-case running time is linear (...) when input formulas are in k-CNF and a fraction of satisfying assignments is greater than a constant. This algorithm is almost the same as the algorithm proposed by Monien and Speckenmeyer in the early 1980s for less than 2n steps 3-SAT decision.Another result of this paper is that if a formula in k-CNF has many satisfying assignments, then there exists a short satisfying assignment, i.e. an assignment of truth values to a small number of variables. The proposed algorithm yields just such a short satisfying assignment. We also show that there exist formulas in general CNF having many satisfying assignments, that have no short satisfying assignments. (shrink)

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.

The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of P, where (...) in general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of P. ;In classical propositional logic, propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies . However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying , and can be provided. ;Von Neumann first proposed that the algebraic structures of the subspaces of Hilbert space be regarded as the propositional structures P of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible and incompatible ; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality ,) applicable to the Plattices; and truth-functionality ) applicable to both the Plattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional ,) semantics for any PQM lattice containing incompatible elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional ) semantics for three-or-higher dimensional Hilbert space PQM structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. ;The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is bivalent, i.e., the value 1 or 0 is assigned to each proposition, and truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. (shrink)

In this dissertation I provide a novel logic of the ordinary-language conditional. First, however, I endeavor to make clearer and more precise just what the objects of the study of the conditional are, as a lack of clarity as to what counts as an instance of a given category of conditional has resulted in deep and significant confusions in subsequent analysis. I motivate for a factual/counterfactual distinction, though not at the level of particular instances of the conditional. Instead, I argue (...) that each individual instance of the conditional may be interpreted either factually or counterfactually, rather than these instances dividing into distinct types. I examine the classic Oswald–Kennedy pair of sentences, typically taken to be the quintessential example of how conditionals must be split into two different categories, to show that they in fact do not demonstrate this. I then present my account of the logic underlying the ordinary-language conditional, the system C3, and a justification of the form it takes. This logic provides distinct interpretations of the conditional as it concerns what is factual or what is counterfactual, respectively. The factual interpretation is true when both antecedent and consequent are true at the actual world, false when the antecedent is true and consequent false, and not truth-apt otherwise. The counterfactual interpretation incorporates a ceteris paribus clause, ensuring that it is not falsified by extraordinary, unforeseeable occurrences, and is true when, at all worlds at which the antecedent is ceteris paribus true, the consequent too is true. It is false when, at any of these worlds the consequent is false; and not truth-apt otherwise. I go on to examine alternative theories of the conditional—from the suppositionalist approach to evaluating the putative indicative conditional, to Stalnaker’s combined indicative and counterfactual account, and Lewis’s analysis of the counterfactual; among a number of others—and offer comparison to my own theory. Finally, I look at various challenges to my account of the conditional. Being a strict conditional (albeit variably so), that of C3 is open to the objection that it fails to match ordinary speakers’ intuitions as regards its truth-value assignments to, for instance, conditionals with necessarily true consequents. I address these so- called paradoxes of the strict conditional, and also discussion the question of truth-preservation in the C3 system in the case of such inferences as those relying on transitivity and that of modus ponens. I maintain that these inferences are indeed truth-preserving under certain, specifiable, conditions, and I close by offering possible avenues for further research. (shrink)

Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in (...) linguistics is that reflexive and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained. (shrink)

I investigate whether Wittgenstein’s “weakly exclusive” Tractarian semantics (as reconstructed by Rogers and Wehmeier) is compositional. In both Tarskian and Wittgensteinian semantics, one has the choice of either working exclusively with total variable assignments or allowing partial assignments; the choice has no bearing on the compositionality of Tarskian semantics, but turns out to make a difference in the Wittgensteinian case. Some philosophical ramifications of this observation are discussed.

This study analyzes the questions on aspects of child custody, visitation rights, or child endangerment that judges pose to forensic psychologists in family law proceedings. Before conducting a psychological evaluation, the legal question in the referral has to be translated into case-specific, forensically relevant issues. The only overarching principle guiding this process is the “best interests of the child” criterion. Literature indicates that judges often struggle to define what variables should be specified for a psychological evaluation in their referral questions. (...) This study aims to contribute to a better understanding of the information judges would like to ascertain from psychological evaluators in child custody and child protection proceedings—an understanding allowing a clearer determination of whether forensic psychologists as experts can deliver this information. Latent Dirichlet allocation (LDA) is used to analyze the referral questions that these judges pose to forensic evaluators in terms of (a) underlying topics (latent dimensions) that can be identified within the referral questions and (b) the probability distributions of legal terms and forensic issues contained in the referral questions. This analysis is based on unclassified text data extracted from German court files. Five topics (latent dimensions) were identified within referral questions resembling cases when the issue was as follows: (a) potential child endangerment in the context of visitation contacts, (b) a possibly limited parenting capacity and its potential effects on child well-being, (c) an impairment of the child has already occurred or could occur, (d) a better option concerning custody and residence, and (e) an unclear topic addressing questions on custody, residence, and visitation in which no specific psychological constructs are involved. In four of the five topics, judges utilize their referral questions to ask for case-group-specific psychological information. In one topic addressing questions on custody, residence, and visitation, judges seem to struggle to define criteria that forensic evaluators should assess. Overall, results help to identify and define more clearly the relevant constructs that forensic experts should examine from the perspective of the courts with the goal of making clearer and more accurate recommendations. (shrink)

The discussion about the Raven Paradox is ever-renewing: after nearly 70 years, many authors propose from time to time new solutions, and many authors state that these solutions are unsatisfactory. It is worthy to be carefully noted that though most arguments in favor or against the paradox are based on the notion of “probability” and on the application of Bayes’ law, not one of them makes use of the Kolmogorov axiomatic theory of probability and on the subsequent notion of “random (...) variable”. This seems to be due to a preference for the purely logical interpretation of the notion of “probability” which makes it possible to assign a probability value to propositions expressing natural (universal) laws. This paper aims at presenting an attempt to contribute a solution to the paradox by the proposal of a different way to express universal natural laws and by the use of a language which does not allow one to apply probability to universal statements. (shrink)

Growing evidence suggests that natural environments – whether in outdoor or indoor settings – foster psychological health and physiological relaxation, indicated by increased wellbeing, reduced stress levels, and increased parasympathetic activity. Greater insight into differential psychological aspects modulating psychophysiological responses to nature-based relaxation videos could help understand modes of action and develop personalized relaxation interventions. We investigated heart rate variability as an indicator of autonomic regulation, specifically parasympathetic activity, in response to a 10-min video intervention in two consecutive studies as (...) well as heart rate. We hypothesized that a nature-based relaxation video elicits HRV increase and HR decrease, with response magnitude being affected by aspects of early life adversity and trait mindfulness. In Study 1, N = 60 participants watched a relaxation video intervention depicting different natural scenery. We analyzed changes in HR and respiratory sinus arrhythmia as a standard HRV measure, both based on 3-min segments from the experimental session, in multiple growth curve models. We found a decrease in HR and increase of RSA during the video intervention. Higher paternal care and lower trait mindfulness observing skills were associated with higher RSA values before but not during video exposure. In Study 2, N = 90 participants were assigned to three video conditions: natural scenery from Study 1, meditation video, or short clip from “The Lord of the Rings.” Again, HR decreased, and RSA increased during video segments, yet without expected group differences across different video types. We found higher parental care and lower parental overprotection to predict higher RSA at different times during the experiment. Interestingly, lower paternal overprotection predicted overall higher RSA. These results suggest a generic relaxation effect of video interventions on autonomic regulation that we discuss in light of different theories mapping restorative effects of natural environments. Further, psychological characteristics like aspects of early life adversity and trait mindfulness could contribute to individual differences in autonomic regulation. This study contributes to a better understanding of autonomic and psychological responses to relaxation videos. (shrink)

We investigate the effect of Lesbian, Gay, Bisexual, and Transgender -supportive corporate policies on credit ratings. To the extent that LGBT-friendly policies are beneficial to the firm and therefore improve its expected cash flows, credit rating agencies should assign more favorable credit ratings to the firm. To alleviate endogeneity concerns, we exploit the variations in the LGBT populations across the states in the U.S. as our instrument. Our instrumental-variable analysis reveals that firms that adopt LGBT-supportive corporate policies enjoy better (...) credit ratings, supporting the stakeholder and good management hypothesis. Further analysis using propensity score matching also yields consistent results. (shrink)

We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single particle (...) consists of two parts. First, a single particle ontic quantum state \|i\rangle \), where \\) is a 3-space wavepacket and \ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \\) acting as a local pilot wave. The joint ontic quantum state \\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \\rangle \) determines the distribution of the \\rangle \)’s over an ensemble. Both \\rangle \) and \\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. (shrink)

The current behavioral consultation case demonstrates how functional behavioral assessment (FBA) data, basic and applied research, teacher preferences, and contextual variables contribute to the decision making process when developing classroom intervention procedures. A male, African-American, fifth-grade general education student was initially referred for his inappropriate vocalizations duringtime designated for independent seatwork. FBA data suggested that this behavior was being reinforced with teacher attention. Additional data showed that he was failing to complete his assignments. An intervention was implemented where the (...) student was given assignments one a time. He was instructed to solicit teacher attention and his next assignment after completing each assignment. Analysis ofteacher ratings for inappropriate vocalizations and assignment performance data suggest that the intervention was effective in increasing assignment completion and decreasing inappropriate verbalizations. Discussion focuses on how the various data playa role in the development and implementation of classroom intervention procedures. (shrink)

I argue that common nouns should be analyzed as variables, rather than as predicates which take variables as arguments. This necessitates several unusual features to the analysis, such as allowing variables to be modally non-rigid, and assigning their values compositionally. However, treating common nouns as variables offers a variety of theoretical and empirical advantages over a more traditional analysis: It predicts the conservativity of nominal quantification, simplifies the analysis of articleless languages, derives the weak reading of sentences with donkey anaphora, (...) solves the proportion problem presented by quantifiers like ‘most’, improves the analysis of the temperature paradox, allows a more unified analysis of bare plurals, and regularizes the correspondence between syntactic categories and semantic types. (shrink)

Purpose This study aims to statistically verify the links of income and education with information and communication technology diffusion across 191 countries of the world taking into account a total of 9 indicators best representing the socio-economic variables. Design/methodology/approach Multivariate regression analysis was used as a prime method to rigorously test the relationships of income and education with ICT diffusion across 191 countries. Statistical Package for the Social Sciences was used to analyze and predict patterns in the data. Findings The (...) results support the hypotheses that income and education are positively related to ICT diffusion. The findings statistically confirm that poverty is a leading cause of digital divide worldwide. Research limitations/implications Academic, policy and practice groups should work in collaboration to fight against digital divide. Present results also imply that digital divide shall never end but rather it can be controlled to an extent with multiple collaborative efforts. Originality/value Prior research assignments on the digital divide concentrate on exploring the links between few socio-economic and ICT variables in select few regions theoretically. The present work addresses this literature gap by developing and testing two hypotheses to statistically investigate the relationships between a broad set of socio-economic and ICT indicators. (shrink)

In this paper, we consider predicate logic with two individual variables and general assignment models (where the set of assignments of the variables into a model is allowed to be an arbitrary subset of the usual one). We prove that there is a statement such that no general assignment model in which it is true can be finitely axiomatized. We do this by showing that the free relativized cylindric algebras of dimension two are not atomic.

BackgroundThere is numerous literature on mechanisms underlying variability of practice advantages. Literature includes both behavioral and neuroimaging studies. Unfortunately, no studies are focusing on practice in constant conditions to the best of our knowledge. Hence it is essential to assess possible differences in mechanisms of neuroplasticity between constant vs. variable practice conditions. The primary objectives of the study described in this protocol will be: to determine the brain’s structural and functional changes following constant and variable practice conditions in (...) motor learning ; to determine the EEG activation and connectivity between cognitive, sensory, and motor cerebral cortex areas in constant and variable practice conditions and as a function of practice time.MethodsThe study will follow the interventional design with two arms. Fifty participants will be randomly assigned to two groups practicing in constant and variable conditions. CG will be practicing only one pattern of step isometric contractions during unimanual index finger abduction, i.e., 90 trials in all training sessions, whereas VG will practice three different patterns. Each will be practiced 30 times per session in variable conditions. Resting-state fMRI, EEG, and motor task proficiency will be examined before and after practice.DiscussionFindings will enhance our understanding of structural and functional neural changes following practice in constant and variable conditions. Therefore, the study can be considered pure research.Clinical Trial RegistrationStudy registered at clinicaltrials.gov on 9 June 2021. Last version update: 21 December 2021.The protocol has been prepared according to the complete SPIRIT checklist, although the item order has been modified in order to comply with the manuscript structure. (shrink)

Recently, philosophers have offered compelling reasons to think that demonstratives are best represented as variables, sensitive not to the context of utterance, but to a variable assignment. Variablists typically explain familiar intuitions about demonstratives—intuitions that suggest that what is said by way of a demonstrative sentence varies systematically over contexts—by claiming that contexts initialize a particular assignment of values to variables. I argue that we do not need to link context and the assignment parameter in this way, and that (...) we would do better not to. (shrink)

The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all (...) x(A V B) -> (A V for all xB). with x not free in A. Validity of EC requires an additional model condition involving the boolean difference of propositions. A QR-model falsifying EC is constructed by forming the disjoint union of two natural arithmetical structures in which negation is interpreted by the minus operation. (shrink)

Variabilism is the view that proper names (like pronouns) are semantically represented as variables. Referential names, like referential pronouns, are assigned their referents by a contextual variable assignment (Kaplan 1989). The reference parameter (like the world of evaluation) may also be shifted by operators in the representation language. Indeed verbs that create hyperintensional contexts, like ‘think’, are treated as operators that simultaneously shift the world and assignment parameters. By contrast, metaphysical modal operators shift the world of assessment only. Names, (...) being variables, refer rigidly in the latter merely intensional contexts, but may vary their reference in hyperintensional contexts. This conforms to the intuition that the content of attitude ascriptions encapsulates referential uncertainty. Furthermore, names in hyperintensional contexts are ambiguous between de re* and de dicto* interpretations. This fact is used to account for asymmetric mistaken identity attributions (for example, Biron thinks Katherine is Rosaline, but he doesn’t think Rosaline is Katherine). -/- The variable theory compares favourably with its alternatives, including Millianism and descriptivism. Millians cannot account for the behaviour of names in hyperintensional contexts, while descriptivists cannot generate a necessary contrast between intensional and hyperintensional contexts. No other theory can capture the facts pertaining to the existentially bound use of names. (shrink)

It is common practice in formal semantics to assume that the context specifies an assignment of values to variables and that the same variables that receive contextually salient values when they occur free may also be bound by quantifiers and λs. These assumptions are at work to provide a unified account of free and bound uses of third person pronouns, namely one by which the same lexical item is involved in both uses. One way to pursue this account is to (...) treat quantifiers and λs as monsters in Kaplan’s sense. We argue that this move should be avoided and explore an alternative route based on the idea that there is a variable assignment coordinate in the context and a variable assignment coordinate in the circumstance of evaluation, with the definition of truth in context identifying them. One fundamental challenge that arises in pursuing a unified account is to explain the difference in the way the gender presuppositions of bound and free pronouns project. The proposal that emerges from the attempt to meet this challenge is a non-indexical account of free third person pronouns and a new conception of the role and structure of assignment functions. (shrink)

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 couched in classical type logic that extends Compositional DRT (Muskens, Linguistics and Philosophy, 19, 143-186, 1996). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics become available. The idea that plural info states are semantically necessary (in addition to non-atomic individuals) is motivated by relative-clause donkey sentences with multiple instances of singular donkey anaphora that have mixed (weak and strong) readings. At the same time, allowing for non-atomic individuals in addition to plural info states enables us to capture the intuitive parallels between singular and plural (donkey) anaphora, while deriving the incompatibility between singular (donkey) anaphora and collective predicates. The system also accounts for empirically unrelated phenomena, e.g., the uniqueness effects associated with singular (donkey) anaphora discussed in Kadmon (Linguistics and Philosophy, 13, 273-324, 1990) and Heim (Linguistics and Philosophy, 13, 131-177, 1990) among others. (shrink)

Kaplan (1989a) insists that natural languages do not contain displacing devices that operate on character—such displacing devices are called monsters. This thesis has recently faced various empirical challenges (e.g., Schlenker 2003; Anand and Nevins 2004). In this note, the thesis is challenged on grounds of a more theoretical nature. It is argued that the standard compositional semantics of variable binding employs monstrous operations. As a dramatic first example, Kaplan’s formal language, the Logic of Demonstratives, is shown to contain monsters. (...) For similar reasons, the orthodox lambda-calculus-based semantics for variable binding is argued to be monstrous. This technical point promises to provide some far-reaching implications for our understanding of semantic theory and content. The theoretical upshot of the discussion is at least threefold: (i) the Kaplanian thesis that “directly referential” terms are not shiftable/bindable is unmotivated, (ii) since monsters operate on something distinct from the assertoric content of their operands, we must distinguish ingredient sense from assertoric content (cf. Dummett 1973; Evans 1979; Stanley 1997), and (iii) since the case of variable binding provides a paradigm of semantic shift that differs from the other types, it is plausible to think that indexicals—which are standardly treated by means of the assignment function—might undergo the same kind of shift. (shrink)

A substitutional account of logical validity for formal first‐order languages is developed and defended against competing accounts such as the model‐theoretic definition of validity. Roughly, a substitution instance of a sentence is defined as the result of uniformly substituting nonlogical expressions in the sentence with expressions of the same grammatical category and possibly relativizing quantifiers. In particular, predicate symbols can be replaced with formulae possibly containing additional free variables. A sentence is defined to be logically true iff all its substitution (...) instances are satisfied by all variable assignments. Logical consequence is defined analogously. Satisfaction is taken to be a primitive notion and axiomatized.For every set‐theoretic model in the sense of model theory there exists a corresponding substitutional interpretation in a sense to be specified. Conversely, however, there are substitutional interpretations – in particular the ‘intended’ interpretation – that lack a model‐theoretic counterpart. The substitutional definition of logical validity overcomes the weaknesses of more restrictive accounts of substitutional validity; unlike model‐theoretic logical consequence, the substitutional notion is trivially and provably truth preserving. In Kreisel's squeezing argument the formal notion of substitutional validity naturally slots into the place of intuitive validity. (shrink)

It is a commonplace of the history of analytic philosophy that Carnap swiftly adopted Tarskian semantics in the mid-1930s. There is no doubt that, in a very general sense, this is true. But to what extent are the innovative technical details characteristic of Tarski's method, specifically the handling of quantification by way of a satisfaction relation between formulas and variable assignments, reflected in Carnap's writings on semantics? Curiously enough, their essentials are in place just before Carnap took the (...) purported Tarskian turn, namely in the definition of analyticity he formulated some time between September 1932 and April 1933, but are missing from his publications on semantics after 1935 until the final chapter of Meaning and Necessity of 1947, at which point we find Carnap reverting to the use of specifically Tarskian techniques in the context of his novel semantics for quantified modal languages. (shrink)

Cumming (2008) uses a puzzle about belief ascription to argue against a Millian semantics, and in favor of a semantics on which names are assigned denotations relative to a shiftable variable assignment. I use Cumming's puzzle to showcase the virtues of a rival, broadly Stalnakerian, treatment of attitude ascriptions that safeguards Millianism. I begin by arguing that Cumming's solution seems unable to account for substitutivity data that helps constitute the very puzzle he uses to motivate his account. Once the (...) substitutivity data is acknowledged, the puzzle actually seems to strengthen, rather than weaken, the Millian position. I then argue that the real force of the puzzle is to place special constraints on our accounts of de re belief ascription. To help bring out the nature of those constraints, I connect aspects of Cumming's puzzle to more familiar problems about belief ascription raised by Quine. I then defend three theses making up a skeletal account of de re belief ascription that promises to cope naturally with the variants of Cumming's puzzle, and integrate them into a broader theory of de re intensionality. (shrink)

ABSTRACT In this paper, I ask whether quantifiers are intensional operators, with variable assignments playing the role of indices. Certain formulations of extensional type theory suggest an affirmative answer, but the most satisfactory among them suffer from a contamination of their semantic ontology with syntactic material. I lay out ‘Fregean’ versions of extensional type theory that are free from syntactic contamination and suggest a negative answer to our question.

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 (...) contexts in an incremental way, starting with the basic notion of context in classical first-order logic, i.e., interpretation contexts formalized as single total variable assignments. (shrink)

It is a commonplace of the history of analytic philosophy that Carnap swiftly adopted Tarskian semantics in the mid-1930s. There is no doubt that, in a very general sense, this is true. But to what extent are the innovative technical details characteristic of Tarski's method, specifically the handling of quantification by way of a satisfaction relation between formulas and variable assignments, reflected in Carnap's writings on semantics? Curiously enough, their essentials are in place just before Carnap took the (...) purported Tarskian turn, namely in the definition of analyticity he formulated some time between September 1932 and April 1933, but are missing from his publications on semantics after 1935 until the final chapter of Meaning and Necessity of 1947, at which point we find Carnap reverting to the use of specifically Tarskian techniques in the context of his novel semantics for quantified modal languages. (shrink)

Slurring is a kind of hate speech that has various effects. Notable among these is variable offence. Slurs vary in offence across words, uses, and the reactions of audience members. Patterns of offence aren’t adequately explained by current theories. We propose an explanation based on the unjust power imbalance that a slur seeks to achieve. Our starting observation is that in discourse participants take on discourse roles. These are typically inherited from social roles, but only exist during a discourse. (...) A slurring act is a speech-act that alters the discourse roles of the target and speaker. By assigning discourse roles the speaker unjustly changes the power balance in the dialogue. This has a variety of effects on the target and audience. We show how these notions explain all three types of offence variation. We also briefly sketch how a role and power theory can help explain silencing and appropriation. Explanatory power lies in the fact that offence is correlated with the perceived unjustness of the power imbalance created. (shrink)

In light of the interrelation between motor and cognitive development and the predictive value of the former for the latter, the secular decline observed in motor coordination ability as early as preschool urges identification of interventions that may jointly impact motor and cognitive efficiency. The aim of this study was twofold. It (1) explored the outcomes of enriched physical education, centered on deliberate play and cognitively challenging variability of practice, on motor coordination and cognitive processing; (2) examined whether motor coordination (...) outcomes mediate intervention effects on children’s cognition, while controlling for moderation by lifestyle factors as outdoor play habits and weight status. Four hundred and sixty children aged 5-10 years participated in a 6-month group randomized intervention in physical education, with or without playful coordinative and cognitive enrichment. The weight status and spontaneous outdoor play habits of children (parental report of outdoor play) were evaluated at baseline. Before and after the intervention, motor developmental level (Movement Assessment Battery for Children) was evaluated in all children, who were then assessed either with a test of working memory (Random Number Generation task), or with a test of attention (from the Cognitive Assessment System, CAS). Children assigned to the ‘enriched’ intervention showed more pronounced improvements in all motor coordination assessments (manual dexterity, ball skills, static/dynamic balance). The beneficial effect on ball skills was amplified by the level of spontaneous outdoor play and weight status. Among indices of executive function and attention, only that of inhibition showed a differential effect of intervention type. Moderated mediation showed that the better outcome of the enriched physical education on ball skills mediated the better inhibition outcome, but only when the enrichment intervention was paralleled by a medium-to-high level of outdoor play. Results suggest that specifically tailored physical activity games provide a unique form of enrichment that impacts children’s cognitive development through motor coordination improvement, particularly object control skills, which are linked to children’s physical activity habits later in life. Outdoor play appears to offer the natural ground for the stimulation by designed physical activity games to take root in children’s mind. (shrink)

The phenomenon of inverse linking, where a noun phrase embedded within another behaves with respect to binding as though it were structurally independent, has proven challenging for theories of the syntax–semantics interface. In this paper I show that, using an LF-movement style approach to the syntax–semantics interface, we can derive all and only the appropriate meanings for such constructions using no semantic operations other than function application and composition. The solution relies neither on a proliferation of lexical ambiguity nor on (...) abandoning the idea that pronouns denote variables, but rather on a straightforward (and standard) reification of assignment functions, which allows us to define abstraction operators within our models. (shrink)

In this paper, we evaluate the project of resurgence of metaphysics based on the pecularity of the quantum domain, a project that is supported by some contemporary philosophers. Beyond the general arguments against scientific realism that are still applicable here, we show that this project is faced with the three following issues that, we believe, make it unrealizable: (a) the problem raised by the realistic interpretation of the wave function, as a description of a ‘concrete physical fact’ of the independent (...) reality; (b) the lack of any experimental counterpart of the (non-local) hidden variables quantum theories, and, in some cases, their incompatibility with the quantum predictions; and (c) the fact that the key-properties of quantum phenomena, like their non-locality, essentially depend on the observables that are used for their description and cannot then be assigned to any ‘independent’ reality. (shrink)

Preference orderings assigned by coherent lower and upper conditional previsions are defined and they are considered to define maximal random variables and Bayes random variables. Sufficient conditions are given such that a random variable is maximal if and only if it is a Bayes random variable. In a metric space preference orderings represented by coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures are given.

This chapter provides some tentative conclusions about the likely linguistic status of context‐sensitive semantic properties. It argues that pragmatism is fully aligned with a standard approach to syntax, and should be the default view of the notion of a linguistic 'context', viz., context is not a well‐behaved linguistic notion. But rather a potentially open‐ended way of marking the role extra‐linguistic factors can play in fixing what is said on an occasion of the use of a linguistic type. Context sensitivity is (...) not restricted to the construal of overt linguistic material. It also appears that the construal of tokens of many constructions depends upon contextual factors that are not explicitly encoded in linguistic material; that is, if pronouns are explicit variables, then there appear to be implicit or covert variables as well. Truth‐value of a sentence in context is assigned relative to the value a coordinate of the index takes under the scope of the operator. (shrink)

Ordinary speakers intuitively assign truth-values to conditional utterances in everyday conversation, but, despite the general ease with which this occurs, it is notoriously difficult to give an account of the implicit logic that is followed in making these truth-value assignments. I propose a twofold logic of the conditional – a relatively simple “factual” logic for conditionals interpreted with regard to what is actually the case, largely following the logic of the material conditional; combined with a variably strict possible-worlds counterfactual (...) logic for conditionals interpreted with regard to with what may be (or may have been) the case, incorporating a ceteris paribus clause. This theory is able to deal with a number of challenges for other prominent views of the conditional, such as counter-intuitive truth-value ascriptions provided by notions of similarity or closeness, and difficulties adequately accounting for phenomena such as reverse Sobel sequences. (shrink)

Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations reflect similarity structure and relations of temporal contiguity. The other is "rule based" because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve (...) complementary functions and can simultaneously generate different solutions to a reasoning problem. The rule-based system can suppress the associative system but not completely inhibit it. The article reviews evidence in favor of the distinction and its characterization. (shrink)

These essays by Old Dominion University students deal with two questions: What impact do their own race, class, gender, and ethnic identities have upon them as students? How do their culture and the university culture interact to affect their ability to learn? The focus of these essays is on the overlap between the students’ identities as students and their identities based on gender, race, class, and ethnic origin. The project began as an assignment in a women’s studies class at Old (...) Dominion University in 1993, when students in a mixed graduate and undergraduate course were asked to write a brief analysis of themselves as students, accounting for the impact of gender, race, and social class on what they studied, what they heard in class, how they were treated in the classroom, how they treated others there, and what their level of comfort in the university was. Invited to add other variables, such as religion, nationality, age, sexual orientation, or disability— if they considered these significant to their identities as students—the students were urged to consider not only the disadvantages these various identities gave them but also the privileges and advantages. The resulting essays stimulated great interest in what students had to say and led to the formation of The Broad Minds Collective—made up of four students from the class as well as its instructor—which set about the task of soliciting and collecting additional essays. Although most essays contain overlapping themes, the editors detected four motifs that encompass virtually every essay included in the book. In the section "Cultural Perceptions and Assumptions," students show their awareness of how culturally defined categories affect education. Essays in "Belonging and Alienation in the Classroom" discuss the students’ level of comfort in the classroom and the degree to which they feel they belong at the university. The essays in "Making Sense of Our Lives Through Education" reveal the students’ use of education to learn more about the forces that shape them. "In Search of an Education" highlights students’ efforts to wrest what they feel they need from a college education. Rather than presenting a "multicultural educational theory" or conducting a sterile sociological study, The Broad Minds Collective has allowed students to speak for themselves.ion is replaced by stories of personal conflict, struggle, and victory. __. (shrink)