Results for 'variable binding'

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  1. Variable Binding Term Operators.John Corcoran, William Hatcher & John Herring - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (12):177-182.
    Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic (...)
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  2.  67
    Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems.Paul Smolensky - 1990 - Artificial Intelligence 46 (1-2):159-216.
  3.  16
    World Variable Binding and Beta-Binding.David Schueler - 2011 - Journal of Semantics 28 (2):241-266.
    This paper investigates the analysis of the de re/de dicto distinction and related facts. I start with the assumption, supported by Cresswell 1990, that the evaluation of the truth of a proposition relative to a particular possible world/situation is mediated via the presence in the syntax of a silent pronoun with type-s denotation. In this system, the de re/de dicto distinction arises from a difference in which an operator binds a given situation pronoun. Percus 2000 shows that such a system (...)
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  4.  20
    Variable Binding Term Operators in $\Lambda $-Calculus.M. W. Bunder - 1979 - Notre Dame Journal of Formal Logic 20 (4):876-878.
  5. Notes on a Semantic Analysis of Variable Binding Term Operators.J. Corcoran & John Herring - 1971 - Logique Et Analyse 55:644-657.
    -/- 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 (...)
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  6.  6
    Languages with Variable-Binding Operators: Categorial Syntax and Combinatorial Semantics.Peter Simons - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 89:239.
  7.  24
    Categorial Languages and Variable-Binding Operators.Adam Nowaczyk - 1978 - Studia Logica 37 (1):27 - 39.
  8.  30
    Quantifier/Variable-Binding.B. H. Slater - 2000 - Linguistics and Philosophy 23 (3):309-321.
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  9. Binding Bound Variables in Epistemic Contexts.Brian Rabern - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy:1-31.
    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 in the epistemic case. 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 (...)
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  10.  52
    The Abstract Variable-Binding Calculus.Don Pigozzi & Antonino Salibra - 1995 - 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 (...)
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  11.  89
    E-Type Pronouns, DRT, Dynamic Semantics and the Quantifier/Variable-Binding Model.S. J. Barker - 1997 - Linguistics and Philosophy 20 (2):195-228.
  12.  22
    Rule Acquisition and Variable Binding: Two Sides of the Same Coin.P. J. Hampson - 1993 - Behavioral and Brain Sciences 16 (3):462-462.
  13. Binding Arguments and Hidden Variables.Jonathan Cohen & Samuel C. Rickless - 2007 - Analysis 67 (1):65-71.
    o (2000), 243). In particular, the idea is that binding interactions between the relevant expressions and natural lan- guage quantifiers are best explained by the hypothesis that those expressions harbor hidden but bindable variables. Recently, however, Herman Cappelen and Ernie Lepore have rejected such binding arguments for the presence of hid- den variables on the grounds that they overgeneralize — that, if sound, such arguments would establish the presence of hidden variables in all sorts of ex- pressions where (...)
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  14. Binding Implicit Variables in Quantified Contexts.Barbara Partee - 1989 - In Caroline Wiltshire, Randolph Graczyk & Bradley Music (eds.), CLS. pp. 342-365.
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  15.  25
    Notes on the Theory of Variable Binding Term Operators.Newton C. A. da Costa & Chris Mortensen - 1983 - History and Philosophy of Logic 4 (1-2):63-72.
    The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.
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  16. Binding On the Fly: Cross-Sentential Anaphora in Variable— Free Semantics.Anna Szabolcsi - 2003 - In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora. Kluwer Academic Publishers. pp. 215--227.
    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 (...)
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  17. An Extension of the Temporal Synchrony Solution to Dynamic Variable Bindings in a Connectionist System.Nam Seog Park, Dave Robertson & Keith Stenning - 1993 - Department of Artificial Intelligence, University of Edinburgh.
     
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  18.  1
    On High-Level Inferencing and the Variable Binding Problem in Connectionist Networks.Steffen Hölldobler - 1990 - In G. Dorffner (ed.), Konnektionismus in Artificial Intelligence Und Kognitionsforschung. Berlin: Springer-Verlag. pp. 180--185.
  19. From Simple Associations to Systematic Reasoning: A Connectionist Representation of Rules, Variables, and Dynamic Binding Using Temporal Synchrony.Lokendra Shastri & Venkat Ajjanagadde - 1993 - Behavioral and Brain Sciences 16 (3):417-51.
    Human agents draw a variety of inferences effortlessly, spontaneously, and with remarkable efficiency – as though these inferences were a reflexive response of their cognitive apparatus. Furthermore, these inferences are drawn with reference to a large body of background knowledge. This remarkable human ability seems paradoxical given the complexity of reasoning reported by researchers in artificial intelligence. It also poses a challenge for cognitive science and computational neuroscience: How can a system of simple and slow neuronlike elements represent a large (...)
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  20. Binding, Compositionality, and Semantic Values.Michael Glanzberg & Jeffrey C. King - 2020 - Philosophers' Imprint 20.
    In this paper, we defend a traditional approach to semantics, that holds that the outputs of compositional semantics are propositional, i.e. truth conditions. Though traditional, this view has been challenged on a number of fronts over the years. Since classic work of Lewis, arguments have been offered which purport to show that semantic composition requires values that are relativized, e.g. to times, or other parameters that render them no longer propositional. Focusing in recent variants of these arguments involving quantification and (...)
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  21. Variable-Binders as Functors.Achille C. Varzi - 1995 - Poznan Studies in the Philosophy of the Sciences and the Humanities 40:303-19.
    This work gives an extended presentation of the treatment of variable-binding operators adumbrated in [3:1993d]. Illustrative examples include elementary languages with quantifiers and lambda-equipped categorial languages. Some remarks are also offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic emerges from the account: the view that logics are true theories in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only “admissible” interpretation structures (for a (...)
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  22.  2
    Grammar-Based Connectionist Approaches to Language-A Connectionist Representation of Rule, Variables, and Dynamic Bindings Using Temporal Synchrony.P. K. Monteiro, M. R. Pascoa & P. Smolensky - 1999 - Cognitive Science 23 (4):589-613.
  23. Towards a Variable-Free Semantics.Pauline Jacobson - 1999 - Linguistics and Philosophy 22 (2):117-185.
    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 (...)
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  24. Binding Into Character.Joshua Dever - 2004 - Canadian Journal of Philosophy 34 (Supplement):29-80.
    Since Kaplan’s "Demonstratives", it has become a common-place to distinguish between the character and content of an expression, where the content of an expression is what it contributes to "what is said" by sentences containing that expression, and the character gives a rule for determining, in a context, the content of an expression. A tacit assumption of theories of character has been that character is autonomous from content – that semantic evaluation starts with character, adds context, and then derives content. (...)
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  25. Bound Variables in Syntax (Are There Any?).Anna Szabolcsi - 1987 - In J. Groenendijk, F. Veltman & M. Stokhof (eds.), Sixth Amsterdam Colloquium Proceedings. Univ of Amsterdam.
    Current theories of grammar handle both extraction and anaphorization by introducing variables into syntactic representations. Combinatory categorial grammar eliminates variables corresponding to gaps. Using the combinator W, the paper extends this approach to anaphors, which appear to act as overt bound variables. [Slightly extended version in Bartsch et al 1989.].
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  26.  66
    Predicate Logic with Flexibly Binding Operators and Natural Language Semantics.Peter Pagin & Dag Westerståhl - 1993 - Journal of Logic, Language and Information 2 (2):89-128.
    A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including donkey sentences and cross-sentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of anaphora, in particular Dynamic Predicate Logic.
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  27.  32
    Foundations of Nominal Techniques: Logic and Semantics of Variables in Abstract Syntax.Murdoch J. Gabbay - 2011 - Bulletin of Symbolic Logic 17 (2):161-229.
    We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' (...)
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  28. Binding Without Identity: Towards a Unified Semantics for Bound and Exempt Anaphors.Yoad Winter & Eric Reuland - unknown
    Expressions such as English himself are interpreted as locally bound anaphors in certain syntactic environments and are exempt from the binding conditions in others. This article provides a unified semantics for himself in both of these uses. Their difference is reduced to the interaction with the syntactic environment. The semantics is based on an extension of the treatment of pronominals in variable-free semantics. The adoption of variable free semantics is inspired by the existence of proxy-readings, which motivate (...)
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  29.  31
    Such: Binding and the Pro-Adjective. [REVIEW]Muffy E. A. Siegel - 1994 - Linguistics and Philosophy 17 (5):481 - 497.
    The facts aboutsuch, then, indicate not just thatsuch is a pro-adjective, but also that binding conditions apply broadly to pro-ADJs and pro-CNs, as well as to a wide range of pro-arguments. If this is true, the CN binding process accomplished by rules (40) and (41) might better be expressed in a system that uses a Cooper (1979) store mechanism. In fact, Stump (p. 144) notes that this could easily be done. Meanings of the type of∨ P n could (...)
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  30.  2
    Variable-Binders as Functors.Achille C. Varzi - 1995 - In Vito Sinisi & Jan Woleński (eds.), The Heritage of Kazimierz Ajdukiewicz. Amsterdam: Rodopi. pp. 303.
  31.  35
    Constraints on Some Other Variables in Syntax.Orin Percus - 2000 - Natural Language Semantics 8 (3):173-229.
    In this paper I assume that syntactic structures contain items that function as variables over possible worlds (or things like possible worlds). I show that in certain syntactic positions we can use some variables but not other. I accordingly motivate a "binding theory" for the items that occupy these positions, and I discuss some consequences of this binding theory.
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  32. Scope and Binding.Anna Szabolcsi - 2011 - In von Heusinger, Maienborn & Portner (eds.), Semantics: An International Handbook of Natural Language Meaning, Vol. 2. de Gruyter Mouton.
    The first part of this article (Sections 1–5) focuses on the classical notions of scope and binding and their formal foundations. It argues that once their semantic core is properly understood, it can be implemented in various different ways: with or without movement, with or without variables. The second part (Sections 6–12) takes up the empirical issues that have redrawn the map in the past two decades. It turns out that scope is not a primitive. Existential scope and distributive (...)
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  33.  46
    Bound Variables and C‐command.Maria Nella Carminati, Lyn Frazier & Keith Rayner - 2002 - Journal of Semantics 19 (1):1-34.
    It has long been assumed in linguistics that bound variable interpretations of pronouns are possible (only) when a quantified expression c‐commands the pronoun. In two studies in which readers' eye movements were recorded, we examined the processing of pronouns bound by universal quantifiers. Experiment 1 compared examples where the quantifier c‐commands the pronoun (‘Every British soldier thought he killed an enemy soldier’) with examples where it doesn't (‘Every British soldier aimed and then he killed an enemy soldier’). Although there (...)
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  34. Scope and Situation Binding in LTAG Using Semantic Unification.Maribel Romero & Laura Kallmeyer - manuscript
    This paper develops a framework for TAG (Tree Adjoining Grammar) semantics that brings together ideas from different recent approaches. Then, within this framework, an analysis of scope is proposed that accounts for the different scopal properties of quantifiers, adverbs, raising verbs and attitude verbs. Finally, including situation variables in the semantics, different situation binding possibilities are derived for different types of quantificational elements.
     
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  35. The Use of the Binding Argument in the Debate About Location.Dan Zeman - 2017 - In Sarah-Jane Conrad & Klaus Petrus (eds.), Meaning, Context and Methodology. Mouton de Gruyter. pp. 191-212.
    In this paper I inquire into the methodological status of one of the arguments that have figured prominently in contemporary debates about the semantics of a variety of expressions, the so-called “Binding Argument”. My inquiry is limited to the case of meteorological sentences like “It is raining”, but my conclusion can be extended to other types of sentences as well. Following Jason Stanley, I distinguish between three interpretations of the argument. My focus is on the third, weakest interpretation, according (...)
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  36.  12
    Free Versus Bound Variables and the Taxonomy of Gaps.Luis Vicente - 2016 - Natural Language Semantics 24 (3):203-245.
    Potts et seq. presents an analysis of gap-containing supplements where the gap is modelled as a variable over the semantic type of the constituent that the as-clause adjoins to. This much allows the meaning of the gap to be resolved purely compositionally, by defining as as a function that allows the anchor to bind the gap variable. This article presents a class of as-clauses where Potts’s analysis seems to break down, in that the gap cannot be modelled as (...)
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  37. Quantification Over Situations Variables in LTAG: Some Constraints.Maribel Romero - unknown
    Some natural language expressions –namely, determiners like every, some, most, etc.— introduce quantification over individuals (or, in other words, they express relations between sets of individuals). For example, the truth conditions of a sentence like (1a) are represented in Predicate Logic (PrL) by binding the..
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  38.  7
    Unbound Riches: Comparative Adjectives and the Argument From Binding.Stefano Predelli - 2003 - Logic and Logical Philosophy 12:341-348.
    Uncontroversially, the semantic interpretation of comparative adjectives such as rich or small depends, among other factors, on a contextually salient comparison standard. Two alternative theories have been proposed in order to account for such contextual dependence: an indexicalist view, according to which comparative adjectives are indexical expressions, and a hidden variable approach, which insists that a comparison standard is contributed as the semantic value of a variable occurring at the level of semantic representation. In this paper, I defend (...)
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  39. The Myth of Occurrence-Based Semantics.Bryan Pickel & Brian Rabern - forthcoming - Linguistics and Philosophy:1-25.
    The principle of compositionality requires that the meaning of a complex expression remains the same after substitution of synonymous expressions. Alleged counterexamples to compositionality seem to force a theoretical choice: either apparent synonyms are not synonyms or synonyms do not syntactically occur where they appear to occur. Some theorists have instead looked to Frege’s doctrine of “reference shift” according to which the meaning of an expression is sensitive to its linguistic context. This doctrine is alleged to retain the relevant claims (...)
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  40. Monsters in Kaplan’s Logic of Demonstratives.Brian Rabern - 2013 - Philosophical Studies 164 (2):393-404.
    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 (...)
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  41.  65
    Stoic Logic and Multiple Generality.Susanne Bobzien & Simon Shogry - 2020 - Philosophers' Imprint 20 (31):1-36.
    We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We (...)
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  42.  63
    Neural Blackboard Architectures of Combinatorial Structures in Cognition.van der Velde Frank & de Kamps Marc - 2006 - Behavioral and Brain Sciences 29 (1):37-70.
    Human cognition is unique in the way in which it relies on combinatorial (or compositional) structures. Language provides ample evidence for the existence of combinatorial structures, but they can also be found in visual cognition. To understand the neural basis of human cognition, it is therefore essential to understand how combinatorial structures can be instantiated in neural terms. In his recent book on the foundations of language, Jackendoff described four fundamental problems for a neural instantiation of combinatorial structures: the massiveness (...)
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  43. Referential and Quantificational Indefinites.Janet Dean Fodor & Ivan A. Sag - 1982 - Linguistics and Philosophy 5 (3):355 - 398.
    The formal semantics that we have proposed for definite and indefinite descriptions analyzes them both as variable-binding operators and as referring terms. It is the referential analysis which makes it possible to account for the facts outlined in Section 2, e.g. for the purely ‘instrumental’ role of the descriptive content; for the appearance of unusually wide scope readings relative to other quantifiers, higher predicates, and island boundaries; for the fact that the island-escaping readings are always equivalent to maximally (...)
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  44.  79
    Animate Vision.Dana H. Ballard - 1991 - Artificial Intelligence 48 (1):57-86.
    Animate vision systems have gaze control mechanisms that can actively position the camera coordinate system in response to physical stimuli. Compared to passive systems, animate systems show that visual computation can be vastly less expensive when considered in the larger context of behavior. The most important visual behavior is the ability to control the direction of gaze. This allows the use of very low resolution imaging that has a high virtual resolution. Using such a system in a controlled way provides (...)
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  45.  50
    Hybrid Languages.Patrick Blackburn & Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):251-272.
    Hybrid languages have both modal and first-order characteristics: a Kripke semantics, and explicit variable binding apparatus. This paper motivates the development of hybrid languages, sketches their history, and examines the expressive power of three hybrid binders. We show that all three binders give rise to languages strictly weaker than the corresponding first-order language, that full first-order expressivity can be gained by adding the universal modality, and that all three binders can force the existence of infinite models and have (...)
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  46. Abrowne@Lgu.Ac.Uk.Antony Browne & Ron Sun - unknown
    Variable binding has long been a challenge to connectionists. Attempts to perform variable binding using localist and distributed connectionist representations are discussed, and problems inherent in each type of representation are outlined.
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  47. Cross-Linguistic Semantics.Maria Bittner - 1994 - Linguistics and Philosophy 17 (1):53 - 108.
    Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is shown to (...)
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  48.  78
    Beyond the Frege Boundary.Edward L. Keenan - 1992 - Linguistics and Philosophy 15 (2):199-221.
    In sentences like Every teacher laughed we think of every teacher as a unary (=type (1)) quantifier - it expresses a property of one place predicate denotations. In variable binding terms, unary quantifiers bind one variable. Two applications of unary quantifiers, as in the interpretation of No student likes every teacher, determine a binary (= type (2)) quantifier; they express properties of two place predicate denotations. In variable binding terms they bind two variables. We call (...)
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  49.  41
    The Processing Domain of Dcope Interaction.Oliver Bott & Fabian Schlotterbeck - 2015 - Journal of Semantics 32 (1):fft015.
    The present study investigates whether quantifier scope is computed incrementally during online sentence processing. We exploited the free word order in German to manipulate whether the verbal predicate preceded or followed the second quantifier in doubly quantified sentences that required the computation of inverse scope. A possessive pronoun in the first quantifier that had to be bound by the second quantifier was used to enforce scope inversion. We tested whether scope inversion causes difficulty and whether this difficulty emerges even at (...)
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  50.  63
    Incremental Dynamics.Jan van Eijck - 2001 - Journal of Logic, Language and Information 10 (3):319-351.
    A new system of dynamic logic is introduced and motivated, witha novel approach to variable binding for incremental interpretation. Thesystem is shown to be equivalent to first order logic and complete.The new logic combines the dynamic binding idea from DynamicPredicate Logic with De Bruijn style variable free indexing. Quantifiersbind the next available variable register; the indexing mechanismguarantees that active registers are never overwritten by newquantifiers actions. Apart from its interest in its own right, theresulting system (...)
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