Results for 'variable binding'

999 found
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  1.  76
    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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  2.  90
    Variable Binding Term Operators.John Corcoran, William Hatcher & John Herring - 1972 - Mathematical Logic Quarterly 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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  3.  18
    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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  4.  23
    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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  5. 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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  6.  8
    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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  7.  40
    Tensor Product Variable Binding and the Representation of Symbolic Structures in Connectionist Systems.Paul Smolensky - 1990 - Artificial Intelligence 46:159-216.
  8.  19
    Variable Binding Term Operators.John Corcoran, William Hatcher & John Herring - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (12):177-182.
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  9.  69
    E-Type Pronouns, DRT, Dynamic Semantics and the Quantifier/Variable-Binding Model.S. J. Barker - 1997 - Linguistics and Philosophy 20 (2):195-228.
  10.  6
    Variable Binding Term Operators in $\Lambda $-Calculus.M. W. Bunder - 1979 - Notre Dame Journal of Formal Logic 20 (4):876-878.
  11.  17
    Categorial Languages and Variable-Binding Operators.Adam Nowaczyk - 1978 - Studia Logica 37 (1):27 - 39.
  12.  22
    Quantifier/Variable-Binding.B. H. Slater - 2000 - Linguistics and Philosophy 23 (3):309-321.
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  13.  3
    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.
  14.  2
    Rule Acquisition and Variable Binding: Two Sides of the Same Coin.P. J. Hampson - 1993 - Behavioral and Brain Sciences 16 (3):462.
  15. 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.
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  16.  58
    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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  17.  39
    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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  18.  26
    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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  19. 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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  20. 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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  21. Monsters and Communication: The Semantics of Contextual Shifting and Sensitivity.Brian Rabern - 2012 - Dissertation, The Australian National University
    This thesis argues for two main points concerning the philosophy of natural language semantics. Firstly, that the objects of assertion are distinct from the entities appealed to in the compositional rules of natural language semantics. Secondly, natural languages contain context-shifting operators known as "monsters". In fact, it will be shown that these theses are simply two sides of the same coin.
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  22. Scope and Binding.Anna Szabolcsi - manuscript
    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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  23.  38
    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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  24.  18
    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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  25.  5
    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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  26. 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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  27. 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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  28.  19
    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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  29.  47
    A General Theory of Abstraction Operators.Neil Tennant - 2004 - Philosophical Quarterly 54 (214):105-133.
    I present a general theory of abstraction operators which treats them as variable-binding term- forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically non- committal). The theory also treats both natural and real numbers (...)
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  30.  31
    Beyond the Frege Boundary.Edward L. Keenan - 1992 - Linguistics and Philosophy 15 (2):199 - 221.
    In sentences likeEvery teacher laughed we think ofevery teacher as aunary (=type ) quantifier — it expresses a property ofone place predicate denotations. In variable binding terms, unary quantifiers bind one variable. Two applications of unary quantifiers, as in the interpretation ofNo student likes every teacher, determine abinary (= (type ) quantifier; they express properties oftwo place predicate denotations. In variable binding terms they bind two variables. We call a binary quantifierFregean (orreducible) if it can (...)
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  31. Weak Crossover, Scope, and Agreement in a Minimalist Framework.Pierre Pica & William Snyder - 1995 - In Susanne Preuss, Martha Senturia, Raul Aranovich & William Byrne (eds.), Proceedings of the 13th West Coast Conference in Linguistics. Cambridge University Press.
    Our paper presents a novel theory of weak crossover effects, based entirely on quantifier scope preferences and their consequences for variable binding. The structural notion of 'crossover' play no role. We develop a theory of scope preferences which ascribes a central role to the AGR-P System.
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  32. 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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  33.  19
    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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  34.  51
    Negation and Negative Concord in Romance.De Swart Henriëtte & A. Sag Ivan - 2002 - Linguistics and Philosophy 25 (4):373-417.
    This paper addresses the two interpretations that a combination ofnegative indefinites can get in concord languages like French:a concord reading, which amounts to a single negation, and a doublenegation reading. We develop an analysis within a polyadic framework,where a sequence of negative indefinites can be interpreted as aniteration of quantifiers or via resumption. The first option leadsto a scopal relation, interpreted as double negation. The secondoption leads to the construction of a polyadic negative quantifiercorresponding to the concord reading. Given that (...)
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  35.  38
    Prehistoric Cognition by Description: A Russellian Approach to the Upper Paleolithic.John Bolender - 2007 - Biology and Philosophy 22 (3):383-399.
    A cultural change occurred roughly 40,000 years ago. For the first time, there was evidence of belief in unseen agents and an afterlife. Before this time, humans did not show widespread evidence of being able to think about objects, persons, and other agents that they had not been in close contact with. I argue that one can explain this transition by appealing to a population increase resulting in greater exoteric (inter-group) communication. The increase in exoteric communication triggered the actualization of (...)
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  36.  64
    Quantification in English is Inherently Sortal.Ed Keenan - 1999 - History and Philosophy of Logic 20 (3-4):251-265.
    Within Linguistics the semantic analysis of natural languages (English, Swahili, for example) has drawn extensively on semantical concepts first formulated and studied within classical logic, principally first order logic. Nowhere has this contribution been more substantive than in the domain of quantification and variable binding. As studies of these notions in natural language have developed they have taken on a life of their own, resulting in refinements and generalizations of the classical quantifiers as well as the discovery of (...)
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  37.  4
    A Sloppy Identity Puzzle.Satoshi Tomioka - 1999 - Natural Language Semantics 7 (2):217-241.
    Sloppy identity under ellipsis is generally attributed to the pronoun in ellipsis being a bound variable. However, sloppy identity can be licensed in structural configurations in which variable binding is ordinarily blocked. This paper provides a solution for this mismatch by reanalyzing the pronouns with the unexpected sloppy readings as E-type pronouns. Under the proposed analysis, the distribution of such pronouns is correctly predicted. It will also be shown that the analysis is successfully extended to sloppy identity (...)
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  38.  17
    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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  39.  5
    Functional Operations in Frege'sbegriffsschrift.Peter M. Simons - 1988 - History and Philosophy of Logic 9 (1):35-42.
    Frege uses Greek letters in two different ways in his Begriffsschrift. One way is the familiar use of bound variables, in conjunction with variable-binding operators, to mark and close argument-places. The other, which is quite unfamiliar, employs letters to mark places for operators to reach into, without thereby closing these places. Frege thereby invents a powerful and compact notation for functional operations which can be recommended even today. His regrettable double use of Greek letters obscured his invention, and (...)
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  40. A Simplified Modal Presentation of the ‘Non-Redundancy’ System.Philippe Schlenker - manuscript
    We give a simplified version of the system introduced in ‘Non-Redundancy’, presented here as a Modal Logic whose primitive elements are finite sequences. It includes a treatment of Condition C, Condition B, Condition A, and the Locality of Variable Binding, but disregards quantification and Weak and Strong Crossover effects, which are treated in the longer paper.
     
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  41.  21
    The Copy Theory of Movement: Spell Out.Kyle Johnson - unknown
    ( ) Di erence in Semantic Displacement a. Total Reconstruction: Mary kaupir ikke skó. ¬ Mary kaupir skó b. Variable Binding: Which book Mary had read e set of propositions such that x Mary had read x, x a book. A guard stands before every bank x if x is a bank then a guard stands before x..
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  42.  22
    Connectionist Inference Models.Ron Sun - manuscript
    The performance of symbolic inference tasks has long been a challenge to connectionists. In this paper, we present an extended survey of this area. Existing connectionist inference systems are reviewed, with particular reference to how they perform variable binding and rule- based reasoning and whether they involve distributed or localist representations. The bene®ts and disadvantages of different representations and systems are outlined, and conclusions drawn regarding the capabilities of connectionist inference systems when compared with symbolic inference systems or (...)
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  43.  6
    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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  44.  5
    Powering Decision Machines with Dynamo.Jan van Eijck - unknown
    Dynamic 10gic programming is the result 0f making dynamic versions 0f first order predicate 10gic executable. The main sources of inspiration for this are the dynamic variable binding strategies that have become fashionable in natural language analysis (DRT [8], Anaphora, Logic [2], DPL [7]), the idea of implementing identity assertions as assignment commands familiar from constraint programming, and more in particular from Alma,-0 [1], and the genera.] injunction to explore logical dynamics emanating from the works of J 01121,11 (...)
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  45. Tense and Intensionality in Specificational Copular Sentences.Maribel Romero - manuscript
    Specificational sentences show Connectivity Effects (Akmajian 1970, Higgins 1979, Halvorsen 1978, Jacobson 1994, among others). For example, an NP like no man embedded in a relative clause in general cannot bind a pronoun outside the relative clause, as illustrated in (3a); but in specificational copular sentences this binding is possible, as in (3b). This effect is called Variable Binding Connectivity. Similarly, the NP a unicorn cannot be interpreted de dicto with respect to the embedded verb look for (...)
     
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  46. Choosing Short: An Explanation of the Similarities and Dissimilarities in the Distribution Patterns of Binding and Covaluation.Mihnea Capraru - manuscript
    Covaluation is the generalization of coreference introduced by Tanya Reinhart. Covaluation distributes in patterns that are very similar yet not entirely identical to those of binding. On a widespread view, covaluation and binding distribute similarly because binding is defined in terms of covaluation. Yet on Reinhart's view, binding and covaluation are not related that way: binding pertains to syntax, covaluation does not. Naturally, the widespread view can easily explain the similarities between binding and covaluation, (...)
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  47. The Antinomy of the Variable: A Tarskian Resolution.Bryan Pickel & Brian Rabern - 2016 - Journal of Philosophy 113 (3):137-170.
    Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables (...)
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  48. A Modal Restriction of R-Mingle with the Variable-Sharing Property.Gemma Robles, José M. Méndez & Francisco Salto - 2010 - Logic and Logical Philosophy 19 (4):341-351.
    A restriction of R-Mingle with the variable-sharing property and the Ackermann properties is defined. From an intuitive semantical point of view, this restriction is an alternative to Anderson and Belnap’s logic of entailment E.
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  49.  64
    Lectures on Government and Binding.Noam Chomsky - 1981 - Foris.
    A more extensive discussion of certain of the more technical notions appears in my paper "On Binding" (Chomsky,; henceforth, OB). ...
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  50.  65
    The Problem of Variable Choice.James Woodward - 2016 - Synthese 193 (4):1047-1072.
    This paper explores some issues about the choice of variables for causal representation and explanation. Depending on which variables a researcher employs, many causal inference procedures and many treatments of causation will reach different conclusions about which causal relationships are present in some system of interest. The assumption of this paper is that some choices of variables are superior to other choices for the purpose of causal analysis. A number of possible criteria for variable choice are described and defended (...)
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