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 (...) Analysis of Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). 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 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 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, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

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 (...) potentially overgenerates, in that a third type of reading is predicted to exist for sentences which actually have only two: de re and de dicto. Percus proposes constraints on the binding of situation pronouns, which correctly rule out these third readings. This paper shows, however, that extrinsic constraints on the binding of situation pronouns are not necessary to rule out the unwanted readings, as long as we develop a more precise theory of binding in the first place. I adapt the binding operator argued for by Büring 2004, originally developed only for overt pronouns, and show that when used as an operator for situation pronouns, the unwanted readings are not predicted to occur. (shrink)

Theabstract variable binding calculus (VB-calculus) provides a formal frame-work encompassing such diverse variable-binding phenomena as lambda abstraction, Riemann integration, existential and universal quantification (in both classical and nonclassical logic), and various notions of generalized quantification that have been studied in abstract model theory. All axioms of the VB-calculus are in the form of equations, but like the lambda calculus it is not a true equational theory since substitution of terms for variables is restricted. A similar problem (...) with the standard formalism of the first-order predicate logic led to the development of the theory of cylindric and polyadic Boolean algebras. We take the same course here and introduce the variety of polyadic VB-algebras as a pure equational form of the VB-calculus. In one of the main results of the paper we show that every locally finite polyadic VB-algebra of infinite dimension is isomorphic to a functional polyadic VB-algebra that is obtained from a model of the VB-calculus by a natural coordinatization process. This theorem is a generalization of the functional representation theorem for polyadic Boolean algebras given by P. Halmos. As an application of this theorem we present a strong completeness theorem for the VB-calculus. More precisely, we prove that, for every VB-theory T that is obtained by adjoining new equations to the axioms of the VB-calculus, there exists a model D such that T s=t iff D s=t. This result specializes to a completeness theorem for a number of familiar systems that can be formalized as VB-calculi. For example, the lambda calculus, the classical first-order predicate calculus, the theory of the generalized quantifierexists uncountably many and a fragment of Riemann integration. (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 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.

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)

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)

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 (...) it is implausible that they exist (Cappelen and Lepore (2005), Cappelen and Lepore (2002)).1 In what follows we respond to Cappelen’s and Lepore’s attempted reductio by bringing out crucial disanalogies between cases where the binding argument is successful and cases where it is not. But we have a deeper purpose than merely to respond to Cappelen and Lepore: we think the attempted reductio goes wrong by not taking sufficiently seriously the nature of the binding relation that holds between quantifiers and arguments/variables, and that our criticism will serve to highlight the nature and importance of this relation. (shrink)

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 (...) given language). (shrink)

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 (...) binding, we argue that a correct understanding of how composition works gives no reason to relativize semantic values, and that propositional semantic values are in fact the preferred option. We take our argument to be mainly empirical, but along the way, we defend some more general theses. Simple propositional semantic values are viable in composition, we maintain, because composition is itself a complex phenomenon, involving multiple modes of composition. Furthermore, some composition principles make adjustments to the meanings of constituents in the course of composition. These adjustments are by triggered syntactic environments. We argue such small contributions of meaning from syntactic structure are acceptable. (shrink)

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 (...) body of systemic knowledge and perform a range of inferences with such speed? We describe a computational model that takes a step toward addressing the cognitive science challenge and resolving the artificial intelligence paradox. We show how a connectionist network can encode millions of facts and rules involving n-ary predicates and variables and perform a class of inferences in a few hundred milliseconds. Efficient reasoning requires the rapid representation and propagation of dynamic bindings. Our model (which we refer to as SHRUTI) achieves this by representing (1) dynamic bindings as the synchronous firing of appropriate nodes, (2) rules as interconnection patterns that direct the propagation of rhythmic activity, and (3) long-term facts as temporal pattern-matching subnetworks. The model is consistent with recent neurophysiological evidence that synchronous activity occurs in the brain and may play a representational role in neural information processing. The model also makes specific psychologically significant predictions about the nature of reflexive reasoning. It identifies constraints on the form of rules that may participate in such reasoning and relates the capacity of the working memory underlying reflexive reasoning to biological parameters such as the lowest frequency at which nodes can sustain synchronous oscillations and the coarseness of synchronization. (shrink)

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.

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' (...) to a binding site in the term, where they are bound); or as functions (since they often, though not always, represent `an unknown'). None of these models is perfect. In every case for the models above, problems arise when trying to use them as a basis for a fully formal mechanical treatment of formal language. The problems are practical—but their underlying cause may be mathematical. The issue is not whether formal syntax exists, since clearly it does, so much as what kind of mathematical structure it is. To illustrate this point by a parody, logical derivations can be modelled using a Gödel encoding (i.e., injected into the natural numbers). It would be false to conclude from this that proof-theory is a branch of number theory and can be understood in terms of, say, Peano's axioms. Similarly, as it turns out, it is false to conclude from the fact that variables can be encoded e.g., as numbers, that the theory of syntax-with-binding can be understood in terms of the theory of syntax-without-binding, plus the theory of numbers (or, taking this to a logical extreme, purely in terms of the theory of numbers). It cannot; something else is going on. What that something else is, has not yet been fully understood. In nominal techniques, variables are an instance of names, and names are data. We model names using urelemente with properties that, pleasingly enough, turn out to have been investigated by Fraenkel and Mostowski in the first half of the 20th century for a completely different purpose than modelling formal language. What makes this model really interesting is that it gives names distinctive properties which can be related to useful logic and programming principles for formal syntax. Since the initial publications, advances in the mathematics and presentation have been introduced piecemeal in the literature. This paper provides in a single accessible document an updated development of the foundations of nominal techniques. This gives the reader easy access to updated results and new proofs which they would otherwise have to search across two or more papers to find, and full proofs that in other publications may have been elided. We also include some new material not appearing elsewhere. (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)

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 (...) an analysis based on Skolem functions. It is explained why certain anaphor types allow proxy-readings whereas others do not. (shrink)

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. (...) One consequence of this autonomy thesis is that the rules for character can contain no variables bound by content-level operators elsewhere in the sentence. Tacit appeal to this consequence features essentially both in Jason Stanley’s recent argument that all contextual ambiguity must be linked to "elements in the actual syntactic structure of the sentence uttered" in his "Context and Logical Form" and in my arguments against character-based theories of complex demonstratives in my "Complex Demonstratives". However, I argue here that the autonomy thesis is unmotivated, and show that we can separate Kaplan’s notion of character into two independent components: an aspect of meaning which is context-sensitive, and an aspect of meaning that is exempted from scopal interactions with other operators. The resulting semantic framework allows constructions similar to Kaplan’s rejected notion of "monsters begat by elegance", but which are both more empirically adequate and more theoretically versatile. Having made the distinction between context-sensitivity and autonomy from scopal interaction, I show how it allows binding into the character of expressions and hence undermines the immediate success of both Stanley’s argument and my former argument against character-based theories of complex demonstratives, and discuss briefly the prospects for reinstating modified versions of those arguments. Finally, I show how that same distinction allows a defusing of Kripke’s modal argument against a descriptive theory of names. Once autonomy from semantic interaction is separated from context-sensitivity, the first of those two alone can be used to capture the modal rigidity of proper names.. (shrink)

The implicit content indicating location associated with “raining” and other weather predicates is a definite description meaning “the location occupied by x,” where the individual variable “x” can be referential or bound. This position has deleterious consequences for certain varieties of radical contextualism.

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 (...) to which postulating variables for locations in the logical form of meteorological sentences is the best available explanation of the binding phenomena that such sentences give rise to. My aim is to show that even in this weak interpretation, the argument cannot be reasonably taken to hold. I accomplish this by showcasing several alternative ways to account for the binding data that have not been, as of yet, ruled out as flawed. (shrink)

In a recent paper, Pickel and Rabern (2016) argue that a dynamic Tarskian semantics resolves Fine’s antinomy of the variable without the radical consequences for semantics proposed by Fine (2003, 2007). While Pickel and Rabern’s basic insight—a parameter of discourse context that tracks occurrences of variable-binding expressions—is important, I will argue that their own Tarskian theory faces a destructive dilemma: either their theory does not resolve Fine’s antinomy as they propose, or their theory does not reflect the (...) intuitive motivation for what they call structured meanings. I suggest that in response to this dilemma we should reject one of the principles that generates Pickel and Rabern’s version of the antinomy. Here Pickel and Rabern’s insight has surprising, but salutary, foundational consequences for semantics. (shrink)

Incomplete penetrance and variable expressivity are non‐Mendelian phenomena resulting in the lack of correlation between genotype and phenotype. Not withstanding the diversity in mechanisms, differential expression of homologous alleles within cells manifests as variations in penetrance and expressivity of mutations between individuals of the same genotype. These phenomena are seen most often in dominantly inherited diseases, implying that they are sensitive to concentration of the gene product. In this framework and the advances in understanding the role of microRNA (miRNA) (...) in fine‐tuning gene expression at translational level, we propose miRNA‐mediated regulation as a mechanism for incomplete penetrance and variable expressivity. The presence of miRNA binding sites at 3′ UTR, co‐expression of target gene–miRNA pairs for genes showing incomplete penetrance and variable expressivity derived from available data lend support to our hypothesis. Single nucleotide polymorphisms in the miRNA target site facilitate the implied differential targeting of the transcripts from homologous alleles. (shrink)

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 (...) be stored, just as NP meanings are, until an appropriate binding CN phrase was encountered. Binding conditions would simply require that a∨ P n meaning not come out of storage until the derivation had emerged from its governing category. The behavior of the pro-adjectivesuch suggests that an expression of any category, if it is legitimately translatable as a variable, may be a fullfledged proform; many principles and mechanisms described to account for the widely studied pronouns in fact apply to nonargument categories. (shrink)

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.

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 (...) a variable over the semantic type of the anchor. I propose that these cases can be unified with those in Potts’s work, as well as a larger class of ellipsis phenomena, by assuming that, under certain conditions, surface gaps are composite entities, containing a bound variable and a free variable that are resolved independently of each other. The bound variable is bound by the anchor, and the free variable is resolved by anaphora to a salient discourse object. (shrink)

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.

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 (...) scope have to be distinguished, leaving few if any run-of-the-mill quantifiers. Scope behavior is also not uniform. At least three classes of expressions emerge: indefinites, distributive universals, and counters. Likewise, the bound variable interpretation of pronouns is joined by co-variation with situations. As a result, the classical notions of scope and binding are likely to end up as building blocks in the varied mechanisms at work in “scope phenomena” and “binding phenomena”, and not as self-contained analyses of those phenomena. (shrink)

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..

Generative grammar is an approach to the study of language which is explicit, mentalistic, and based on the claim that the ability to acquire language is innately specified. This chapter outlines some of the recent history leading up to contemporary generative grammar. It provides some context for the emergence of Principles and Parameters and the basic gist of the Principles and Parameters approach. Chomsky is a fundamental contribution to the study of human language in its effort to develop a new (...) theory of what is universal across languages and what is variable. In the beginning of the 1990s, Chomsky developed a new model, called the Minimalist Program. The main idea behind the model of grammar labeled Government and Binding was developed by Chomsky in several publications. The chapter also outlines some of the current research trends within the Minimalist Program. (shrink)

The BTB domain is a protein–protein interaction motif that is found throughout eukaryotes. It determines a unique tri‐dimensional fold with a large interaction surface. The exposed residues are highly variable and can permit dimerization and oligomerization, as well as interaction with a number of other proteins. BTB‐containing proteins are numerous and control cellular processes that range from actin dynamics to cell‐cycle regulation. Here, we review findings in the field of transcriptional regulation to illustrate how the high variability of the (...) BTB has allowed related transcription factors to evolve different functional abilities. We then report how recent work has showed that, in spite of their high sequence divergence and apparently unrelated functions, many BTB‐containing proteins have at least one shared role: the recruitment of degradation targets to E3 ubiquitin ligase complexes. Taken together, these findings illustrate diverse and convergent functions of a versatile protein–protein interaction domain. BioEssays 28: 1194–1202, 2006. © 2006 Wiley Periodicals, Inc. (shrink)

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 (...) about synonymy and substitution while respecting the compositionality principle. Thus, Salmon (Philos Rev 115(4):415, 2006) and Glanzberg and King (Philosophers’ Imprint 20(2):1–29, 2020) offer occurrence-based accounts of variable binding, and Pagin and Westerståhl (Linguist Philos 33(5):381–415, 2010c) argue that an occurrence-based semantics delivers a compositional account of quotation. Our thesis is this: the occurrence-based strategies resolve the apparent failures of substitutivity in the same general way as the standard expression-based semantics do. So it is a myth that a Frege-inspired occurrence-based semantics affords a genuine alternative strategy. (shrink)

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.

Phenotypic divergence among animal species may be due in part to species‐specific (SS) regulation of gene expression by small, non‐coding regulatory RNAs termed “microRNAs”. This phenomenon can be modulated by several variables. First, microRNA genes vary by their level of conservation, many of them being SS, or unique to a particular evolutionary lineage. Second, microRNA expression levels vary spatially and temporally in different species. Lastly, while microRNAs bind the 3′UTR of target genes in order to silence their expression, the (...) class='Hi'>binding sites themselves are often non‐conserved. The variability of the miRNA‐target paradigm between different species is thus multifactorial, and this paradigm has only just started to gain attention from researchers in various fields. Here we present and discuss recent findings regarding the characteristics and implications of SS microRNA regulation. (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)

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 (...) the indexicalist view against an influential argument favoring the hidden variable approach, the so-called argument from binding. I argue that independent evidence favors an understanding of comparison standards as functions, and that on such a conception of comparison standards the evidence put forth by the argument from binding is naturally accountable within an indexicalist treatment. (shrink)

This article explores a phenomenon found in Berber whereby the extraction of dative arguments (of verbs, nouns and prepositions) gives rise to two occurrences of wh. One is a wh-word located in Spec,C and the other a wh-clitic in the dative form located in C (wh-clitic-doubling). Close examination reveals that the wh-word in Spec,C functions as an operator base-generated in its scope position and the dative wh-clitic in C provides it with a derivational link to the variable in the (...) dative position it binds (wh-Cliticisation). Wh-clitic-doubling and wh-Cliticisation amount to direct evidence for Cliticisation as a derivational interpretive mechanism of Grammar that obviates the need for indexing (Lebeaux 1983, Chomsky 1986, 1995). They also provide evidence for the conclusion in Kayne (1989) that Cliticisation is an instance of Head-Movement, more precisely, feature-based Head-Movement. (shrink)

Soames thinks the dependencies show up in the semantics if they are generated by variable binding. That will only partially overlap with Pinillos's ambitions for the notion of de jure codesignation. This chapter contributes towards 'domesticating' the kind of predicates that fans of de jure codesignation are friendly to, that is, making them seem less alien and somewhat less 'magical'. It surveys a novel kind of semantic structure that has been posited by Mark Richard, Kit Fine, Ángel Pinillos, (...) and others. It focuses on anaphora, especially cases that cannot be handled by a 'bound‐variable' analysis, and distinguishes our target view from other treatments of anaphora. The chapter discusses the semantics of attitude reports and discusses two kinds of complex anaphoric dependency. It explains a difference in how functions in a programming language can be sensitive to the identity of their operands. (shrink)

The paper highlights proof-theoretic semantics as providing natural resources for capturing semantic variation in natural language. The semantic variations include:Distinction between extensional predication and attribution to intensional transitive verbs a non-specific object.Omission of a verbal argument in a transitive verb.Obtaining sameness of meaning of sentences with transitive verbs with omitted object and existentially quantified object.Blocking unwarranted entailments in adjective–noun combinations.Capturing quantifier scope ambiguity.Obtaining context dependent quantifier domain restriction. The proof-theoretic resources employed to capture the above semantic variations include:The use of (...) different kinds of formal parameters and different ways of binding them to predicates.Omission of a premise from a proof-rule.Basing meanings on derivations in meaning-conferring proof-systems.Appealing to substructurality of I/E-rules.Controlling the order of rule applications in derivations.Controlling the open formulas participating in a context within a sequent. (shrink)

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 (...) consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

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 (...) when used for cognitive modelling. q 2001 Elsevier Science Ltd. All rights reserved. (shrink)

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 (...) of the binding problem, the problem of 2, the problem of variables, and the transformation of combinatorial structures from working memory to long-term memory. This paper aims to show that these problems can be solved by means of neural “blackboard” architectures. For this purpose, a neural blackboard architecture for sentence structure is presented. In this architecture, neural structures that encode for words are temporarily bound in a manner that preserves the structure of the sentence. It is shown that the architecture solves the four problems presented by Jackendoff. The ability of the architecture to instantiate sentence structures is illustrated with examples of sentence complexity observed in human language performance. Similarities exist between the architecture for sentence structure and blackboard architectures for combinatorial structures in visual cognition, derived from the structure of the visual cortex. These architectures are briefly discussed, together with an example of a combinatorial structure in which the blackboard architectures for language and vision are combined. In this way, the architecture for language is grounded in perception. Perspectives and potential developments of the architectures are discussed. Key Words: binding; blackboard architectures; combinatorial structure; compositionality; language; dynamic system; neurocognition; sentence complexity; sentence structure; working memory; variables; vision. (shrink)