Variable-Free Semantics Research Articles

Binding without variables: Solving the under-generation problems

The variable-free semantics of Jacobson (1999, 2000, 2014) derives binding relations by the local application of the z-rule. This rule, however, under- generates binding. This paper makes two contributions: (i) replacing the z-rule with a more flexible rule called i (a la the W-combinator of Szabolcsi 1992), which allows for more binding relations; (ii) enriching Jacobson’s variable-free system and proposing a two-dimensional analysis to account for the interactions between scoping and binding. Issues to be covered include binding into adjuncts, possessor binding, scope ambiguity, inverse linking, weak crossover, and ‘paycheck pronouns’.

The syntax and compositional semantics of English ONE

In this paper, I analyse the syntax and compositional semantics of the unity cardinal one in English. I argue that the three different uses of one, namely as a determiner, as a DP pronoun and as a prosortal can be accounted for with a single, monosemic analysis. It will be argued that an NP-ellipsis account is not able to provide a unified account of the major uses. However, it will be argued that anaphoric uses of one always involve predicate anaphora. Therefore, a variable-free semantics will be adopted, and it will be shown that in such a framework, one can indeed provide a uniform account for all three uses, using type-shifting operations and Skolem-functions.

ASL Loci: Variables or Features?

American Sign Language famously disambiguates pronoun antecedents with the use of space. In ASL, both referential and quantificational NPs can be signed at different locations (‘loci’) in the signing space. Pronouns can later retrieve these NPs by pointing at the same locus. Many analyses of ASL pronouns assume that these spatial loci are the overt realization of formal variables (Lillo-Martin and Klima 1990, a.o.), based on the observations that there are arbitrarily many loci and that pronoun ambiguity can be resolved under multiple levels of embedding. In this paper, I argue that loci should not be analyzed as variables, but rather as morphosyntactic features. First, I show that the variable-based analysis under-generates: it is possible for two loci-sharing pronouns to appear free in the same expression but nevertheless receive different interpretations. Second, I show that loci share certain important properties with morphosyntactic features, including their behavior under focus-sensitive operators and their ability to induce complex agreement patterns. These results directly bear on the theory of Variable-Free Semantics (Jacobson 1999), which posits that the logic underlying natural language does not make use of formal variables. As proof of concept, I provide a variable-free fragment of ASL loci.

Direct Compositionality and Variable-Free Semantics: The Case of Binding into Heads

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Binding Alongside Hamblin Alternatives Calls for Variable-free Semantics

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Nothing else for 'something else': A variable-free account

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Relational Nouns, Pronouns, and Resumption

This paper presents a variable-free analysis of relational nouns in Glue Semantics, within a Lexical Functional Grammar (LFG) architecture. Relational nouns and resumptive pronouns are bound using the usual binding mechanisms of LFG. Special attention is paid to the bound readings of relational nouns, how these interact with genitives and obliques, and their behaviour with respect to scope, crossover and reconstruction. I consider a puzzle that arises regarding relational nouns and resumptive pronouns, given that relational nouns can have bound readings and resumptive pronouns are just a specific instance of bound pronouns. The puzzle is why is it impossible for bound implicit arguments of relational nouns to be resumptive? The puzzle is highlighted by a well-known variety of variable-free semantics, where pronouns and relational noun phrases are identical both in category and (base) type. I show that the puzzle also arises for an established variable-based theory. I present an analysis of resumptive pronouns that crucially treats resumptives in terms of the resource logic linear logic that underlies Glue Semantics: a resumptive pronoun is a perfectly ordinary pronoun that constitutes a surplus resource; this surplus resource requires the presence of a resumptive-licensing resource consumer, a manager resource. Manager resources properly distinguish between resumptive pronouns and bound relational nouns based on differences between them at the level of semantic structure. The resumptive puzzle is thus solved. The paper closes by considering the solution in light of the hypothesis of direct compositionality. It is argued that a directly compositional version of the theory is possible, although perhaps not desirable. The implications for direct compositionality are considered.

Binding Alongside Hamblin Alternatives Calls for Variable-free Semantics

No abstract.

Direct Compositionality and Variable-Free Semantics: The Case of Binding into Heads

No abstract.

Function Domains in Variable-Free Semantics

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Paycheck Pronouns, Bach-Peters Sentences, and Variable-Free Semantics

This paper argues for the hypothesis of direct compositionality (as in, e.g., Montague 1974), according to which the combinatory syntactic rules specify a set of well-formed expressions while the semantic combinatory rules work in tandem to directly supply a model-theoretic interpretation to each expression as it is "built" in the syntax. (This thus obviates the need for any level like LF and, concomitantly, for any rules mapping surface structures to such a level.) I focus here on one related group of phenomena: the interaction of "paycheck" pronouns with Weak Crossover effects and i-within-i effects. These interactions were studied in Jacobson (1977) as they show up in Back-Peters sentences. There I argued that these interactions show that paycheck pronouns have a complex representation at LF; here I show that all of the observations in this earlier work are compatible with the hypothesis of direct compositionality. The key tool is the adoption of a variation-free semantics (a semantics which makes no use of variables as part of the semantic machinery). In addition to the general consequences for the syntax/semantics interface, there are two other main results. First, I provide new arguments for a variable-free semantics. For example, it will be shown that under this view the paycheck reading of a pronoun comes for free; most other theories posit additional mechanisms and/or an additional lexical meaning for pronouns, and thus paycheck and regular pronouns are only accidentally homophonous. Second, I reiterate one of the central points in Jacobson (1977): this is that the first pronoun in a Bach-Peters sentence is indeed a paycheck pronoun, and hence nothing special needs to be said about these sentences nor does any new machinery need to be invoked for them.

Antecedent Contained Deletion and Pied-Piping: Evidence for a Variable-Free Semantics

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Antecedent Contained Deletion in a Variable-Free Semantics

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