Online research in philosophy

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.

The tableau substitution rule in free variable tableau reasoning is destructive, for in general, T has consequences that T0 lacks. We show how this destructive feature can be eliminated in favour of a set-up that replaces tableau substitution with the generation and incremental merge of variable constraints on tableau branches. The approach diifers from other constraint based techniques in tableau reasoning in that we constrain tableau branches rather than clauses, and use disunification constraints rather than unification constraints. We prove soundness and completeness, with the completeness proof based on a new way to generate models from open tableaux.

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux.

First we have individual variables, as usual in first-order logics. (We do not have individual constants, but this is a minor point.) The propositional logic LP has justification constants, but in FOLP these are generalized to allow individual variables as arguments. Thus we have as justification constants c, c(x), c(x, y), . . . . Similarly LP has justification variables, but in FOLP these can be parametrized with individual variables p, p(x), p(x, y), . . . . To keep terminology in line with past papers, we will still refer to things as justification constants and justification variables, even though they have structure to them. As in LP, justification terms are built up from justification constants and justification variables using ·, +, ! as usual. In addition there is a new constructor, genx, introduced by Artemov, and there is one further new constructor, exsx, introduced in this paper. If t is a justification term and x is an individual variable, genxt and exsxt are justification terms. An individual variable x is free in a justification term unless it is bound by genx or exsx. More specifically, the free variables of p(x, y, . . .) and of c(x, y, . . .) are {x, y, . . .}, the free variables of s · t and of s + t are the free variables of s together with the free variables of t, the free variables of !s are the free variables of s, and the free variables of genxt and of exsxt are the free variables of t except for x. Formulas are built up from atomic formulas, including ⊥, in the way standard in first-order logic, together with the additional formation rule: t:X is a formula provided t is a justification term, X is a formula, and all free variables of X occur in t. We assume ⊃, ⊥, and ∀ are basic, with other connectives and quantifier defined. The axiomatization used here is a combination of an LP axiomatization and a standard axiomatization of first-order logic, together with a version of the Barcan formula, and one additional axiom that corresponds to the converse Barcan formula..

Free choice permission, a crucial test case concerning the semantics/ pragmatics boundary, usually receives a pragmatic treatment. But its pragmatic features follow from its semantics. We observe that free choice inferences are defeasible, and defend a semantics of free choice permission as strong permission expressed in terms of a modal conditional in a nonmonotonic logic.

In this paper, I examine the syntax-semantics of subjunctive clauses in (Modern) Greek. These clauses are headed by the particle na and contain a dependent verbal form with no formal mood features: the perfective nonpast (PNP). I propose that the semantics of na is temporal: it introduces the variable now (n) into the syntax. This is necessary because the apparent present tense in the PNP cannot introduce n. The PNP, instead, contains a dependent time variable. This variable cannot be interpreted as a free variable – hence it cannot be identified with the utterance time of the context. This analysis relies on two premises. One is the (quite influential) idea that pronouns and tenses are analogous creatures (Partee 1973, 1984, Heim 1998, Kratzer 1998, and others). The other premise is that at least some polarity items are expressions that contain variables that cannot be interpreted deictically (Giannakidou 1998, 2001). In the present work I suggest to enlarge the domain of phenomena that can receive a unified treatment across individuals, worlds, and tenses, and treat the subjunctive mood as a non-deictic time, thus an instance of a polarity dependency of the temporal kind. It is my hope that the analysis proposed here for the PNP can be used to analyze verbal subjunctives in Romance languages, and perhaps also infinitival forms in English, but investigation of this question will have be left for the future.

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.

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.