This article offers a unified theory of the licensing of Negative and Positive Polarity Items, focusing on the acceptability conditions of PPIs of the some-type, and NPIs of the any-type. It argues that licensing has both a syntactic and a semantic component. On the syntactic side, the acceptability of PIs is checked in constituents; in fact, for any given PI, only some constituents, referred to as `domains', are eligible for the evaluation of that PI. The semantic dimension of licensing consists (...) in the sensitivity of PIs to the monotonicity properties of the syntactic environments they find themselves in. Two pieces of evidence support the semantic dimension of what I call the ‘environment-based’ approach defended here: PIs are subject to flip-flop and certain inferences affect their acceptability by modifying the monotonicity of their environment. A third property, called ‘entanglement’ and so far unnoticed, is described: the acceptability of PIs depends on the acceptability of other PIs in the same syntactic environment. The latter property is exploited to determine what semantic property some is sensitive to: it turns out that, contrary to the consensus among researchers, some is acceptable in the complement of the set of environments in which any is acceptable, and vice versa. (shrink)

The superlative quantifiers, at least and at most, are commonly assumed to have the same truth-conditions as the comparative quantifiers more than and fewer than. However, as Geurts & Nouwen have demonstrated, this is wrong, and several theories have been proposed to account for them. In this paper we propose that superlative quantifiers are illocutionary operators; specifically, they modify meta-speech acts.Meta speech-acts are operators that do not express a speech act, but a willingness to make or refrain from making a (...) certain speech act. The classic example is speech act denegation, e.g. I don't promise to come, where the speaker is explicitly refraining from performing the speech act of promising What denegations do is to delimit the future development of conversation, that is, they delimit future admissible speech acts. Hence we call them meta-speech acts. They are not moves in a game, but rather commitments to behave in certain ways in the future. We formalize the notion of meta speech acts as commitment development spaces, which are rooted graphs: The root of the graph describes the commitment development up to the current point in conversation; the continuations from the root describe the admissible future directions.We define and formalize the meta-speech act GRANT, which indicates that the speaker, while not necessarily subscribing to a proposition, refrains from asserting its negation. We propose that superlative quantifiers are quantifiers over GRANTs. Thus, Mary petted at least three rabbits means that the minimal number n such that the speaker GRANTs that Mary petted n rabbits is n = 3. In other words, the speaker denies that Mary petted two, one, or no rabbits, but GRANTs that she petted more.We formalize this interpretation of superlative quantifiers in terms of commitment development spaces, and show how the truth conditions that are derived from it are partly entailed and partly conversationally implicated. We demonstrates how the theory accounts for a wide variety of phenomena regarding the interpretation of superlative quantifiers, their distribution, and the contexts in which they can be embedded. (shrink)

Recent research has shown that the superlative quantifiers at least and at most do not have the same type of truth conditions as the comparative quantifiers more than and fewer than. We propose that superlative quantifiers are interpreted at the level of speech acts. We relate them to denegations of speech acts, as in I don’t promise to come, which we analyze as excluding the speech act of a promise to come. Calling such conversational acts that affect future permissible speech (...) acts “meta-speech acts,” we introduce the meta-speech act of a GRANT of a proposition as a denial to assert the negation of that proposition. Superlative quantifiers are analyzed as quantifiers over GRANTS. Thus, John petted at least three rabbits means that the minimal number n such that the speaker GRANTs the proposition that John petted n rabbits is n = 3. We formalize this interpretation in terms of commitment states and commitment spaces, and show how the truth conditions that are derived from it are partly entailed and partly conversationally implicated. We demonstrate how the theory accounts for a wide variety of distributional phenomena of superlative quantifiers, including the contexts in which they can be embedded. (shrink)

This dissertation investigates the ways in which natural language restricts the domains of quantifiers. Adverbs of quantification are analyzed as quantifying over situations. The domain of quantifiers is pragmatically constrained: apparent processes of "semantic partition" are treated as pragmatic epiphenomena. The introductory Chapter 1 sketches some of the background of work on natural language quantification and begins the analysis of adverbial quantification over situations. Chapter 2 develops the central picture of "semantic partition" as a side-effect of pragmatic processes of anaphora (...) resolution. I argue that the apparent effects of topic/focus articulation and presuppositional information on the interpretation of quantifiers are not the result of a direct and local mechanism of sentence grammar. Instead, I develop an analysis where the link is established via the anaphoric dependence of quantifier domains on the discourse context. Chapter 3 discusses the analysis of conditional clauses as quantifier restrictors, concentrating on the question whether conditional clauses restrict quantifiers directly or indirectly. A treatment is explored which has if-clauses constrain the value of the hidden domain variable of the restricted quantifier. Chapter 4, on unless-clauses, and Chapter 5, on only if- and even if-clauses, present some issues in the compositional analysis of complex conditional clauses. These chapters significantly expand the data coverage of the theory of A-quantification. Building on previous work of mine on exceptives, I analyze unless-clauses as exceptive operators on A-quantifiers. The analysis of only if-clauses, treated as conditional clauses that combine if with the focus adverb only, unearthes some interesting new properties. Chapter 6, finally, examines the phenomenon of donkey-anaphora in the light of the results of the previous chapters. I show that a solution to the proportion problem may become possible once we combine the situation-semantic approach to adverbial quantification with the pragmatic theory developed in Chapter 2 and further elaborated in the analysis of donkey anaphora in complex conditionals. (shrink)

Positive polarity items (PPIs) are generally thought to have the boring property that they cannot scope below negation. The starting point of the paper is the observation that their distribution is significantly more complex; specifically, someone/something-type PPIs share properties with negative polarity items (NPIs). First, these PPIs are disallowed in the same environments that license yet type NPIs; second, adding any NPI-licenser rescues the illegitimate constellation. This leads to the conclusion that these PPIs have the combined properties of yet-type and (...) ever-type NPIs: what appears to be a prohibition is nothing but “halfway licensing”. The paper goes on to propose a unification of the analyses of rescuable PPIs, NPIs, and negative concord, and questions the grounding of polarity sensitivity in the scalar or the referential semantics of the items involved. (shrink)