We revisit a typological puzzle due to Horn (Doctoral Dissertation, UCLA, 1972) regarding the lexicalization of logical operators: in instantiations of the traditional square of opposition across categories and languages, the O corner, corresponding to ‘nand’ (= not and), ‘nevery’ (= not every), etc., is never lexicalized. We discuss Horn’s proposal, which involves the interaction of two economy conditions, one that relies on scalar implicatures and one that relies on markedness. We observe that in order to express markedness and to (...) account for a bigger typological puzzle, namely the absence of lexicalizations of ‘XOR’ (= exclusive or), ‘all-or-none’, and many other imaginable logical operators, one must restrict the basic lexicalizable elements to a small set of primitives. We suggest that an ordering based perspective, following Keenan and Faltz (Boolean semantics for natural language, 1985), makes the stipulated primitives that we arrive at more natural. We also propose a modification to Horn’s proposal, based on recent work on implicatures, in which only the implicature condition is operative and in which markedness is part of the definition of the alternatives for scalar implicatures rather than an independent condition. (shrink)

We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...) the lexicalized operators are all upward or downward monotone, an observation known as the Monotonicity Universal. We propose a logical explanation of lexical gaps and of the Monotonicity Universal, based on the dynamic behaviour of connectives and quantifiers. We define update potentials for logical operators as procedures to modify the context, under the assumption that an update by \( \phi \) depends on the logical form of \( \phi \) and on the speech act performed: assertion or rejection. We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language. Finally, we show that on this framework the Monotonicity Universal follows from the logical properties of the updates that correspond to each operator. (shrink)

Positive Polarity indefinites, such as some in English, are licensed in simplex negative sentences as long as they take wide scope over negation. When it surfaces under a clausemate negation, some can in principle take wide scope either by movement or by some semantic mechanism; e.g., it can take pseudoscope if it is interpreted as a choice function variable. Therefore, there is some uncertainty regarding the way in which PPI indefinites get licensed: can pseudoscope suffice? In this article we show, (...) using novel data from Hindi-Urdu and English, that pseudoscope is not sufficient, and that it is the syntactic position of PPI indefinites at LF, rather than their actual scope, which is relevant for licensing. These facts support a unified view of PPI indefinites as generalized quantifiers, and disfavor analyses where they are, or can be, interpreted as choice function variables. (shrink)

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)

Given current data, only a few binary Boolean operators are expressed in lexically simple fashion in the world's languages: and, or, nor. These do not occur in every combination, for example, nor is not observed by itself. To explain these cross‐linguistic patterns, we propose an encoding of Boolean operators as update procedures to accept or reject information in a context. We define a measure of conceptual simplicity for such updates, on which attested operators are conceptually simpler than the remaining Booleans. (...) Moreover, we show that language evolution selects for the attested lexical inventories by minimizing the complexity of using a lexical inventory compositionally to convey precise information. (shrink)

It is well known that the interpretation of quantificational expressions in the comparative clause poses a serious challenge for semantic analyses of the English comparative. In this paper, we develop a new analysis of the comparative clause designed to meet this challenge, in which a silent occurrence of the negative degree quantifier no interacts with other quantificational expressions to derive the observed range of interpretations. Although our analysis incorporates ideas from previous analyses, we show that it is able to account (...) for a broader range of facts than other approaches, with a minimum of construction-specific stipulations. We demonstrate that the analysis can be embedded within a general syntactic and semantic architecture for the comparative, and although our analysis focuses on the English data, we give evidence of its potential for crosslinguistic application. We conclude with a discussion of the implications of our approach for the analysis of “split-scope” phenomena in nominal quantification. (shrink)

The goal of this paper is to propose a unified approach to the split scope readings of negative indefinites, comparative quantifiers, and numerals. There are two main observations that justify this approach. First, split scope shows the same kinds of restrictions across these different quantifiers. Second, split scope always involves low existential force. In our approach, following Sauerland, natural language determiner quantifiers are quantifiers over choice functions, of type <<,t>,t>. In split readings, the quantifier over choice functions scopes above other (...) operators (such as intensional verbs like must or can). Determiner quantifiers leave a choice-function trace when they move and this trace combines with the noun restriction, which is interpreted low. That split scope always involves low existential force is derived, without stipulation, from Kratzer’s idea that low existential force can be achieved via binding (into the noun restriction). (shrink)

We discuss presupposition, the phenomenon whereby speakers mark linguistically the information that is presupposed or taken for granted, rather than being part of the main propositional content of a speech act. Expressions and constructions carrying presuppositions are called “presupposition triggers”, forming a large class including definites and factive verbs. The article first introduces the range of triggers, the basic properties of presuppositions such as projection and cancellability, and the diagnostic tests used to identify them. The reader is then introducedto major (...) models of presupposition from the last 50 years, separated into three classes: Frege-Strawson derived semantic models, pragmaticmodels such as that offered by Stalnaker, and dynamic models. Finallywe discuss some of the main current issues in presupposition theory. These involve accommodation, which occurs when a hearer's knowledge state is adjusted to meet the speaker's presuppositions; presupposition failure, which occurs when a presupposition is false; the interaction between presuppositions and attitudes; and the triggering problem, i.e., the problem of explaining why presuppositions occur in the first place. (shrink)

This paper is about conjunctions and disjunctions in the scope of non-doxastic atti- tude verbs. These constructions generate a certain type of ignorance implicature. I argue that the best way to account for these implicatures is by appealing to a notion of contex- tual redundancy (Schlenker, 2008; Fox, 2008; Mayr and Romoli, 2016). This pragmatic approach to ignorance implicatures is contrasted with a semantic account of disjunctions under `wonder' that appeals to exhausti cation (Roelofsen and Uegaki, 2016). I argue that (...) exhausti cation-based theories cannot handle embedded conjunctions, so a pragmatic account of ignorance implicatures is superior. (shrink)