The Projection Problem for Predicates of Taste

Utterances of simple sentences containing taste predicates (e.g. "delicious", "fun", "frightening") typically imply that the speaker has had a particular sort of first-hand experience with the object of predication. For example, an utterance of "The carrot cake is delicious" would typically imply that the speaker had actually tasted the cake in question, and is not, for example, merely basing her judgment on the testimony of others. According to one approach, this 'acquaintance inference' is essentially an implicature, one generated by the Maxim of Quality together with a certain principle concerning the epistemology of taste (Ninan 2014). We first discuss some problems for this approach, problems that arise in connection with disjunction and generalized quantifiers. Then, after stating a conjecture concerning which operators 'obviate' the acquaintance inference and which do not, we build on Anand and Korotkova 2018 and Willer and Kennedy Forthcoming by developing a theory that treats the acquaintance requirement as a presupposition, albeit one that can be obviated by certain operators.

SOME OBSERVATIONS ABOUT GENERALIZED QUANTIFIERS IN LOGICS OF IMPERFECT INFORMATION

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s definitions are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström’s quantifiers.

The Indefiniteness of Definiteness

This paper is about definiteness, and more specifically about the difficulties involved in getting clear on which noun phrases should be classified as definite, or more properly, which have uses which can be so classified. A number of possibilities are considered. First we consider some traditional proposals—those analyzing definiteness in terms of strength, uniqueness, or familiarity. Following that, three more recent proposals are presented, which have been put forward in the wake of Montague’s analysis of NPs as generalized quantifiers—those proposed by Jon Barwise and Robin Cooper (1981), Barbara Partee (1986), and Sebastian Löbner (2000). The tentative conclusion is that Russell’s uniqueness characteristic (suitably modified) holds up well against the others.

Coercion in Languages in Flux

The classical view of semantics that we inherited from Montague is that natural languages are formal languages where semantics specifies the interpretations which can be associated with expressions of the language. In this context coercion might be seen as a slight but formally specifiable disturbance in the formal semantics which shows how the canonical interpretation of an expression can be modified by its linguistic context. In recent years an alternative to the formal language view of natural language has developed which sees the interpretation of language as a more local and dynamic process where the interpretation of expressions can be modified for the purposes of the utterance at hand. This presents linguistic semantics as a dynamic, somewhat chaotic, system constrained by the need to communicate. An interpretation of an expression will work in communication if it is close enough to other interpretations your interlocutor might be familiar with and there is enough evidence in the ambient context for her to approximate the interpretation you intended. On this view of language as a system in flux, coercion is not so much a disturbance in the semantic system but rather a regularization of available interpretations leading to a more predictable system. I will present some of the reasons why I favour the view of language in flux (but nevertheless think that the techniques we have learnt from formal semantics are important to preserve). I will look at some of the original examples of coercion discussed in the Pustejovskian generative lexicon and suggest that the possibilities for interpretation are broader than might be suggested by Pustejovsky’s original work. Finally, I will suggest that coercion can play a central role in compositional semantics taking two examples: (1) individual vs. frame-level properties and (2) dynamic generalized quantifiers and property coercion.

Quantifiers, generalized

Generalized quantifiers are logical tools with a wide range of uses. As the term indicates, they generalize the ordinary universal and existential quantifiers from first-order logic, ‘∀x’ and ‘∃x’, which apply to a formula A(x), binding its free occurrences of x. ∀xA(x) says that A(x) holds for all objects in the universe and ∃xA(x) says that A(x) holds for some objects in the universe, that is, in each case, that a certain condition on A(x) is satisfied. It is natural then to consider other conditions, such as ‘for at least five’, ‘at most ten’, ‘infinitely many’ and ‘most’. So a quantifier Q stands for a condition on A(x), or, more precisely, for a property of the set denoted by that formula, such as the property of being non-empty, being infinite, or containing more than half of the elements of the universe. The addition of such quantifiers to a logical language may increase its expressive power. A further generalization allows Q to apply to more than one formula, so that, for example, Qx(A(x),B(x)) states that a relation holds between the sets denoted by A(x) and B(x), say, the relation of having the same number of elements, or of having a non-empty intersection. One also considers quantifiers binding more than one variable in a formula. Qxy,zu(R(x,y),S(z,u)) could express, for example, that the relation (denoted by) R(x,y) contains twice as many pairs as S(z,u), or that R(x,y) and S(z,u) are isomorphic graphs. In general, then, a quantifier (the attribute ‘generalized’ is often dropped) is syntactically a variable-binding operator, which stands semantically for a relation between relations (on individuals), that is, a second-order relation. Quantifiers are studied in mathematical logic, and have also been applied in other areas, notably in the semantics of natural languages. This entry first presents some of the main logical facts about generalized quantifiers, and then explains their application to semantics.

Descriptive Complexity of Probabilistic Complexity Classes through Second Order Generalized Quantifiers

Complexidade Descritiva lida com a relação entre definibilidade lógica e complexidade computational em estruturas finitas. Como exemplo no caso de classes de complexidade probabilísticas, temos que BPP é equivalente à classe de problemas definíveis por uma versão randômica da lógica de ponto-fixo infracionário com contagem BPIFP(C). Neste artigo, nós mostramos que podemos definir lógicas com quantificadores generalizados de segunda ordem equivalentes à classes de complexidade probabilísticas. Estes quantificadores são usados para simular o comportamento de máquinas de Turing probabilísticas.