The logic of reflexivity and reciprocity

A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And as a result, inferences such as 'Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle' are shown to be first-order.

1991

Natural Language Semantics, 1993

This paper begins with a discussion of CUMULATIVITY (e.g., 'P(a) & P(b) implies P(a+b)'), formalized using a verb phrase operator. Next, the meanings of distributivity markers such as each and non-distributivity indicators such as together are considered. An existing analysis of each in terms of quantification over parts of a plurality is adopted. However, together is problematic, for it involves a cancellation or negation of the quantification associated with each. (The four boys together owned exactly three cars could not be true if each of the boys owned three cars, though the same sentence without together could be.) A refinement of this idea of negated quantification over parts is proposed as an analysis for non-distributivity operators. It is then worked out in the system described in Cooper (1983), in which positive and negative extensions are assigned. Presuppositions connected with plural reference are considered at this point as well. Finally, the cumulativity operator is argued to be quantificational and therefore sensitive to contextual domain selection. This context sensitivity is claimed to be the source of distributive readings that appear in the absence of modifiers like each and non-distributive or collective readings that arise without together.

2002

The Chimwi:ni reflexive construction has thus far resisted a satisfactory analysis. In this paper I will argue that it should be analyzed as involving a complex predicate and that the reflexive phrase should not be taken to be a syntactic anaphor, as has been standard, but a part of the predicate. I start out by providing a definition of complex predicate and showing the position that the Chimwi:ni reflexive construction occupies in a classification of complex predicates. In section 2, I describe the salient properties of this construction and show the main difficulties that other analyses have had for accounting for them. In 3, I show that this construction shares many features with the Chicheŵa reciprocal construction and present the analysis of this construction in Alsina (1993, 2001). In 4, I extend this analysis to the Chimwi:ni reflexive construction showing how all of its properties are accounted for. And I conclude with the main points of the paper.

In his rich "The Truth Predicate vs. the Truth Connective. On taking connectives seriously."

Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal <i>for</i>-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial <i>for</i>-adverbials, habituals, and the quantifier <i>all</i>.

1998

This paper investigates different readings of plural and reciprocal sentences and how they can be derived from syntactic surface structures in a systematic way. The main thesis is that these readings result from different ways of inserting logical operators at the level of Logical Form. The basic operator considered here is a cumulative mapping from predicates that apply to singularities onto the corresponding predicates that apply to pluralities. Given a theory which allows for free insertion of such operators, it can then be shown that the lexical semantics of the reciprocal expressions each other/one another consists of exactly two components, namely an anaphoric variable and a non-identity statement. This receives further support from the observation that it is exactly these two components that can be focused by only; all that remains to be done is to correctly manipulate these components at the level of LF.

Linguistic Typology, 2011

2009