**Research Article**

# Relational domains and the interpretation of reciprocals

## Authors

- First online:

DOI: 10.1007/s10988-012-9117-x

## Abstract

We argue that a comprehensive theory of reciprocals must rely on a general taxonomy of restrictions on the interpretation of relational expressions. Developing such a taxonomy, we propose a new principle for interpreting reciprocals that relies on the interpretation of the relation in their scope. This principle, the Maximal Interpretation Hypothesis (MIH), analyzes reciprocals as partial polyadic quantifiers. According to the MIH, the partial quantifier denoted by a reciprocal requires the relational expression REL in its scope to denote a maximal relation in REL’s interpretation domain. In this way the MIH avoids a priori assumptions on the available readings of reciprocal expressions, which are necessary in previous accounts. Relying extensively on the work of Dalrymple et al. (Ling Philos 21:159–210, 1998), we show that the MIH also exhibits some observational improvements over Dalrymple et al.’s Strongest Meaning Hypothesis (SMH). In addition to deriving some attested reciprocal interpretations that are not expected by the SMH, the MIH offers a more restrictive account of the way context affects the interpretation of reciprocals through its influence on relational domains. Further, the MIH generates a reciprocal interpretation at the predicate level, which is argued to be advantageous to Dalrymple et al.’s propositional selection of reciprocal meanings. More generally, we argue that by focusing on restrictions on relational domains, the MIH opens the way for a more systematic study of the ways in which lexical meaning, world knowledge and contextual information interact with the interpretation of quantificational expressions.

### Keywords

Reciprocals Relational domains Quantifiers## Acknowledgments

This paper develops and extends some of the main ideas in Sabato and Winter (2005). The work of the authors was partially supported by an Israeli Science Foundation grant “Formal Semantics of the SMH” (2005/2006) to the second author. In addition, the work of the first author was partially supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities. The work of the second author was partially supported by two grants of the Netherlands Organisation for Scientific Research (NWO): “Reciprocal Expressions and Relational Processes in Language” (2007/2008) and a VICI grant number 277-80-002, “Between Logic and Common Sense: the formal semantics of words” (2010–2015). The first author is also grateful for financial help of Technion, Israel Institute of Technology, while working on her MSc thesis (Sabato 2006). For remarks and discussions, we are grateful to Lev Beklemishev, Arik Cohen, Mary Dalrymple, Nissim Francez, Alon Itai, Sophia Katrenko, Ed Keenan, Beth Levin, Alda Mari, Sam Mchombo, Stanley Peters, Galit Sassoon, Maria Spychalska, Assaf Toledo and Hanna de Vries, as well as to audiences at *Amsterdam Colloquium* (2005), *Mathematics of Language* (2005) and *Workshop on Logic, Language, Information and Computation* (2011), at the workshops on reciprocals (Utrecht and Berlin 2007), as well as at talks at Tel-Aviv University, Technion, Radboud University Nijmegen, New York University and UCLA. Special thanks to Martin Everaert, Na’ama Friedmann, Nir Kerem, Ya’acov Peterzil, Eva Poortman, Eric Reuland, Remko Scha, Marijn Struiksma and Joost Zwarts for extensive discussions in various stages of this work. We thank two anonymous L&P reviewers for their useful comments on a previous version. The illustrations in Fig. 5 were made by Ruth Noy Shapira.

### Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.