Technical Report MSC-2006-05

Title: The Semantics of Reciprocal Expressions in Natural Language
Authors: Sivan Sabato
Supervisors: Yoad Winter
Abstract: The interpretation of reciprocal expressions such as each other and one another exhibits a remarkably wide variation in different contexts. Specifically, the predicate in the scope of the reciprocal expression affects its interpretation. Consider the following examples of two minimally different sentences with reciprocal expressions:

1. Dan, John and Mary saw each other 2. Dan, John and Mary followed each other.

Sentence (1) entails that every person in the specified group saw every other person in the group, while sentence (2) does not entail the analogous claim, that each person followed each of the others. This contrast exemplifies two possibilities for the truth conditions of sentences with reciprocal sentences, out of many more that have been identified in the literature.

We propose a new formal system for predicting the interpretation of reciprocal expressions in a given context. This system is based on a principle called the Strongest Meaning Hypothesis (SMH) that was proposed in Dalrymple et. al (1998) (henceforth DKKMP) to account for the effect of contextual factors on the truth conditions of different reciprocal sentences. The SMH as formulated on DKKMP chooses the strongest meaning that is consistent with relevant contextual information, out of an independently defined set of meanings for reciprocals.

The system proposed by DKKMP is thus composed of two components: One is the SMH, and the other is the set of meanings the SMH chooses from. The new system we propose is based on the critical observation made in DKKMP about the weakening of the interpretation of a reciprocal sentence by contextual factors. However, unlike DKKMP, we implement the SMH as a mapping from semantic restrictions on the predicate's denotation into the interpretation of the reciprocal, with no independent assumptions about available reciprocal meanings. This new implementation also defines the loose notion of `relevant contextual information' used by DKKMP, and identifies this information solely with a formal concept of semantic restrictions of predicates.

We implement the SMH as a local maximality principle. According to this principle, a reciprocal sentence is consistent with models in which no pairs of non-identical individuals in the antecedent set can be added to the denotation of the predicate, while remaining within its semantic restriction. Our formulation of the SMH allows a systematic analysis of types of predicates and the truth conditions they induce on reciprocal sentences that contain them.

We analyze the connection between semantic restrictions, interpretations of reciprocal sentences, and several meanings that are proposed in the literature for reciprocal sentences. We show that in our system, the reciprocal meanings Weak Reciprocity (WR) (Langendoen, 1978) and Inclusive Alternative Ordering (IAO) (Kanski, 1987) cannot be derived as the strongest meanings of any reciprocal sentence.

We also show that the meaning derived by the SMH for a reciprocal sentence should have a lower bound that prevents unlimited weakening of the truth conditions of a simple reciprocal sentence. We argue that `partitioned' interpretations of reciprocal sentences are always due to partitioning that is independent of the semantics of the reciprocal.

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