Semantics of the Barwise sentence: insights from expressiveness, complexity and inference

Abstract

In this paper, we study natural language constructions which were first examined by Barwise: The richer the country, the more powerful some of its officials. Guided by Barwise's observations, we suggest that conceivable interpretations of such constructions express the existence of various similarities between partial orders such as homomorphism or embedding (strong readings). Semantically, we interpret the constructions as polyadic generalized quantifiers restricted to finite models (similarity quantifiers). We extend the results obtained by Barwise by showing that similarity quantifiers are not expressible in elementary logic over finite models. We also investigate whether the proposed readings are sound from the cognitive perspective. We prove that almost all similarity quantifiers are intractable. This leads us to first-order variants (weak readings), which only approximate the strong readings, but are cognitively more plausible. Driven by the question of ambiguity, we recall Barwise's argumentation in favour of strong readings, enriching it with some arguments of our own. Given that Barwise-like sentences are indeed ambiguous, we use a generalized Strong Meaning Hypothesis to derive predictions for their verification. Finally, we propose a hypothesis according to which conflicting pressures of communication and cognition might give rise to an ambiguous construction, provided that different semantic variants of the construction withstand different pressures involved in its usage.

Interactive Semantic Alignment Model: Social Influence and Local Transmission Bottleneck

“…Hence, the two pressures are likely to compromise each other in language learning, use and semantic alignment. The question is whether this trade-off might have some deeper bearing on language (see, for example, Kalociński and Godziszewski 2018).…”