Explaining gaps in the logical lexicon of natural languages: A decision-theoretic perspective on the square of Aristotle

The Informativeness/Complexity Trade-Off in the Domain of Boolean Connectives

“…Overall, the current paper provides a proof of concept for an account of semantic universals in the domain of connectives based on the informativeness/complexity trade-off model. Along with similar recent studies in other domains of logical/functional vocabulary (Steinert-Threlkeld, 2019;Carcassi, 2020;Denić, Steinert-Threlkeld, and Szymanik, 2020;Enguehard and Spector, 2021), the current paper offers a promising prospect for the explanation of cross-linguistic universals in logical vocabularies within the trade-off model, motivating further research in the domain. Particularly interesting issues include empirical underpinnings of parameters affecting the model and the extent of their domain-specificity, as well as the model's compatibility with grammar-internal explanations of semantic universals (e.g., Romoli, 2015).…”

“…In contrast toEnguehard and Spector (2021), who fully integrate their analysis within (a version of) the Rational Speech Act model, my goal in the current paper is to show that a fairly conservative reformulation of existing accounts byHorn (1972) andKatzir and Singh (2013) employing the trade-off model provides a satisfactory account of the lexicalisation pattern in the domain of connectives. One major difference between my analysis andEnguehard and Spector (2021) is that my analysis crucially assumes that negation adds to the complexity of inventories while Enguehard and Spector do not rely on this assumption. At the same time, the scope of the analysis is also different.…”

“…2018) andEnguehard and Chemla (2021) have successfully extended a semantic constraints on content vocabularies-connectedness-to logical vocabularies/operations, i.e., quantifiers and exhaustification.2 While writing up the current paper, I was made aware of a closely related study byEnguehard and Spector (2021), who independently propose an account of the lexicalisation gap in the 'O-corner' in the square of opposition in the quantificational domain, based on the notion of informativeness/cost trade-off. In contrast toEnguehard and Spector (2021), who fully integrate their analysis within (a version of) the Rational Speech Act model, my goal in the current paper is to show that a fairly conservative reformulation of existing accounts byHorn (1972) andKatzir and Singh (2013) employing the trade-off model provides a satisfactory account of the lexicalisation pattern in the domain of connectives. One major difference between my analysis andEnguehard and Spector (2021) is that my analysis crucially assumes that negation adds to the complexity of inventories while Enguehard and Spector do not rely on this assumption.…”

Quantifiers in Natural Language: Efficient Communication and Degrees of Semantic Universals

“…On the one hand, the first experiment shows that the semantic typology of quantifiers, a functional part of the lexicon, can be explained by efficient communication. Building on Reference [26], this is the first of a growing number of results suggesting that the same pressures shape semantic systems in domains of function words in addition to content words, from indefinites [27] to logical connectives [28,29] to person systems [30]. More provocatively, the two experimental results, taken together, suggest that semantic universals may be epiphenomenal: while empirically true, they arise as a consequence of a fundamental pressure for efficient communication and do not themselves stand in need of independent explanation.…”

“…Since that pioneering work, similar analyses have been carried out for color terms [20,44], container terms [45], and numeral systems [46]. Starting with the precursor to the present paper, Reference [26], the framework has also been applied to several domains of function words, from indefinites [27] to logical connectives [28,29] to person systems [30]. These studies suggest that efficient communication shapes the structure of the semantic systems of the world's languages, across both content and function words.…”