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| "title": "Investigating information-theoretic properties of the typology of spatial demonstratives", |
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| "first": "Sihan", |
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| "last": "Chen", |
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| "email": "sihanc@mit.edu" |
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| "first": "Richard", |
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| "last": "Futrell", |
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| "email": "rfutrell@uci.edu" |
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| { |
| "first": "Kyle", |
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| "last": "Mahowald", |
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| "email": "mahowald@utexas.edu" |
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| "text": "Spatial deictic demonstratives (e.g., \"here\" and \"from there\") denote spatial relations between speaker(s) and referent(s) and play a crucial role in cognition and language processing (Levinson, 2006) . Languages vary in the complexity of their spatial demonstrative systems, both in the granularity of their distal levels (e.g. English has two distal levels \"here\" and \"there\", with an optional third distal level \"(over) there\", whereas Kaba has four) as well as in the extent of syncretism across their possible orientations: PLACE, GOAL, and SOURCE. English has syncretism between the place and goal demonstratives (\"I am there\", \"I am going there\") but distinguishes the source demonstratives (\"I am coming from there\" is not the same as \"I am coming there\", see Table 1 ), whereas Finnish has unique words for each orientation, at each distal level (Table 2) Using data from Nintemann et al. (2020), we explore the variability in complexity and informativity across spatial demonstrative systems using spatial deictic lexicons from 223 languages. We argue from an information-theoretic perspective (Shannon, 1948) that spatial deictic lexicons fall on an efficient frontier, balancing informativity and GOAL PLACE SOURCE D1 t\u00e4nne t\u00e4\u00e4ll\u00e4 t\u00e4\u00e4lt\u00e4 D2 sinne siell\u00e4 sielt\u00e4 D3 tuonne tuolla tuolta Tishby et al., 2000; Strouse and Schwab, 2017; Zaslavsky et al., 2018) , where a world state U (distal levels and orientations for a referent) is mentally represented by the speaker as meaning M , which is encoded with words W using a languagespecific encoder q(w | m) and then decoded by a Bayesian listener. To this end, informativity is defined as the mutual information between words and world states, and complexity is defined as the mutual information between mental representations of meaning and words. An efficient lexicon optimizes a tradeoff of these two factors (Eq. 1). The relationship between meaning and world states is determined by a cost function (Eq. 2) that defines a penalty for confusing distal levels and orientations. Broadly, this approach lets us ask: given a prior and a cost function, if a language has n spatial adverb wordforms, how should those n wordforms be distributed across m slots in the paradigm? We predict that attested systems are more efficient than the logically possible paradigms that are rare or unattested in world languages.", |
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| "text": "(Shannon, 1948)", |
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| "text": "Tishby et al., 2000;", |
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| "text": "Strouse and Schwab, 2017;", |
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| "text": "Zaslavsky et al., 2018)", |
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| "raw_str": "J IB [q] = I[M : W ] Complexity \u2212\u03b2 \u2022 I[W : U ] Informativity (1) p(u | m) \u221d \u00b5 C rr \u2032 +C \u03b8\u03b8 \u2032", |
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| "text": "We make three main contributions. First, we find that among all the 21,146 theoretically possible lexicons, real lexicons lie near the efficient frontier (Fig. 1) for appropriate choice of cost function and prior \"need probability\" over meanings (Regier et al., 2015) , thus adding deictic adverbs to the growing list of lexical semantic domains whose form can be explained in terms of informationtheoretic efficiency (e.g. Zaslavsky et al., 2018 Mollica et al., 2021; Kemp and Regier, 2012; Zaslavsky et al., 2019; Deni\u0107 et al., 2021) . Second, Figure 1 : Each colored point represents a real lexicon, with the horizontal axis denoting the complexity and the vertical axis denoting the informativity. The gray points represent simulated lexicons. The real lexicons fall along an efficient frontier (minimizing Eq. 1 for some choice of tradeoff parameter \u03b2). The points are jittered to avoid overlap.The parameters here are as follows: \u00b5 = 0.3, C P S =1.3, and C P G = 0.8.", |
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| "text": "Zaslavsky et al., 2018", |
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| "text": "Mollica et al., 2021;", |
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| "text": "Kemp and Regier, 2012;", |
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| "text": "Zaslavsky et al., 2019;", |
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| "text": "Deni\u0107 et al., 2021)", |
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| "text": "(Fig. 1)", |
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| "text": "we investigate the minimal properties that the cost function and prior must have such that actual lexicons lie on the efficient frontier, finding that the key properties are (1) the cost for confusing GOAL and SOURCE is higher than that for confusing PLACE with SOURCE, which is then higher than that for confusing PLACE and GOAL, and (2) the SOURCE orientation has the least prior probability. Both of these properties are plausible for this semantic domain and consistent with prior observations in the cognitive science literature, specifically regarding asymmetries between the source and goal orientations (Papafragou, 2006 (Papafragou, , 2010 Nikitina, 2009) . Third, we find that the IB approach does not fully capture the patterns in human lexicons, as there are theoretically efficient lexicons that are unattested. We then introduce the notion of systematicity, which means that the pattern of distinctions should be consistent across distal levels and orientations. We show that real lexicons are systematic in addition to balancing between informativity and complexity.", |
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| "text": "In addition to being explanatory for the typology of spatial demonstratives, we believe these methodological innovations could be fruitfully applied to information-theoretic analyses in other typological domains.", |
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