Testing the Robustness of Laws of Polysemy and Brevity versus Frequency Antoni Hern´ andez-Fern´ andez 2 , Bernardino Casas 1 , Ramon Ferrer-i-Cancho 1 , and Jaume Baixeries 1 1 Complexity & Quantitative Linguistics Lab, Laboratory for Relational Algorithmics, Complexity and Learning (LARCA), Departament de Ci` encies de la Computaci´ o, Universitat Polit` ecnica de Catalunya, Barcelona, Catalonia. {bcasas, jbaixer, rf errericancho}@cs.upc.edu 2 Complexity & Quantitative Linguistics Lab, Laboratory for Relational Algorithmics, Complexity and Learning (LARCA), Institut de Ci` encies de l ′ Educaci´ o, Universitat Polit` ecnica de Catalunya, Barcelona, Catalonia. antonio.hernandez@upc.edu Corresponding author : antonio.hernandez@upc.edu Abstract. The pioneering research of G. K. Zipf on the relationship between word frequency and other word features led to the formula- tion of various linguistic laws. Here we focus on a couple of them: the meaning-frequency law, i.e. the tendency of more frequent words to be more polysemous, and the law of abbreviation, i.e. the tendency of more frequent words to be shorter. Here we evaluate the robustness of these laws in contexts where they have not been explored yet to our knowl- edge. The recovery of the laws again in new conditions provides support for the hypothesis that they originate from abstract mechanisms. Keywords: Zipf law, polysemy, brevity, word frequency. 1 Introduction The linguist George Kingsley Zipf (1902-1950) is known for his investigations on statistical laws of language [20, 21]. Perhaps the most popular one is Zipfs law for word frequencies [20], that states that the frequency of the i-th most frequent word in a text follows approximately f ∝ i -α (1) where f is the frequency of that word, i their rank or order and α is a constant (α ≈ 1). Zipfs law for word frequencies can be explained by information theoretic models of communication and is a robust pattern of language that presents invariance with text length [9] but dependency with respect to the linguistic units considered [5]. The focus of the current paper are a couple of linguistic laws that are perhaps less popular: – Meaning-frequency law [19], the tendency of more frequent words to be more polysemous