Predicate-Induced Permutation Groups

Natural languages abound in combinatorial phenomena that are related to the predicate of the sentence and its ability to permute noun phrase arguments. After compiling several illustrative phenomena of natural languages, I propose a novel analysis in terms of permutation groups, a concept borrowed from mathematical combinatorics that is ubiquitous in applied sciences. I show that each natural language predicate of degree n (n natural number) can be associated with two permutation groups of degree n. The first group measures the predicate’s flexibility to permute arguments in two independent events, whereas the second group captures permutations in two dependent events. These groups serve as linguistic tools to help predict the predicate’s grammaticality pattern in a range of natural language constructions.