Predicate-Induced Permutation Groups
Matthias Gerner · Journal of Semantics · 2011
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. COMBINATORICS IN LINGUISTICS: A REVIEWIn philosophy and linguistics, combinatorial tools have been discussed previously, notably the concepts of reflexivity, symmetry and transitivity, which are the ingredients of equivalence relations.Scholars were mainly interested in philosophical and cognitive accounts of the concepts of equality, identity, similarity and so on.Quine (1969: 114-38) and Sovran (1992: 329) remarked, for example, that the notion of similarity notoriously resists any formal characterization as it fails to be transitive and thus to be an equivalence relation.Several scholars also introduced the combinatorial notion of permutation to linguistics-in the context of generalized quantifier theory.On the following two pages, I illustrate this use of permutation and explain how it differs from the use made in this article.Barwise & Cooper (1981) pioneered the view of noun phrases and noun determiners as quantifiers, called generalized quantifiers.Using typetheoretic notations (and replacing the Montagovian symbol 'e' for 'entity' by '1'), we can distinguish three types of generalized quantifiers:(i) quantifiers are full noun phrases like John, these students, all teachers;