Non-commutative Logic for Compositional Distributional Semantics

Distributional models of natural language use vectors to provide a contextual foundation for meaning representation. These models rely on large quantities of real data, such as corpora of documents, and have found applications in natural language tasks, such as word similarity, disambiguation, indexing, and search. Compositional distributional models extend the distributional ones from words to phrases and sentences. Logical operators are usually treated as noise by these models and no systematic treatment is provided so far. In this paper, we show how skew lattices and their encoding in upper triangular matrices provide a logical foundation for compositional distributional models. In this setting, one can model commutative as well as non-commutative logical operations of conjunction and disjunction. We provide theoretical foundations, a case study, and experimental results for an entailment task on real data.