Paper: Towards a Formal Distributional Semantics: Simulating Logical Calculi with Tensors

ACL ID S13-1001
Title Towards a Formal Distributional Semantics: Simulating Logical Calculi with Tensors
Venue Joint Conference on Lexical and Computational Semantics
Session
Year 2013
Authors

The development of compositional distribu- tional models of semantics reconciling the em- pirical aspects of distributional semantics with the compositional aspects of formal seman- tics is a popular topic in the contemporary lit- erature. This paper seeks to bring this rec- onciliation one step further by showing how the mathematical constructs commonly used in compositional distributional models, such as tensors and matrices, can be used to sim- ulate different aspects of predicate logic. This paper discusses how the canonical iso- morphism between tensors and multilinear maps can be exploited to simulate a full-blown quantifier-free predicate calculus using ten- sors. It provides tensor interpretations of the set of logical connectives required to model propositional calculi. It suggest...