Towards a Model Theory for Distributed Representations
This work addresses a foundational challenge in AI for integrating symbolic and subsymbolic reasoning, but it appears incremental as it explores one possible approach without broad empirical validation.
The paper tackles the problem of combining distributed and discrete representations by developing a model theory for first-order logic based on real-valued vectors, presenting its properties and a simple query-answering approach.
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We present a model theory/semantics for first order logic based on vectors of reals. We describe the model theory, discuss some interesting properties of such a system and present a simple approach to query answering.