KR2020Proceedings of the 17th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 12-18, 2020.

Edited by

ISSN: 2334-1033
ISBN: 978-0-9992411-7-2

Sponsored by
Published by

Copyright © 2020 International Joint Conferences on Artificial Intelligence Organization

Stable and Supported Semantics in Continuous Vector Spaces

  1. Yaniv Aspis(Imperial College London)
  2. Krysia Broda(Imperial College London)
  3. Alessandra Russo(Imperial College London)
  4. Jorge Lobo(Imperial College London, ICREA, Universitat Pompeu Fabra)


  1. Logic programming, answer set programming, constraint logic programming-General
  2. Nonmonotonic logics, default logics, conditional logics-General


We introduce a novel approach for the computation of stable and supported models of normal logic programs in continuous vector spaces by a gradient-based search method. Specifically, the application of the immediate consequence operator of a program reduct can be computed in a vector space. To do this, Herbrand interpretations of a propositional program are embedded as 0-1 vectors in $\mathbb{R}^N$ and program reducts are represented as matrices in $\mathbb{R}^{N \times N}$. Using these representations we prove that the underlying semantics of a normal logic program is captured through matrix multiplication and a differentiable operation. As supported and stable models of a normal logic program can now be seen as fixed points in a continuous space, non-monotonic deduction can be performed using an optimisation process such as Newton's method. We report the results of several experiments using synthetically generated programs that demonstrate the feasibility of the approach and highlight how different parameter values can affect the behaviour of the system.