Stable and supported semantics in continuous vector spaces
File(s)
Supporting information
Author(s)
Aspis, Y
Broda, K
Russo, A
Lobo, J
Type
Conference Paper
Abstract
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 R and program reducts are represented as matrices in ℝ . 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. N N×N
Date Issued
2020-09-12
Date Acceptance
2020-09-01
Citation
17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020, 2020, 1, pp.58-67
ISBN
9781713825982
Publisher
https://proceedings.kr.org/2020/7/
Start Page
58
End Page
67
Journal / Book Title
17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020
Volume
1
Copyright Statement
© 2020 International Joint Conferences on Artificial Intelligence Organization
Sponsor
IBM United Kingdom Ltd
Identifier
https://proceedings.kr.org/2020/7/
Grant Number
PO 4603 458 249
Source
17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020
Publication Status
Published
Start Date
2020-09-12
Finish Date
2020-09-18
Coverage Spatial
Rhodes, Greece
Date Publish Online
2020-09-12