Stable and Supported Semantics in Continuous Vector Spaces

2020 ◽  
Author(s):  
Yaniv Aspis ◽  
Krysia Broda ◽  
Alessandra Russo ◽  
Jorge Lobo
Keyword(s):  
Logic Program ◽  
Matrix Multiplication ◽  
Vector Spaces ◽  
Continuous Space ◽  
Continuous Vector ◽  
Novel Approach ◽  
Gradient Based ◽  
Normal Logic ◽  
Parameter Values ◽  
Normal Logic Program

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.

Modular Matrix Multiplication on a Linear Array.

1983 ◽  
Author(s):  
I. V. Ramakrishnan ◽  
P. J. Varman
Keyword(s):  
Linear Array ◽  
Matrix Multiplication

Min-Plus Matrix Multiplication: 10834

2002 ◽  
Vol 109 (8) ◽  
pp. 763
Author(s):  
Sung Soo Kim ◽  
Richard Johnsonbaugh ◽  
Ronald E. Prather ◽  
Donald Knuth
Keyword(s):  
Matrix Multiplication
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