Major 2 Satisfiability Logic in Discrete Hopfield Neural Network

Abstract

Existing satisfiability (SAT) is composed of a systematic logical structure with definite literals in a set of clauses. The key problem of the existing SAT is the lack of interpretability of a logical structure that leads to low variability of the retrieved neuron states. Thus, a new non-systematic SAT with higher interpretability is needed to reduce the repetition of the patterns of the final neuron states. This paper presents Major 2 Satisfiability (MAJ2SAT) by emphasizing a ratio of 2 Satisfiability (2SAT) clauses present in non-systematic SAT. Hence, different compositions of MAJ2SAT are implemented in a Discrete Hopfield Neural Network (DHNN) by adopting an Exhaustive Search as a training algorithm. Various performance metrics are utilized to measure the compatibility and behaviour of MAJ2SAT in DHNN. Overall, the formulation of MAJ2SAT offers an alternative logical structure in the field of data mining that involves a more dynamic composition of literals and clauses.

KEYWORDS:

• Discrete Hopfield neural network
• Major 2 Satisfiability
• artificial neural network
• satisfiability logic
• symbolic integration

MSC SUBJECT CLASSIFICATIONS:

• 68T07
• 68R07

Acknowledgements

We would like to thank Nik Fathihah Abu Hassan for the technical help and writing assistance. This research was funded by Fundamental Research Grant Scheme (FRGS), Ministry of Education Malaysia grant number 203/PMATHS/6711804 and Universiti Sains Malaysia (USM).

Disclosure statement

No potential conflict of interest was reported by the author(s).