A Smooth Transition Between Induction and Deduction: Fast Abductive Learning Based on Probabilistic Symbol Perception

TL;DR

This paper introduces Probabilistic Symbol Perception (PSP), an optimization algorithm that enables a smooth transition between induction and deduction in abductive learning, reducing computational costs while maintaining correctness.

Contribution

The paper proposes a novel PSP algorithm that improves abductive learning efficiency by better utilizing prediction, symbol relationships, and experience, with a new data structure for low-complexity transfer.

Findings

PSP achieves lower computational complexity in abductive learning.

Experiments show promising results in efficiency and accuracy.

The method maintains correctness while optimizing the induction-deduction transition.

Abstract

Abductive learning (ABL) that integrates strengths of machine learning and logical reasoning to improve the learning generalization, has been recently shown effective. However, its efficiency is affected by the transition between numerical induction and symbolical deduction, leading to high computational costs in the worst-case scenario. Efforts on this issue remain to be limited. In this paper, we identified three reasons why previous optimization algorithms for ABL were not effective: insufficient utilization of prediction, symbol relationships, and accumulated experience in successful abductive processes, resulting in redundant calculations to the knowledge base. To address these challenges, we introduce an optimization algorithm named as Probabilistic Symbol Perception (PSP), which makes a smooth transition between induction and deduction and keeps the correctness of ABL unchanged. We leverage probability as a bridge and present an efficient data structure, achieving the transfer from a continuous probability sequence to discrete Boolean sequences with low computational complexity. Experiments demonstrate the promising results.