Differentiable Meta-Logical Programming

Zihan Ye, Hikaru Shindo, Devendra Singh Dhami, Kristian Kersting

Keywords: meta interpreter, differentiable forward chaining inference, first order logic

TL;DR: We realize a differentiable logical meta interpreter (DLMI) using differentiable forward-chaining reasoning in first-order logic.

Abstract:

Deep learning uses an increasing amount of computation and data to solve very specific problems. By stark contrast,
human minds solve a wide range of problems using a fixed amount of computation and limited experience. One
ability that seems crucial to this kind of general intelligence is meta-reasoning, i.e., our ability to reason about reasoning. To make deep learning do more from less, we propose the differentiable logical meta interpreter (DLMI). The key idea is to realize a meta-interpreter using differentiable forward-chaining reasoning in first-order logic. This directly allows DLMI to reason and even learn about its own operations. This is different from performing object-level deep reasoning and learning, which refers in some way to entities external to the system. In contrast, DLMI is able to reflect or introspect, i.e., to shift from meta-reasoning to object-level reasoning and vice versa. Among many other experimental evaluations, we illustrate this behavior using the novel task of "repairing Kandinsky patterns", i.e., how to edit the objects in an image so that it agrees with a given logical concept.

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