From Probabilistic Programming to Complexity-based Programming

TL;DR

This paper introduces CompLog, a novel computational framework inspired by probabilistic programming and Simplicity Theory, which uses Kolmogorov complexities for inference instead of probabilities, enabling new measures of unexpectedness.

Contribution

CompLog is a new system that replaces probabilistic inference with complexity-based measures, offering a different approach to modeling and reasoning about uncertainty.

Findings

Enables computation of ex-post and ex-ante unexpectedness measures

Uses Kolmogorov complexities via ASP programs for inference

Provides examples of generating descriptions and handling disjunction and negation

Abstract

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms proposed by Simplicity Theory, relying on the computation of two Kolmogorov complexities (here implemented as min-path searches via ASP programs) rather than probabilistic inference. The proposed system enables users to compute ex-post and ex-ante measures of unexpectedness of a certain situation, mapping respectively to posterior and prior subjective probabilities. The computation is based on the specification of world and mental models by means of causal and descriptive relations between predicates weighted by complexity. The paper illustrates a few examples of application: generating relevant descriptions, and providing alternative approaches to disjunction and to negation.