Logic + probabilistic programming + causal laws

Abstract

Probabilistic planning attempts to incorporate stochastic models directly into the planning process, which is the problem of synthesizing a sequence of actions that achieves some objective for a putative agent. Probabilistic programming has rapidly emerged as a key paradigm to integrate probabilistic concepts with programming languages, which allows one to specify complex probabilistic models using programming primitives like recursion and loops. Probabilistic logic programming aims to further ease the specification of structured probability distributions using first-order logical artefacts. In this article, we briefly discuss the modelling of probabilistic planning through the lens of probabilistic (logic) programming. Although many flavours for such an integration are possible, we focus on two representative examples. The first is an extension to the popular probabilistic logic programming language PROBLOG, which permits the decoration of probabilities on Horn clauses-that is, prolog programs. The second is an extension to the popular agent programming language GOLOG, which permits the logical specification of dynamical systems via actions, effects and observations. The probabilistic extensions thereof emphasize different strengths of probabilistic programming that are particularly useful for non-trivial modelling issues raised in probabilistic planning. Among other things, one can instantiate planning problems with growing and shrinking state spaces, discrete and continuous probability distributions, and non-unique prior distributions in a first-order setting.

Keywords: first-order logic; probabilistic programming; statistical relational learning.