Logic, Probability and Action: A Situation Calculus Perspective

TL;DR

This paper surveys recent advances in integrating logic, probability, and actions within the situation calculus, aiming to develop a general-purpose language for reasoning about uncertain, dynamic environments in AI and robotics.

Contribution

It reviews recent results on the integration of logic, probability, and actions in the situation calculus and explores reduction theorems and programming interfaces for this formalism.

Findings

Reduction theorems facilitate reasoning in probabilistic situation calculus.

Programming interfaces enable practical implementation of the formalism.

Results are applicable to various probabilistic relational models.

Abstract

The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and probability allows us to further quantify the weight and ratio of the worlds that must satisfy a property. To that end, numerous developments have been undertaken, culminating in proposals such as probabilistic relational models. While this progress has been notable, a general-purpose first-order knowledge representation language to reason about probabilities and dynamics, including in continuous settings, is still to emerge. In this paper, we survey recent results pertaining to the integration of logic, probability and actions in the situation calculus, which is arguably one of the oldest and most well-known formalisms. We then explore reduction theorems and programming interfaces for the language. These results are motivated in the context of cognitive robotics (as envisioned by Reiter and his colleagues) for the sake of concreteness. Overall, the advantage of proving results for such a general language is that it becomes possible to adapt them to any special-purpose fragment, including but not limited to popular probabilistic relational models.