Logic, Probability and Action: A Situation Calculus Perspective

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

An Answer Set Programming-based Implementation of Epistemic Probabilistic Event Calculus

We describe a general procedure for translating Epistemic Probabilistic Event Calculus (EPEC) action language domains into Answer Set Programs (ASP), and show how the Python-driven features of the ASP solver Clingo can be used to provide efficient computation in this probabilistic setting. EPEC supports probabilistic, epistemic reasoning in domains containing narratives that include both an agent’s own action executions and environmentally triggered events. Some of the agent’s actions may be belief-conditioned, and some may be imperfect sensing actions that alter the strengths of previously held beliefs. We show that our ASP implementation can be used to provide query answers that fully correspond to EPEC’s own declarative, Bayesian-inspired semantics