A modal aleatoric calculus for probabilistic reasoning: extended version

TL;DR

This paper introduces a new probabilistic modal logic framework for multi-agent systems where agents' actions and beliefs are inherently stochastic, extending modal logic with novel syntax, semantics, and proof calculi.

Contribution

It develops a novel syntax and semantics for a probabilistic modal logic, generalizing modal logic, with sound and complete proof systems for reasoning about stochastic multi-agent systems.

Findings

Presented a new syntax and semantics for probabilistic modal logic.

Established sound and complete calculus for base semantics.

Discussed applications to reasoning about game-playing agents.

Abstract

We consider multi-agent systems where agents actions and beliefs are determined aleatorically, or "by the throw of dice". This system consists of possible worlds that assign distributions to independent random variables, and agents who assign probabilities to these possible worlds. We present a novel syntax and semantics for such system, and show that they generalise Modal Logic. We also give a sound and complete calculus for reasoning in the base semantics, and a sound calculus for the full modal semantics, that we conjecture to be complete. Finally we discuss some application to reasoning about game playing agents.