Extending and Automating Basic Probability Theory with Propositional Computability Logic

TL;DR

This paper introduces a novel probability theory based on propositional computability logic, enabling automation of uncertainty reasoning by leveraging the logic's event/game framework, and explores its foundational properties and isomorphisms.

Contribution

It extends classical probability theory with propositional computability logic, providing a new formalism that facilitates automated reasoning about uncertainty.

Findings

Establishes basic properties of the new probability theory.

Identifies an isomorphism between set operations and computability logic operations.

Demonstrates potential for automating uncertainty reasoning.

Abstract

Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which is central to probability theory. The probability theory based on CoL is therefore useful for {\it automating} uncertainty reasoning. We describe some basic properties of this new probability theory. We also discuss a novel isomorphism between the set operations and computability logic operations.