# A First-Order Logic for Reasoning about Knowledge and Probability

## TL;DR

This paper introduces a first-order probabilistic epistemic logic that integrates knowledge and probability operators for multiple agents, extending prior propositional frameworks with formal semantics and completeness proofs.

## Contribution

It develops the first-order extension of Fagin and Halpern's logic, providing syntax, semantics, and a completeness theorem for reasoning about knowledge and probability among many agents.

## Key findings

- Established a formal semantics for the logic
- Proved strong completeness of the axiomatic system
- Extended propositional logic to first-order logic for multi-agent reasoning

## Abstract

We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of Fagin and Halpern from (J.ACM 41:340-367,1994). We define its syntax and semantics, and prove the strong completeness property of the corresponding axiomatic system.