# A Reasoning System for a First-Order Logic of Limited Belief

## TL;DR

This paper introduces a highly expressive, decidable, and tractable first-order logic of limited belief, along with a reasoning system and experimental results demonstrating its practical benefits.

## Contribution

It develops a new logic of limited belief that balances expressiveness and computational feasibility, and presents an implementation with experimental validation.

## Key findings

- Logic remains decidable in first-order and tractable in propositional cases.
- The reasoning system effectively utilizes the logic for practical reasoning tasks.
- Experimental results show improved reasoning efficiency with limited belief.

## Abstract

Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning decidable or even tractable. While a number of such logics have been proposed in the past, they tend to remain for theoretical analysis only and their practical relevance is very limited. In this paper, we aim to go beyond the theory. Building on earlier work by Liu, Lakemeyer, and Levesque, we develop a logic of limited belief that is highly expressive while remaining decidable in the first-order and tractable in the propositional case and exhibits some characteristics that make it attractive for an implementation. We introduce a reasoning system that employs this logic as representation language and present experimental results that showcase the benefit of limited belief.