# Subset models for justification logic

## TL;DR

This paper introduces a novel subset-based semantics for justification logic, providing a versatile framework that can incorporate probabilistic measures and unify existing approaches.

## Contribution

It presents a new subset semantics for justification logic, proves soundness and completeness, and extends to probabilistic and traditional models.

## Key findings

- New semantics for justification logic based on subset relations
- Semantic framework that can incorporate probability measures
- Unifies existing approaches to probabilistic evidence in justification logic

## Abstract

We introduce a new semantics for justification logic based on subset relations. Instead of using the established and more symbolic interpretation of justifications, we model justifications as sets of possible worlds. We introduce a new justification logic that is sound and complete with respect to our semantics. Moreover, we present another variant of our semantics that corresponds to traditional justification logic. These types of models offer us a versatile tool to work with justifications, e.g.~by extending them with a probability measure to capture uncertain justifications. Following this strategy we will show that they subsume Artemov's approach to aggregating probabilistic evidence.