Lattice-Based Graded Logic: a Multimodal Approach

TL;DR

This paper introduces a qualitative, lattice-based graded logic framework using multimodal operators to handle uncertain and incomplete knowledge, providing semantics and axiomatization for expert reasoning without precise numerical certainty.

Contribution

It presents a novel multimodal logic with a lattice structure for symbolic grades, offering a new way to model uncertainty qualitatively in logical reasoning.

Findings

Semantics and axiomatization of the proposed logic

Links with related approaches to uncertainty

Potential applications in managing incomplete knowledge

Abstract

Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical formulas. Uncertain information is expressed by means of parameterized modal operators. We propose a semantics for this multimodal logic and give a sound and complete axiomatization. We study the links with related approaches and suggest how this framework might be used to manage both uncertain and incomplere knowledge.