Non-Monotonic S4F Standpoint Logic (Extended Version with Proofs)

TL;DR

This paper introduces S4F Standpoint Logic, a new formalism that unifies modal and standpoint logics to represent multiple viewpoints with non-monotonic reasoning, analyzing its complexity and acceptance mechanisms.

Contribution

It generalizes S4F and standpoint propositional logic, providing a unified framework for multi-viewpoint non-monotonic reasoning with complexity analysis.

Findings

S4F Standpoint Logic is not more complex than its components.

The framework supports credulous and sceptical acceptance.

Illustrated with a practical example.

Abstract

Standpoint logics offer unified modal logic-based formalisms for representing multiple heterogeneous viewpoints. At the same time, many non-monotonic reasoning frameworks can be naturally captured using modal logics, in particular using the modal logic S4F. In this work, we propose a novel formalism called S4F Standpoint Logic, which generalises both S4F and standpoint propositional logic and is therefore capable of expressing multi-viewpoint, non-monotonic semantic commitments. We define its syntax and semantics and analyze its computational complexity, obtaining the result that S4F Standpoint Logic is not computationally harder than its constituent logics, whether in monotonic or non-monotonic form. We also outline mechanisms for credulous and sceptical acceptance and illustrate the framework with an example.