Paraconsistent reasoning for inconsistency measurement in declarative process specifications

Abstract

Inconsistency is a core problem in fields such as AI and data-intensive systems. In this work, we address the problem of measuring inconsistency in declarative process specifications, with an emphasis on linear temporal logic (LTL). As we will show, existing inconsistency measures for classical logic cannot provide a meaningful assessment of inconsistency in LTL in general, as they cannot adequately handle the temporal operators. We therefore propose a novel paraconsistent semantics for LTL over fixed traces (LTL${}_{\text{ff}}$) as a framework for time-sensitive inconsistency measurement. We develop and implement novel approaches for (element-based) inconsistency measurement, and propose a novel semantics for reasoning in LTL${}_{\text{ff}}$ in the presence of preference relations between formulas. We implement our approach for inconsistency measurement with Answer Set Programming and evaluate our results with real-life data sets from the Business Process Intelligence Challenge.