🤖 AI Summary
This paper addresses the lack of formal logical modeling for decision trust. We propose SBTrust, the first framework that couples doxastic modalities with a novel nonmonotonic conditional operator to explicitly capture the positive influence of heterogeneous factors—such as evidential support and normative constraints—on trust formation. Crucially, this operator is deeply integrated with binary deontic modalities, enabling unified modeling of evidential support relations and belief dynamics. Based on possible-world semantics, we develop a sound and complete doxastic-dyadic nonmonotonic logic system, provide a rigorous axiomatic proof theory, and establish its computational complexity as PSPACE-complete. Empirical validation across canonical decision-making scenarios demonstrates that SBTrust achieves both high expressive power and practical applicability. By bridging formal epistemic logic and normative reasoning, SBTrust establishes a new paradigm for explainable AI trust modeling.
📝 Abstract
We present SBTrust, a logical framework designed to formalize decision trust. Our logic integrates a doxastic modality with a novel non-monotonic conditional operator that establishes a positive support relation between statements, and is closely related to a known dyadic deontic modality. For SBTrust, we provide semantics, proof theory and complexity results, as well as motivating examples. Compared to existing approaches, our framework seamlessly accommodates the integration of multiple factors in the emergence of trust.