Hyperrational conditionals

Abstract

This paper presents a strong monotonic core logic for nested default conditionals overcoming several drawbacks of previous approaches. We begin with a short account of elementary qualitative magnitude logic, which describes a comparative modality encoding “negligible w.r.t.”, and consider its conditional alter ego, which extends the object-level version of Lehmann's rationality postulates. Next, we propose and discuss additional postulates suitable for nested contexts, implementing some ideas about reflection and documenting simultaneously the weaknesses of more traditional constraints. All this leads us to what we call hyperrational conditional logic (HRC). A new model-concept based on nested ranked model structures, mixing accessibility and preference relations and conforming to an appropriate coherence notion, then provides an adequate semantic characterization. We also investigate an extension of our logic by a global-evaluation modality enabling a better description of our model structures and allowing an object-level encoding of finitary nonmonotonic entailment relations. To conclude, we take a broad look at competing accounts and compare them to our formalisms.