The Hierarchy of Hyperlogics: A Knowledge Reasoning Perspective

Summary

We discuss the hierarchy of hyperlogics from a knowledge reasoning perspective. Hyperproperties generalize trace properties by relating multiple traces. Recently, logics for hyperproperties have been obtained from standard logics by adding variables for traces or paths to temporal logics like LTL and CTL*, and by adding the equal-level predicate to first-order and second-order logics, like monadic first-order logic of order and MSO. The resulting hierarchy of hyperlogics provides interesting opportunities for knowledge reasoning research: many epistemic properties and system properties in multi-agent systems, like distributivity, are hyperproperties. At the same time, first-order and second-order reasoning methods become applicable to hyperproperties.