Honesty in Partial Logic

We propose an epistemic logic in which knowledge is fully introspective and implies truth, although truth need not imply epistemic possibility. The logic is presented in sequential format and is interpreted in a natural class of partial models, called balloon models. We examine the notions of honesty and circumscription in this logic: What is the state of an agent that ‘only knows φ’ and which honest φ enable such circumscription? Redefining stable sets enables us to provide suitable syntactic and semantic criteria for honesty. The rough syntactic definition of honesty is the existence of a minimal stable expansion, so the problem resides in the ordering relation underlying minimality. We discuss three different proposals for this ordering, together with their semantic counterparts, and show their effects on the induced notions of honesty.