Knowledge-Now and Knowledge-All

Abstract

In this paper, we propose a logical framework extending the standard epistemic logic with a new knowledge operator which captures the knowledge about (physically) necessary facts, e.g., scientific knowledge. Semantically, the truth of depends on not only the epistemically indistinguishable worlds from the current real world but also the relevant (physically) possible worlds which are clearly distinguishable. Essentially, is a bundle of the standard epistemic modality and a necessity-like modality. We axiomatize the corresponding epistemic logic completely in single- and multi-agent cases with interesting interaction axioms between the two epistemic operators.