Epistemic Łukasiewicz logic of partial knowledge

Abstract

We offer a new logic, called Epistemic Łukasiewicz logic of partial knowledge that is represented as multimodal epistemic Łukasiewicz logic Ktext{L} _text {P}(n) with n knowledge operators Box _i(1 le i le n) interpreted in a non-archimedean monadic MV-algebra. We choose knowledge operators, which can be estimated by some grading (different kinds of knowledge): absolute knowledge or partial knowledge. We consider a very special type of partial knowledge. Actually, we take infinitesimal elements (the radical) of perfect MV-algebras as a range of this estimation. The choice of infinitesimal elements seems suitable for actual situations like a measure of partial information.