Epistemic Łukasiewicz logic of partial knowledge

Abstract

AbstractWe offer a new logic, called Epistemic Łukasiewicz logic of partial knowledge that is represented as multimodal epistemic Łukasiewicz logic $$K\text{\L} _\text {P}(n)$$ K Ł P ( n ) with n knowledge operators $$\Box _i$$ □ i $$(1 \le i \le n)$$ ( 1 ≤ i ≤ 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.