Some Epistemic Extensions of G\"odel Fuzzy Logic

In this paper, we introduce some epistemic extensions of G\"odel fuzzy logic whose Kripke-based semantics have fuzzy values for both propositions and accessibility relations such that soundness and completeness hold. We adopt belief as our epistemic operator, then survey some fuzzy implications to justify our semantics for belief is appropriate. We give a fuzzy version of traditional muddy children problem and apply it to show that axioms of positive and negative introspections and Truth are not necessarily valid in our basic epistemic fuzzy models. In the sequel, we propose a derivation system $K_F$ as a fuzzy version of classical epistemic logic $K$. Next, we establish some other epistemic-fuzzy derivation systems $B_F, T_F, B_F^n$ and $T_F^n$ which are extensions of $K_F$, and prove that all of these derivation systems are sound and complete with respect to appropriate classes of Kripke-based models

Other Buds in Membrane Computing

It is well-known the huge Mario’s contribution to the development of Membrane Computing. Many researchers may relate his name to the theory of complexity classes in P systems, the research of frontiers of the tractability or the application of Membrane Computing to model real-life situations as the Quorum Sensing System in Vibrio fischeri or the Bearded Vulture ecosystem. Beyond these research areas, in the last years Mario has presented many new research lines which can be considered as buds in the robust Membrane Computing tree. Many of them were the origin of new research branches, but some others are still waiting to be developed. This paper revisits some of these buds