Two Consistent Many-Valued Logics for Paraconsistent Phenomena

In this reviewing paper, we recall the main results of our papers [24, 31] where we introduced two paraconsistent semantics for Pavelka style fuzzy logic. Each logic formula a is associated with a 2 x 2 matrix called evidence matrix. The two semantics are consistent if they are seen from 'outside'; the structure of the set of the evidence matrices M is an MV-algebra and there is nothing paraconsistent there. However, seen from "inside,' that is, in the construction of a single evidence matrix paraconsistency comes in, truth and falsehood are not each others complements and there is also contradiction and lack of information (unknown) involved. Moreover, we discuss the possible applications of the two logics in real-world phenomena.

A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.