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.

Egalitarian state-transition systems (extended version)

We argue that considering transitions at the same level as states, as first-class citizens, is advantageous in many cases. Namely, the use of atomic propositions on transitions, as well as on states, allows temporal formulas and strategies to be more powerful, general, and meaningful. We define egalitarian structures and logics, and show how they generalize well-known state-based, event-based, and mixed ones. We present translations from egalitarian to non-egalitarian settings that, in particular, allow the model checking of LTLR formulas using Maude’s LTL model checker. We have implemented these translations as a prototype in Maude itself.