ABSTRACT. While an abstract characterization of truth-functionality in terms of a property called `cancellation' is known since long, an extension of this result so as to cover broader classes of logics characterized by semantics that extend the notion of truth-functionality resists a simple-minded approach.  In our contribution we discuss some difficulties encountered alongside this task and propose a solution to the characterization quest, for the case of nondeterministic semantics, and also show how the study of such properties is of paramount importance for the effort of understanding the semantical mechanism underlying the combination of logics through the fibring method.

ABSTRACT. Fuzzy negations are an important mathematical tool in approximate reasoning as well as in decision making.  This fundamental role of fuzzy negation has led to the introduction of an analogous notion for several extensions of fuzzy logics, and in particular for typical hesitant fuzzy elements (HFE).  We here assume, nevertheless, that a fundamental point for defining fuzzy negations is the necessity of a partial order on the HFE set.  For that matter we entertain the use of the Xu-Xia-partial order, which satisfies the antitonicity property of typical hesitant fuzzy negations (THFN). We propose then that each THFN based on Xu-Xia order determines a non-deterministic negation and we study several classes of non-deterministic negations and also relate them to fuzzy negations.

ABSTRACT. Many-valued logics received several criticisms since their birth. Among their main opponents was the Polish logician Roman Suszko. In the mid-70s, at a conference held in Craców, he called into question the very nature of many-valuedness by claiming the existence of "but two truth-values", a statement nowadays recognized as Suszko's Thesis. Suszko's motivation for his ideas lies in defending the existence of a double semantic role expressed by truth-values. This duplicity is revealed by him in drawing the difference between algebraic and logical values. According to him, even though we can have more than two algebraic values, there are only two genuine logical ones: truth and falsehood. The philosophical content of his ideas finds support in a technical result called Suszko's Reduction, a theorem that shows that every Tarskian logic may be characterized by a bivalent semantics. Several interesting lines of investigation have arisen from Suszko's ideas. It is the purpose of the present talk to survey the main developments in the area. Our exposition will show not only the main results that corroborate Suszko's ideas, but also those that pose limitations to them and have been leading to discussions about their meaning.

ABSTRACT. Model Checking is an automatic verification technique for large state transition systems. The technique has been used successfully to debug complex computer hardware and communication protocols. Now, it is beginning to be used for complex hybrid (continuous/discrete) systems as well. The major disadvantage of the technique is a phenomenon called the State Explosion Problem. This problem is impossible to avoid in worst case. However, by using sophisticated data structures and clever search algorithms, it is now possible to verify hybrid systems with astronomical numbers of states.