# Matteo Cristani

- March 2017

###### Multivalued Logics and Alternative Negation Operators

Since the first two decades of the twentieth century, many logicians, including Kleene (K3), Belnap (B4), Lukasiewicz (LL), GĂ¶del (GL) and Orlowska (PL) have dealt with the problem of defining logical systems that are able to accommodate multivalued interpretations of the logical meanings. These are the so-called multivalued logics, a vast field of research that involved also a deep revision by generalization of the formerly defined target domain for interpretations, namely the Boolean algebras. The definition of MV-Algebras, and the re-definition of MV-Logics, as based on that interpretation model, has driven several deep researches in the field of Logic. Starting with a general and deep study proposed by Belluce and Di Nola, we generalize the notion of negation in a MV-Logic, and explain how this can be accommodated at a purely semantical level. This study brings to the construction of a number of abstract models of MV-logics with negation operators and also introduces new notions, such as pseudo-projection and pseudo-neagation, that extend the traditional ones of projection and negation. We show that there exists a limited number of combinations satisfying the new version of the constraints introduced by Belluce and Di Noia, and provide such a classification for the case of three-valued logic, by accommodating the possible combinatorics in K3.

- November 2015

###### Defeasible logic. A non monotonic approach to plausible conclusions.

Non monotonic reasoning is the family of methods employed in formal logic to obtain conclusions that are derived from inconsistent or incomplete knowledge. Usually, non monotonic logical systems are devised to allow conclusions that can contain contradictions, or that can be sorted to contradiction elimination by means of some form of priority mechanism. In the seminar we provide the fundamentals of Defeasible Logic, that is a skeptical non monotonic logical system able to derive conclusions in presence of contradictions. The approach is motivated by legal reasoning, scientific reasoning and more generally by the representation of plausibility, intended to manage proofs by incorporation of them. We then introduce computational methods to treat defensible logic and investigate logical classical issues and modern aspects.