# Giangiacomo Gerla, University of Salerno, ITALY. Ggerla104@gmail.com

**Scientific Interests: I am interested in fuzzy logic, approximate reasoning, point-free geometry and learning processes in mathematics.**

**1736 citations on Google Scholar.**

**By the following links it is possible to read the list of my papers on the different subjects. ****People interested on some particular paper of mine are invited to send me an e-mail.**

**In http://www.dmi.unisa.it/people/gerla/www/ it is possible to take directly several papers of mine.**

**- FUZZY SUBSETS, FUZZY RELATIONS, FUZZY TOPOLOGY: **Some basic notions in fuzzy mathematics

**- FUZZY ALGEBRAS, CODE THEORY, FUZZY SEMIGROUPS : **Some basic notions in fuzzy mathematics

**- FUZZY CLOSURE OPERATORS, EXTENSION PRINCIPLE : **The theory of fuzzy closure operators. Also, I propose an extension principle to associate every notion in classic mathematics into a corresponding notion in fuzzy mathematics

**- FUZZY LOGIC : **Graded approach to fuzzy logic (Pavelka style). In particolar, I explore the possibility of an approach to fuzzy logic based on the notion of 'effective' and therefore 'continuous' closure operator' (see my book *'Fuzzy Logic: Mathematical Tools for Approximate Reasoning', *Kluwer Academic Press).

**- FUZZY LOGIC PROGRAMMING, FUZZY CONTROL, SIMILARITY LOGIC: **One gives basic definitions for fuzzy programming theory, and one shows that fuzzy control is a particular case of this theory. One define a logic taking in account of the synonymy.

**- FUZZY COMPUTABILITY**: The notions of *fuzzy computability, effectively enumerable fuzzy subset, * *decidable fuzzy subset, fuzzy Turing Machine *are defined. This in account of the fact that the effectiveness is on the basis of any logic.

**- PROBABILISTIC LOGIC :** I start from the idea that a logic is a system to obtain, given a partial information on a possible world, further information. In particular, if * B* denotes the set of events in a world probabilistic in nature and

**([0,1]) the set of intervals, then a partial information is a map**

*I**v*:

*-> I([0,1]). If A is an event (a formula), the the meaning of the interval v(A) is that even if I dont known the exact probability of A, I am sure that this probability is in the interval v(A). A model of the 'theory' v is a (finitely additive) probability which is in accordance with the constraints given by v.*

**B**- POINT-FREE GEOMETRY BASED ON INCLUSION AND CONNECTION **:** Attempts to axiomatize the Euclidean geometry by assuming the notion of region as a primitive. The points are defined by suitable *'abstraction processes'*, i.e. sequences of nested regions. In accordance with Whitehead ideas, the relations 'inclusion' and 'connection' are assumed as primitives.

- POINT-FREE GEOMETRY BASED ON FUZZY LOGIC, One assume as a primitive the 'distance' between regions and the 'diameter' of a region. Also, one proposes fuzzy logic for a suitable axiomatization of point-free geometry. This is obtained by admitting vague predicates as 'small', 'close', 'almost intirely contained'. These predicates are the basis for a naive geometry of the common men.

- CLASSICAL LOGIC**:** Some results in modal logic and in limit-computation.

- **DIDATTICA DELLA MATEMATICA ED ALTRO:** L'interesse principale è quello di esaminare le potenzialità della logica matematica per lo sviluppo delle capacità logiche. Ciò nell'ambito delle attività del Gruppo di Ricerca in Didattica della Matematica dell'Università di Salerno.