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 I([0,1]) the set of intervals, then a partial information is a map v : B -> 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. 


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.