GIANGIACOMO GERLA
Department of Mathematics, University of Salerno, Via Ponte Don
Melillo 84084 Fisciano (SA) ITALY gerla@unisa.it
INTERESTED IN: Fuzzy Logic, Fuzzy set theory, Fuzzy model theory,
Vagueness, Fuzzy control, Multi-Valued Logic, Approximate Reasoning, Similarity
Logic, Fuzzy Computability, Decidable and Effectively enumerable fuzzy sets,
Extension principle in fuzzy mathematics, Witnessed models, Abstract logic,
Closure operators, Point-free geometry, Pedagogical features of
logic.
DIDATTICA,
SCIENTIFIC
INTERESTS LIST OF
PAPERS P G
LIBRI
&TENTATIVI
DI FONDARE LA MATEMATICA, Vol. I, Il primo
di due volumetti che raccolgono le mie lezioni di Matematiche Complementari. I
libri si occupano di fondamenti della matematica e quindi di paradossi,
geometria, algebra, insiemi, metodo assiomatico, logica ed altro. Questo volume
si riferisce alla matematica dai greci agli insiemi numerici. Acquistabile
presso Ilmiolibro. Utile per concorsi A047 e per tutti i
concorsi coinvolgenti la matematica. Versione ridotta di entrambi i libri scaricabile
gratuitamente.
&TENTATIVI
DI FONDARE LA MATEMATICA, Vol. II, Il
secondo dei due volumetti. Parla della matematica che va dalla teoria degli
insiemi in avanti. Acquistabile presso Ilmiolibro. Utile per
concorsi A047 e per tutti i concorsi coinvolgenti la matematica. INDICE
&LOGICA FUZZY: I PARADOSSI DELLA VAGHEZZA Il libro si occupa di quei ragionamenti che coinvolgono nozioni vaghe come quelle di "alto", "vicino" ed altro. Parla quindi di logica fuzzy. Tra le altre cose tratta il paradosso del mucchio di grano, del mentitore , degli indiscernibili. Ha carattere divulgativo e richiede solo nozioni elementari di matematica. Acquistabile presso Ilmiolibro Versione ridotta scaricabile gratuitamente
AppuntidimieicorsidilogicamatematicapressoilCorsodilaureainmatematicadiSalerno.Acquistabilepresso Ilmiolibro. Versione ridotta scaricabile gratuitamente. INDICE
&CALCOLATORI: COSA POSSONO FARE E COSA NO, Raccoglie le lezioni del mio corso di teoria della computabilità. Si occupa di automi finiti, di macchine di Turing, di macchine a registri e di relativi teoremi limitativi. Acquistabile presso Ilmiolibro. Versione ridotta scaricabile gratuitamente INDICE
&FUZZY LOGIC: MATHEMATICAL TOOLS FOR APPROXIMATE REASONING, KluwerEditor. Il libro ha carattere avanzato ed è consigliabile per chi, interessato alla logica fuzzy, abbia una buona base matematica
Contents, Preface, Some pages,Google books Comment: Belohlavek,Bharath Hajek, Gylys,Gottwald
ARTICOLI
MODEL
THEORY FOR FUZZY LOGIC (fuzzy subalgebras, withessed structures,
ultraproduct, quotient, logical equivalence, witnessed models, ...)
-
Di Nola A., G. Gerla, Lattice valued algebras, Stocastica XI-2,3 (1987)
137-150 (model theory for fuzzy subalgebras
theory).
-
Di Nola A., G. Gerla, Fuzzy models of
first order languages, Zeitschr. f. math. Logik und Grundlagen d.
Math., 32 1986 (332-340). (model theory for fuzzy
logic)
- G. Gerla, The category of the Fuzzy Models and Lowenheim-Skolem Theorem, Mathematics of Fuzzy Systems T.U.V. Verlag Koln, W. Germany (1986) 121-141. (quotient and ultrapowers for fuzzy logic). pdf
-
G. Gerla, Multi-valued logic to transform potential into actual objects,
Studia Logica, 86 (2007) 69-87. (submission 2005: The paper is related
with the "witnessed models" (see the interesting Hajek's series of papers on
the witnessed models). The definition of the existential quantifier in fuzzy
logic is used to analyze a general way to pass from a potential existence to an
actual existence. In a witnessed model these notions
coincide).
-
G. Gerla, Compactness and effectivity for fuzzy logics: discussing on some
criticisms. My unfortunate paper I suggest to read: It is an opinion
paper devoted to expose some criticisms on the actual approach to fuzzy logic.
This is a Guinness World Record paper !!! Indeed it was submitted to six
journals usually well-disposed towards fuzzy logic and it was rejected by six
journals (with no convincing motivation, in my opinion).
FUZZY COMPUTABILITY (The notions of recursively enumerable fuzzy subset and decidable fuzzy subsets are defined. In accordance the possibility for a Church thesis for fuzzy logic is discussed. Limitative theorems for fuzzy logic are exposed).
-
G. Gerla, Sharpness Relation and Decidable Fuzzy Sets, IEEE Trans. on
Automatic Control, AC-27 5 (1982) 1113 (there are fuzzy subsets with no
decidable sharpened
version)
-
G. Gerla, Effectiveness and Gödel Theorems in Fuzzy Logic, (An extended
abstract of Chapter 11 in my fuzzy logic
book)
-
G. Gerla, Effectiveness and Multi-valued Logic, Journal of Symbolic
Logic, 71 (2006) 137-162. (effective domain theory as a general basis for
fuzzy
computability)
-
L. Biacino, G. Gerla, Fuzzy Logic, Continuity and Effectiveness, Archive
for Mathematical Logic, 41, 2002, 643-667 (One proves that a fuzzy
semantics is axiomatizable if and only if the related logical consequence
operator is
continuous)
-
G. Gerla, Multi-valued logic, Effectiveness and domains, in Lecture Notes
in Computer Science 4497, Springer 2007, 336-347. (The connection with the
notions of fuzzy Turing machines and fuzzy grammar given in literature is
investigated and one proves the inadequateness of these definitions).
PROBABILITY
LOGIC AS A FUZZY LOGIC (Some probabilistic logics are considered from
the point of view of approximate reasoning theory, i.e. by a fuzzy set of
logical axioms + fuzzy inference
rules)
-
L. Biacino, G.Gerla, Boolean Fuzzy Logic and generalized Capacities,
International Journal of General Systems, 32 (2003) 321-342. (Capacity
measure as valued theories in a Boolean fuzzy
logic).
-
G. Gerla, Probability like functionals. J. of Math. Anal. Appl., 216
(1997) 438-465 (Envelopes as theories of a fuzzy logic whose models are the
probabilities: the theories are the envelopes, the models are the
probabilities).
-
G. Gerla, The probability that Tweety is Able to Fly., International
Journal of Intelligent Systems, 9 (1994) 403-409. (is the probability that
a bird similar with Tweety is able to fly: similarity-based probabilistic
evaluation of a singular
event).
-
D. Calabrò, G. Gerla, L. Scarpati, Extension principle and probabilistic
inferential process. Lectures on Soft Computing and Fuzzy Logic,
(2001) Springer-Verlag, 113-127.(an expert system probabilistic in nature based
on the ideas in Tweety
paper).
-
G. Gerla, Probability Logic: Syntax, Busefal 47 1994. (inference rules
for probability logic).
-
D. Calabrò, G. Gerla, Processi inferenziali probabilistici e sistemi
esperti. Tecnical Report 001-A of the Soft Computing Laboratory, del
Dipartimento di Matematica ed Informatica, 2002 (un sistema esperto di natura
probabilistica a partire da
data-bases).
-
Coppola C., Gerla G., Pacelli T., Similarities for Crisp and Fuzzy
Probabilistic Expert Systems, Studies in Fuzziness and Soft Computing,
Ed. Kacprzk J., Springer, 224 (2008)
23-42.
CLOSURE
OPERATORS AND FUZZY LOGIC (An abstract approach to fuzzy logic based
on closure operators in accordance with Tarski's point of view. A fuzzy logic
is a continuous operators, we call "immediate consequence operator" in the
lattice of all fuzzy subsets of the set of sentences of a given language. A
theory is a fixed point of such an
operator)
-
L. Biacino, G. Gerla, Closure Operators in fuzzy set theory. Fuzzy sets in
approximate reasoning and information systems, edited by J. C. Bezdek, D.
Dubois and H. Prade, Kluwer Academic Publishers (1998). (The basic
definitions)
-
G. Gerla, Closure Operators, Fuzzy Logic and Constraints , in Fuzzy Sets,
Logics and Reasoning About Knowledge, D. Dubois, H. Prade E.P. Klement,
Eds, Vol. 15 in the Applied Logic Series, Kluwer Academic Publishers, 1999,
101-120. (fuzzy logic is a tool to manage information on the truth values of
the formulas, i.e. to manage
constraints)
-
G. Gerla, Stratified operators and graded consequence operator. Extended
abstract from Chapter 7 of my book in Fuzzy Logic) (The theory of the fuzzy
closure operators is related with the theory of graded consequences
relations)
-
L. Biacino, G. Gerla, Necessities generated by an initial valuation,
Busefal 41 (1989), 7-14 (The class of necessities is considered as a
closure systems)
-
G. Gerla, Fuzzy Metalogic for Crisp Logics on Discovering the World by Fuzzy
Logic. V. Novak and I. Perfilieva (Eds), Physica-Verlag, Heidelberg,
2000, 175-191. (One considers fuzzy logics arising from a fuzzyfication of the
main metalogic
notions)
EXTENSION
PRINCIPLE. (A general extension principle for closure operators is
proposed. This enables us to extend several notion in classical mathematics to
the fuzzy framework. In particular we show that it is possible to extend any
classical inferential apparatus into a fuzzy inferential
apparatus)
-
G. Gerla, Closure Operators: an extension principle. Busefal 56
(1994). (The basic
definitions)
-
L. Biacino, G. Gerla, An extension principle for closure operators, J. of
Math. Anal. Appl., 198 (1996) 1-24.
-
G. Gerla, L. Scarpati, Extension Principles for Fuzzy Set Theory, Journal
of Information Sciences, 106 (1998)
49-69.
SIMILARITY-BASED FUZZY LOGIC (A fuzzy logic is proposed in which the unification is based on the similarity between two predicate and not on the perfect matching)
-
A. Fontana, F. Formato, G. Gerla, Similarity-based Logic Programming: a fuzzy
resolution rule. LPSC'98, Manchester,
1998.
-
A. Fontana, F. Formato, G. Gerla, Extending Unification trough similarity
relations, BUSEFAL, 70 (1997).
-
L. Biacino, G. Gerla, M. Ying, Approximate Reasoning Based on Similarity.
Math. Log. Quart., 46 (2000), 77-86.
-
L. Biacino, G. Gerla, Logics with Approximate premises, International J. of
Intell. Syst. 13 (1998)
1-10.
-
C. Crisconio, D. Donato, G. Gerla, Similarity Logic and Translations,
Intern. J. of Uncertainty, Fuzzyness and Knowledge-based Systems, 12
(2004) 257-267. (is the translation of a correct proof again a correct proof
?)
-
F. Formato, G. Gerla, M. Sessa, Similarity-based Unification, Fundamenta
Informaticae, 41 (2000) 393-414.
SIMILARITIES
AND FUZZY ORDERS (Fuzzy relations extending the notion of equivalence
and
order)
-
C. Crisconio, G. Gerla, Similarities and fuzzy orders in approximate reasoning,
in New logic for the New Economy, Ed. Scientifiche
Italiane.
-
G. Gerla, M. Scarpati, Galois connection among fuzzy groups, similaritiee and
distances (any similarity defines a fuzzy group and
conversely)
-
F. Formato, G. Gerla, L. Scarpati, Fuzzy subgroups and similarities, Soft
Computing 3 (1999) 16
-
G. Gerla, Representation theorems for Fuzzy orders and Quasimetrics, Soft
Computing, 8 (2004) 571-580 (fuzzy orders are represented as fuzzy
inclusions and related with non symmetric distances. Unfortunately, I
discovered that all the results were long time proved by Dr. Ulrich Bodenhofer
in a series of beatiful
papers).
-
G. Gerla, Fuzzy submonoids, fuzzy preorders and quasimetrics, Fuzzy Sets
and Systems, 157 (2006) 2356-2370. (any fuzzy preorder defines a fuzzy
submonoid and
conversely).
- Coppola C., Gerla G., Pacelli T. - Convergence and fixed
points by fuzzy orders, Fuzzy Sets and Systems, 159 (2008)
1178-1190.
FUZZY
CONTROL BASED ON FUZZY LOGIC PROGRAMMING (One proves that the system
of rules in the implication-based and triangular norm-based fuzzy control can
be interpreted as fuzzy programs. This gives, in my opinion, a rigorous
interpretation of fuzzy control as a chapter of formal logic. Also, this
suggests several new tools and possibilities for fuzzy
control)
-
G. Gerla, Approximate reasoning to unify norm based and implication-based fuzzy
control.
-
G. Gerla, Fuzzy Control as a fuzzy Deduction System, Fuzzy Sets and
Systems, 121 (2001)
409-425.
-
G. Gerla, Fuzzy Logic Programming and Fuzzy Control, Studia Logica, 79
(2005) 231-254.
-
G. Gerla, Fuzzy Control and Fuzzy Logic Programming by Mathematica. An
implementation in Mathematica of classical logic programming and fuzzy logic
programming is
proposed)
PARADOXES
AND
VAGUENESS
-
G. Gerla, Why I have an extraterrestial ancestor, in Percorsi
incrociati, in honour of Vittorio Cafagna, Rubettino Ed.,
179-191 (2010) (Paradoxes like "Heap paradox" in fuzzy set theory,
paradox in relativity theory.
)
-
F. Formato, G. Gerla, Grasping Infinity by Finite Sets, Math. Log.
Quart. 44 (1998) 383-393.(The infinity axiom is satisfied by the class of
finite sets)
-
G. Gerla, Approximate similarities and Poincaré Paradox,
Notre Dame Journal of Formal Logic, 49 (2008) 203-226.
(Poincaré paradox about the indiscernibility. I propose a solution of
such a paradox based on fuzzy logic and point-free
geometry.
COMPUTABILITY (Recursion theory. Two papers related with limit-computability).
-
G. Gerla, Una generalizzazione della gerarchia di Ershov, B.U.M.I. 5 16-B (1979)
765-778. (The Ershov hierarcy is generalized. The paper concerns the notion of
tt-reducibility, btt-reducibility and
jump).
-
G. Criscuolo, G. Gerla, tt-riducibilità e limiti ricorsivi, Le
Matematiche 31 (1979) 94-103. (The Ershov hierarcy is generalized. The paper concerns the notion
of tt-reducibility, btt-reducibility and
jump).
POINT-FREE GEOMETRY (In accordance with a proposal of Whitehead in "Process and Reality", one considers some possible approaches to geometry in which the regions are assumed as primitives and the points are defined by "abstraction processes", i.e. by considering suitable sequences of regions). I suggest to read the expository chapter I write for the Handbook of incidence geometry.
-
C. Coppola, G. Gerla, A. Miranda, Point-free foundation of geometry and
multi-valued logic, Notre Dame Journal of Formal Logic, vol 51,
(2010) 383-405. (The primitives are the regions and a graded
inclusion).
-
G. Gerla, A. Miranda, Graded inclusion and point-free geometry. Int. J. of
Pure and Applied Mathematics, 11 (2004) 63-81. (The primitives are the
regions and a graded inclusion
relation).
-
L. Biacino, G. Gerla, Connection structures, Notre Dame J. of Formal
Logic, 32 (1991) 242-247. (The primitives are the regions and the
connection relation, i.e. contact or overlapping
relation).
-
L. Biacino, G. Gerla, Connection structures: comparing Grzegorczyk's and
Whitehead's Definitions of point, Notre Dame Journal of Formal Logic,
37 (1996) 431-439. (One considers different definitions of point in point-free
geometry)
-
G. Gerla, Point-free geometry, Handbook of incidence geometry by
Buekenhout F. and Kantor W. (1995) (A chapter on point-free geometry)
.
-
G. Gerla, Pointless Metric Spaces, J. Symbolic Logic, 55
(1990)207-219. (The primitives are the regions, the diameter and the inferior
distance between
regions)
-
G. Gerla, R. Volpe, Geometry Without Points, Amer. Math.
Monthly, 92 (1985) 707-711.(A brief
introduction)
-
G. Gerla, Diameter and Distances in Fuzzy Spaces, BUSEFAL 49
(1991-92)83-90. (As an example of pointless metric space, we define the notions
of diameter and distance in the class of fuzzy subsets of a metric
space)
-
A. Di Concilio, G. Gerla, Quasi-metric spaces and point-free geometry,
Math. Struct. in Comp. Science 16 (2006)
115-137.
-
G. Gerla, Popper's verisimilitude theory and point-free geometry, Journal
of Philosophical Logic, 36 (2007)
707-733.
-
G. Gerla, A. Miranda, Mathematical features of Whitehead's point-free geometry.
in Handbook of Whiteheadian Process Thought, Michel Weber and William
Desmond, Jr. (eds.), Frankfurt / Lancaster, Ontos Verlag, Process Thought
vol.2, 2008.
-
C. Coppola, G. Gerla, T. Pacelli, The category of fuzzy subsets and point-free
ultrametric
spaces.
Si
suggerisce anche di leggere l'interessante tesi di laurea magistrale del Dott.
A. Pecoraro di cui sono stato relatore, Formalizzazione della geometria
senza punti di A. N.
Whitehead
MODAL
LOGIC
-
G. Gerla, A Note on the Principle of Predication, Notre Dame Journal
of Formal Logic, 23 (1982) 471-472. (One proves that the Principle of
Predication in Modal logic about De Dicto modalities is
unsound)
-
G. Gerla, Transformational semantics for first order modal logic,Logique et
Analysis, 117-118 (1987) 69-79. (The claim that it "is possible A" in the
world w is interpreted as "it is possible to transform w into a world in which
A is true". So, any group of transformation gives a
modality).
-
Gerla G., Vaccaro V., Modal Logic and Model Theory, Studia Logica, 43 (1984)
203-216.
ARTICOLI
DIVULGATIVI
-
G. Gerla, Un punto dal volto di Gatto, Periodico di Matematiche,
I e II, 3 (2006) 9-20, 4 (2006) 15-25. (si mostra che è sensato
definire punti che abbiano una forma, ad esempio punti quadrati, punti
triangolari)
-
G. Gerla, La logica fuzzy ed il paradosso del mucchio di
grano
-
G. Gerla, Destini
programmati.
- F. Gerla, G. Gerla, Programmed destinies. pdf
- M. Cautiero, G. Gerla,Un testo scolastico del 1897, gli "Elementi di Geometria" di Giuseppe Veronese, Periodico di Matematiche, 1-2 (1988) 17-32. pdf.