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di Giangiacomo Gerla 292 pagine, acquistabile a 9,74 euro presso il sito http://ilmiolibro.kataweb.it/default.asp |
GIANGIACOMO GERLA Department of Mathematics
and Information Sciences, Via Ponte Don
Melillo 84084 Fisciano (SA) ITALY gerla@unisa.it INTERESTED
IN: Fuzzy
Logic, Vagueness, Fuzzy control, Multi-Valued Logic, Approximate Reasoning,
Similarity Logic, Fuzzy Computability, Decidable and Effectively enumerable
fuzzy sets, Extension principle, Abstract logic, Closure operators,
Point-free geometry, Pedagogical features of Logic. DIDATTICA SCIENTIFIC INTERESTS PAPERS P |
D
O W N L O A D A R E A
My wonderful
book I suggest to buy
- G. Gerla. Fuzzy Logic: Mathematical Tools for
Approximate reasoning (Kluwer Editor).
Contents, Preface, Some pages Hajek-comment, Gottwald-comment, Gylys-comment, Belohlavek-comment,
Model
theory for fuzzy logic
- 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.
- G. Gerla, Multi-valued
logic to transform potential into actual objects (the definition of the existential quantifier in fuzzy
logic is used to analyze a general way to pass from a potential existent to an
actual existence.
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 (there are fuzzy subset with
no decidable sharpened version)
- G. Gerla Effectiveness
and Gödel
Theorems in Fuzzy Logic
- G. Gerla Effectiveness in Fuzzy Logic (effective domain theory as
a general basis for fuzzy computability
- G. Gerla Church thesis for fuzzy computability (is there an
analogous of Church thesis for fuzzy logic ?)
- L. Biacino, G. Gerla, Fuzzy Logic, Continuity and Effectiveness. (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. (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 (Capacity measure as valued
theories in a Boolean fuzzy logic).
- G. Gerla, Probability like functionals. (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. (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. (an expert system probabilistic in nature based
on the ideas in Tweety paper).
- G. Gerla, Probability Logic: Syntax. (inference rules for probability
logic).
- D. Calabrò, G. Gerla, Processi inferenziali probabilistici e
sistemi esperti. (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.
Si suggerisce anche la lettura della seguente tesi che credo
possa essere una premessa per i trattamento dell’informazione di tipo
probabilistico in caso di incompletezza.
Assuntina Cembalo, Bireticoli per il trattamento
dell’informazione. Tesi di Laurea
Magistrale.
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 class 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. (The basic definitions)
- G. Gerla, Closure
Operators, Fuzzy Logic and Constraints (Fuzzy logic is a tool to
manage information on the truth values of the formulas, i.e. to manage
constraints on truth values)
- G. Gerla, Stratified
operators and graded consequence operator. (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 (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. (The basic definitions)
- L. Biacino, G. Gerla, An extension principle for closure operators.
- G. Gerla, L. Scarpati, Extension
Principles for Fuzzy Set Theory.
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. Fontana, F. Formato, G. Gerla, Extending
Unification trough similarity relations.
- L. Biacino, G. Gerla, M. Ying, Approximate Reasoning Based on Similarity.
- L. Biacino, G. Gerla, Logics with Approximate premises.
- C. Crisconio, D. Donato, G. Gerla, Similarity
Logic and Translations (is the
translation of a correct proof again a correct proof ?)
- F. Formato, G. Gerla, M. Sessa, Similarity-based Unification
Similarities
and fuzzy orders (Fuzzy
relations extending the notion of equivalence and order)
- C.
Crisconio, G. Gerla, Similarities
and fuzzy orders in approximate reasoning, New logic for the New economy, Ed. Scientifiche Italiane.
- G. Gerla, M. Scarpati, Galois connection among fuzzy groups and similarities (any similarity
defines a fuzzy group and conversely)
- F. Formato, G. Gerla, L. Scarpati, Fuzzy
subgroups and similarities.
- G. Gerla, Representation theorems for Fuzzy orders and Quasimetrics. (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, Connecting fuzzy submonoids,
fuzzy preorders and quasimetrics
(any fuzzy preorder defines
a fuzzy submonoid and conversely).
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.
- G. Gerla, Fuzzy Logic Programming and Fuzzy Control.
- 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 (Paradoxes like “Heap paradox” in fuzzy set theory, paradox
in relativity theory. To appear in a volume in honour of Vittorio
Cafagna)
- F. Formato, G. Gerla, Grasping
Infinity by Finite Sets (The infinity axiom
is satisfied by the class of finite sets)
- G. Gerla, ,
Poincaré Paradox (Poincaré paradox
about the indiscernibility. A solution of such a paradox is proposed which is
based on fuzzy logic and point-free geometry.
Point-free
Geometry (In accordance with a proposal of Whitehead in
“Process and Reality”, one consider 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
- G. Gerla, A. Miranda, Graded
inclusion and point-free geometry. (The primitives are the regions and a graded inclusion
relation).
- L. Biacino, G. Gerla, Connection structures. (The primitives are
the regions and the connection relation, i.e. contact or overlapping relation).
- L. Biacino, G. Gerla, Connection
structures: Grzegorczyk’s and Whitehead’s Definitions
of point. (One consider different definitions of point in
point-free geometry)
- G. Gerla, Point-free
geometry. (A chapter on point-free geometry from the Handbook of
incidence geometry by Buekenhout F. and Kantor W.
(1995).
- G. Gerla, Pointless Metric
Spaces. (The primitives are the
regions, the diameter and the inferior distance between regions)
- G. Gerla, R. Volpe, Geometry
Without Points. (A brief introduction)
- G. Gerla, Diameter and Distances in Fuzzy Spaces. (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.
- G. Gerla, A. Miranda, Whitehead
point-free geometry.
- G. Gerla, Popper’s
verisimilitude theory and
point-free geometry.
- C. Coppola, G. Gerla, T. Pacelli, The
category of fuzzy subsets and point-free ultrametric
spaces.
NOTA: Si suggerisce anche di
leggere l’interessante tesi di laurea magistrale del Dott. A. Pecoraro di cui
sono stato relatore
A. Pecoraro, Formalizzazione della
geometria senza punti di A. N. Whitehead
Modal logic
- G. Gerla, A
Note on the Principle of Predication. (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. (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).
Articoli divulgativi
- G. Gerla, Un punto dal volto di Gatto. (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.