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.

 

 D O W N L O A D   A R E A

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. INDICE  

 

&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

 

&LINGUAGGIO E VERITA'

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). pdf 

- 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) pdf

- 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).pdf

- 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). pdf

 

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)  pdf

- G. Gerla, Effectiveness and Gödel Theorems in Fuzzy Logic, (An extended abstract of Chapter 11 in my fuzzy logic book) pdf

- 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) pdf

- 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) pdf

- 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). pdf

 

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). pdf 

- 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). pdf

- 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). pdf

- 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). pdf

- G. Gerla, Probability Logic: Syntax, Busefal 47 1994. (inference rules for probability logic). pdf

- 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). pdf

- 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. pdf

 

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) pdf

- 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) pdf

- 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) pdf

- 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) pdf

- 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) pdf

 

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) pdf

- L. Biacino, G. Gerla, An extension principle for closure operators, J. of Math. Anal. Appl., 198 (1996) 1-24. pdf

- G. Gerla, L. Scarpati, Extension Principles for Fuzzy Set Theory, Journal of Information Sciences, 106 (1998) 49-69. pdf

 

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. pdf

- A. Fontana, F. Formato, G. Gerla, Extending Unification trough similarity relations, BUSEFAL, 70 (1997). pdf

- L. Biacino, G. Gerla, M. Ying, Approximate Reasoning Based on Similarity. Math. Log. Quart., 46 (2000), 77-86. pdf

- L. Biacino, G. Gerla, Logics with Approximate premises, International J. of Intell. Syst. 13 (1998) 1-10. pdf

- 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 ?) pdf

- F. Formato, G. Gerla, M. Sessa, Similarity-based Unification, Fundamenta Informaticae, 41 (2000) 393-414. pdf

 

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. pdf

- G. Gerla, M. Scarpati, Galois connection among fuzzy groups, similaritiee and distances (any similarity defines a fuzzy group and conversely) pdf

- F. Formato, G. Gerla, L. Scarpati, Fuzzy subgroups and similarities, Soft Computing 3 (1999) 16 pdf

- 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). pdf

- 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). pdf

- Coppola C., Gerla G., Pacelli T. - Convergence and fixed points by fuzzy orders, Fuzzy Sets and Systems, 159 (2008) 1178-1190. pdf-

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. pdf

- G. Gerla, Fuzzy Control as a fuzzy Deduction System,  Fuzzy Sets and Systems, 121 (2001) 409-425. pdf

- G. Gerla, Fuzzy Logic Programming and Fuzzy Control, Studia Logica, 79 (2005) 231-254. pdf

- G. Gerla, Fuzzy Control and Fuzzy Logic Programming by Mathematica. An implementation in Mathematica of classical logic programming and fuzzy logic programming is proposed) nb

 

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. ) pdf

- 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) pdf

- 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. pdf

 

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). pdf

- 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). pdf

 

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). pdf

- 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). pdf

- 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). pdf

- 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) pdf

- G. Gerla, Point-free geometry, Handbook of incidence geometry by Buekenhout F. and Kantor W. (1995) (A chapter on point-free geometry) . pdf

- 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) pdf

- G. Gerla, R. Volpe, Geometry Without Points,  Amer. Math. Monthly, 92 (1985) 707-711.(A brief introduction) pdf

- 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) pdf

- A. Di Concilio, G. Gerla, Quasi-metric spaces and point-free geometry, Math. Struct. in Comp. Science 16 (2006) 115-137. pdf

- G. Gerla, Popper's verisimilitude theory and point-free geometry, Journal of Philosophical Logic, 36 (2007) 707-733. pdf

- 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. pdf

- C. Coppola, G. Gerla, T. Pacelli, The category of fuzzy subsets and point-free ultrametric spaces. pdf

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. Whiteheadpdf

 

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) pdf

- 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). pdf

- Gerla G., Vaccaro V., Modal Logic and Model Theory, Studia Logica, 43 (1984) 203-216. pdf

 

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)  pdf

- G. Gerla, La logica fuzzy ed il paradosso del mucchio di grano pdf

- G. Gerla, Destini programmati. pdf

- 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.