Nando Prati - Academia.edu (original) (raw)

Papers by Nando Prati

Journal of Symbolic Logic, 1994

Partial models of the theory New Foundations (NF) introduced by Quine have already appeared in th... more Partial models of the theory New Foundations (NF) introduced by Quine have already appeared in the literature, but in every model the membership set of NF is missing. On the other hand, Jensen showed that “NF + Urelements” is consistent with respect to ZF and, in the model built there, the membership set of the theory exists, Here we build a partial model of NF from the one of Jensen in which the membership set exists.

Many discussions have been made on the problem of (i) What are Fuzzy Sets? since the origin of th... more Many discussions have been made on the problem of (i) What are Fuzzy Sets? since the origin of the theory. Due to the structure of Fuzzy Sets the first impression that many people have is that Fuzzy Sets are the distribution of a probability. Recent developments of many theories of uncertainty measures (belief functions, possibility and fuzzy measures, capacities) can make also think that a Fuzzy Set is the distribution of an uncertainty measure. Other problems arising inside the theory of Fuzzy Sets itself compel to seek a clear answer to the problem (i).

In this paper we introduce a new and more general kind of cooperative games in which players have... more In this paper we introduce a new and more general kind of cooperative games in which players have many alternatives to choose, or many goals to try to realize, but also have the possibility of abstaining or of being absent for a while. In these games we define coalitions and study their properties observing how it is possible to obtain all the classical definitions of cooperative game theory inside this new setting.

An axiomatization of fuzzy classes more general than usual fuzzy sets is proposed. Connections an... more An axiomatization of fuzzy classes more general than usual fuzzy sets is proposed. Connections and interpretations with other axiomatizations of set theory and fuzzy set theory are investigated.

In this paper we sketch the development and give a model of the formal version of a generalizatio... more In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.

Fuzzy Sets and Systems

Abstract In this paper, we introduce crisp utility functions with range in the class of fuzzy num... more Abstract In this paper, we introduce crisp utility functions with range in the class of fuzzy numbers. These utility functions can be employed to prove a generalization of the classical result of Cantor using partially ordered sets as domain of the utility functions. In particular, for every partially ordered countable set, we prove that it can be represented by an order preserving function (utility).

Journal of Symbolic Logic, Dec 1, 1994

Stochastica Revista De Matematica Pura Y Aplicada, 1988

Jsyml, 1994

The Genericity Conjecture, as stated in Beller-Jensen-Welch [82], is the following: (*) If O # / ... more The Genericity Conjecture, as stated in Beller-Jensen-Welch [82], is the following: (*) If O # / ∈ L[R], R ⊆ ω then R is generic over L. We must be precise about what is meant by "generic". Definition. (Stated in Class Theory) A generic extension of an inner model M is an inner model M [G] such that for some forcing notion P ⊆ M : (a) M, P is amenable and p is M, P-definable for ∆ ∼ 0 sentences. (b) G ⊆ P is compatible, closed upwards and intersects every M, P-definable dense D ⊆ P. A set x is generic over M if it is an element of a generic extension of M. And x is strictly generic over M if M [x] is a generic extension of M. Though the above definition quantifies over classes, in the special case where M = L and O # exists these notions are in fact first-order, as all L-amenable classes are ∆ ∼ 1 definable over L[O # ]. ¿From now on assume that O # exists.

Stochastica Revista De Matematica Pura Y Aplicada, 1992

Rivista Di Matematica Per Le Scienze Economiche E Sociali, 2001

We describe in this paper a variance reduction method based on control variates. The technique us... more We describe in this paper a variance reduction method based on control variates. The technique uses the fact that, if all stochastic assets but one are replaced in the payoff function by their mean, the resulting integral can most often be evaluated in closed form. We exploit this idea by applying the univariate payoff as control variate and develop a general Monte Carlo procedure, called Mean Monte Carlo (MMC). The method is then tested on a variety of multifactor options and compared to other Monte Carlo approaches or numerical techniques. The method is of easy and broad applicability and gives good results especially for low to medium dimension and in high volatility environments.

Theory and Decision, 2004

In this paper we study coalitions of indirect stockholders of a company showing that they can hav... more In this paper we study coalitions of indirect stockholders of a company showing that they can have different controlling power, and therefore different relevance in the control problem. We then introduce a suitable classification, and three algorithms to find all the coalitions of all relevances.

In this paper we sketch the development and give a model of the formal version of a generalizatio... more In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.

Fuzzy Sets and Systems, 1991

Fuzzy Sets and Systems, 1992

Two axiomatizations of fuzzy set theory have been proposed by Chapin and Weidner. The comparison ... more Two axiomatizations of fuzzy set theory have been proposed by Chapin and Weidner. The comparison and the interpretations between these axiomatizations and ZF already begun by Weidner is carried on further; in particular it is shown that ZF can be interpreted in both theories.

Journal of Symbolic Logic, 1994

Journal of Symbolic Logic, 1994

Mathematical Logic Quarterly, 1993

T h e theory New Foundations (NF) of Quine was introduced in [14]. This theory is finitely axioma... more T h e theory New Foundations (NF) of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [a] and

Journal of Symbolic Logic, 1994

Partial models of the theory New Foundations (NF) introduced by Quine have already appeared in th... more Partial models of the theory New Foundations (NF) introduced by Quine have already appeared in the literature, but in every model the membership set of NF is missing. On the other hand, Jensen showed that “NF + Urelements” is consistent with respect to ZF and, in the model built there, the membership set of the theory exists, Here we build a partial model of NF from the one of Jensen in which the membership set exists.

Many discussions have been made on the problem of (i) What are Fuzzy Sets? since the origin of th... more Many discussions have been made on the problem of (i) What are Fuzzy Sets? since the origin of the theory. Due to the structure of Fuzzy Sets the first impression that many people have is that Fuzzy Sets are the distribution of a probability. Recent developments of many theories of uncertainty measures (belief functions, possibility and fuzzy measures, capacities) can make also think that a Fuzzy Set is the distribution of an uncertainty measure. Other problems arising inside the theory of Fuzzy Sets itself compel to seek a clear answer to the problem (i).

In this paper we introduce a new and more general kind of cooperative games in which players have... more In this paper we introduce a new and more general kind of cooperative games in which players have many alternatives to choose, or many goals to try to realize, but also have the possibility of abstaining or of being absent for a while. In these games we define coalitions and study their properties observing how it is possible to obtain all the classical definitions of cooperative game theory inside this new setting.

An axiomatization of fuzzy classes more general than usual fuzzy sets is proposed. Connections an... more An axiomatization of fuzzy classes more general than usual fuzzy sets is proposed. Connections and interpretations with other axiomatizations of set theory and fuzzy set theory are investigated.

In this paper we sketch the development and give a model of the formal version of a generalizatio... more In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.

Fuzzy Sets and Systems

Abstract In this paper, we introduce crisp utility functions with range in the class of fuzzy num... more Abstract In this paper, we introduce crisp utility functions with range in the class of fuzzy numbers. These utility functions can be employed to prove a generalization of the classical result of Cantor using partially ordered sets as domain of the utility functions. In particular, for every partially ordered countable set, we prove that it can be represented by an order preserving function (utility).

Journal of Symbolic Logic, Dec 1, 1994

Stochastica Revista De Matematica Pura Y Aplicada, 1988

Jsyml, 1994

The Genericity Conjecture, as stated in Beller-Jensen-Welch [82], is the following: (*) If O # / ... more The Genericity Conjecture, as stated in Beller-Jensen-Welch [82], is the following: (*) If O # / ∈ L[R], R ⊆ ω then R is generic over L. We must be precise about what is meant by "generic". Definition. (Stated in Class Theory) A generic extension of an inner model M is an inner model M [G] such that for some forcing notion P ⊆ M : (a) M, P is amenable and p is M, P-definable for ∆ ∼ 0 sentences. (b) G ⊆ P is compatible, closed upwards and intersects every M, P-definable dense D ⊆ P. A set x is generic over M if it is an element of a generic extension of M. And x is strictly generic over M if M [x] is a generic extension of M. Though the above definition quantifies over classes, in the special case where M = L and O # exists these notions are in fact first-order, as all L-amenable classes are ∆ ∼ 1 definable over L[O # ]. ¿From now on assume that O # exists.

Stochastica Revista De Matematica Pura Y Aplicada, 1992

Rivista Di Matematica Per Le Scienze Economiche E Sociali, 2001

We describe in this paper a variance reduction method based on control variates. The technique us... more We describe in this paper a variance reduction method based on control variates. The technique uses the fact that, if all stochastic assets but one are replaced in the payoff function by their mean, the resulting integral can most often be evaluated in closed form. We exploit this idea by applying the univariate payoff as control variate and develop a general Monte Carlo procedure, called Mean Monte Carlo (MMC). The method is then tested on a variety of multifactor options and compared to other Monte Carlo approaches or numerical techniques. The method is of easy and broad applicability and gives good results especially for low to medium dimension and in high volatility environments.

Theory and Decision, 2004

In this paper we study coalitions of indirect stockholders of a company showing that they can hav... more In this paper we study coalitions of indirect stockholders of a company showing that they can have different controlling power, and therefore different relevance in the control problem. We then introduce a suitable classification, and three algorithms to find all the coalitions of all relevances.

In this paper we sketch the development and give a model of the formal version of a generalizatio... more In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.

Fuzzy Sets and Systems, 1991

Fuzzy Sets and Systems, 1992

Two axiomatizations of fuzzy set theory have been proposed by Chapin and Weidner. The comparison ... more Two axiomatizations of fuzzy set theory have been proposed by Chapin and Weidner. The comparison and the interpretations between these axiomatizations and ZF already begun by Weidner is carried on further; in particular it is shown that ZF can be interpreted in both theories.

Journal of Symbolic Logic, 1994

Journal of Symbolic Logic, 1994

Mathematical Logic Quarterly, 1993

T h e theory New Foundations (NF) of Quine was introduced in [14]. This theory is finitely axioma... more T h e theory New Foundations (NF) of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [a] and