Osvaldo Skliar - Academia.edu (original) (raw)

Papers by Osvaldo Skliar

A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences... more A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences of bases of human DNA. The results obtained are displayed using the Square Wave Transform (SWT), an SWM tool. It is hypothesized that the results of this analysis can be of interest, in certain cases, to understand the functional role of some of those sequences. Preliminary data which make this hypothesis plausible are presented.

Preprints, 2024

A presentation is provided of a structural approach for the concurrent teaching of introductory p... more A presentation is provided of a structural approach for the concurrent teaching of introductory propositional calculus and set theory. The existence of isomorphism is shown between each law (or tautology) of propositional calculus and the form of a corresponding set which is equal to the universal set U considered.

bioRxiv, 2023

A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences... more A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences of bases of human DNA. The results obtained are displayed using the Square Wave Transform (SWT), an SWM tool. It is hypothesized that the results of this analysis can be of interest, in certain cases, to understand the functional role of some of those sequences. Preliminary data which make this hypothesis plausible are presented.

How to cite Complete issue More information about this article Journal's homepage in redalyc... more How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System

A review is presented of the correspondence existing in both classical bivalent logic (BL) and ca... more A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the equality of a) a set whose structure is isomorphic to the law considered in propositional calculus and b) the universal set. In addition to the operations of CFL considered previously by the authors, initial attention is given to the operations with infinite sets by considering two of them: the union of sets and the intersection of sets. Attention is also given to how propositional calculus in BL can be considered a particular case of propositional calculus in CFL, and how the theory of classical sets can be considered a particular case of the theory of fuzzy sets according to CFL.

ScienceOpen Preprints, 2023

A review is presented of the correspondence existing in both classical bivalent logic (BL) and ca... more A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the equality of a) a set whose structure is isomorphic to the law considered in propositional calculus and b) the universal set. In addition to the operations of CFL considered previously by the authors, initial attention is given to the operations with infinite sets by considering two of them: the union of sets and the intersection of sets. Attention is also given to how propositional calculus in BL can be considered a particular case of propositional calculus in CFL, and how the theory of classical sets can be considered a particular case of the theory of fuzzy sets according to CFL.

The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously... more The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT is used to analyze a sequence of samples (that is, of measured values) taken from an electroencephalographic recording. A computational tool, available at

Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the valid... more Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the validity of categorical syllogisms, and are used here for the analysis of diverse categorical syllogisms. As a preliminary example of a possible generalization of the use of inclusion diagrams, consideration is given also to an argument that includes more than two premises and more than three terms, the classic major, middle and minor terms in categorical syllogisms.

A description is provided of a method – the Set Equality Method (SEM) – to determine the validity... more A description is provided of a method – the Set Equality Method (SEM) – to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered – that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In s...

This is a variation of a previously presented method [1] for characterizing the shapes of plane f... more This is a variation of a previously presented method [1] for characterizing the shapes of plane figures. In addition to retaining the advantages of the original method, this variant includes one more: It is no longer necessary to halt a (simulated) diffusion process during the transient stage; that is, before arriving at an equilibrium. On the contrary, the longer the process takes, the more noticeable the difference becomes between the concave parts and the convex parts of the contours of the figures analyzed. Key words: shape characterization, contours of plane figures, diffusion process, concav-ities, convexities.

A presentation is provided of a method — the Membership Table Method (MTM) — to determine the val... more A presentation is provided of a method — the Membership Table Method (MTM) — to determine the validity of categorical syllogisms. This method makes it possible for each syllogism to be assigned a specific set. If this set is equal to the universal set U, then the categorical syllogism considered is valid, and if that set is not equal to U, then that categorical syllogism is not valid. In other words, any categorical syllogism is valid if and only if its respective set, according to the MTM, is equal to the universal set U. The conclusion of a valid categorical syllogism whose premises are true is true.

Revista de Matemática: Teoría y Aplicaciones, 2009

The notions “regularity index” and “randomness index” previously introduced for binary strings (2... more The notions “regularity index” and “randomness index” previously introduced for binary strings (2-ary) have been modified slightly and generalized for m-ary strings (m = 2, 3, 4, . . .). These notions are complementary and the regular/random dichotomy has been replaced by a gradation of values of regularity and of randomness. With this approach, the more regular an m-ary string, the less random it is, and vice versa. The distributions of frequencies of different length strings —2-ary and 3-ary strings— according to their indices of randomness, are shown by histograms.

The Square Wave Method (SWM), previously introduced for the analysis of signals and images, is pr... more The Square Wave Method (SWM), previously introduced for the analysis of signals and images, is presented here as a mathematical tool suitable for the analysis of time series and signals. To show the potential that the SWM has to analyze many different types of time series, the results of the analysis of a time series composed of a sequence of 10,000 numerical values are presented here. These values were generated by using the Mathematical Random Number Generator (MRNG).

Zenodo, 2022

A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validi... more A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered -- that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In some cases, as will be specified, it is possible to provide a second test for the validity of a syllogism whose validity was already proven, thus providing information about the logical form of categorical syllogisms.

This is a variation of a previously presented method [1] for characterizing the shapes of plane f... more This is a variation of a previously presented method [1] for characterizing the shapes of plane figures. In addition to retaining the advantages of the original method, this variant includes one more: it is no longer necessary to halt a (simulated) diusion process during the transient stage; that is, before arriving at an equilibrium. On the contrary, the longer the process takes, the more noticeable the dierence becomes between the concave parts and the convex parts of the contours of the figures analyzed.

Uniciencia, 2016

We present a new combinatorial approach to compute the transition probability corresponding to an... more We present a new combinatorial approach to compute the transition probability corresponding to an arbitrary pair of positions of a particle which follows a random walk on an n-dimensional lattice.The formulas presented here differ in form from the ones previously obtained for the same problem with another approach. Obviously the same numerical results follow from either one of these two approaches.

Revista de Matemática: Teoría y Aplicaciones, 2008

The “Square-Wave Method” (SWM) presented here is a new method for the systematic analysis of sign... more The “Square-Wave Method” (SWM) presented here is a new method for the systematic analysis of signals – either locally or globally – depending on only one variable (time). The SWM is based on a technique (previously described elsewhere) for the representation of this type of signals using a sum of trains of square waves. The SWM is applied here to several analytically characterized signals and to an audio signal.

ArXiv, 2018

A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although i... more A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although it is very simple, and easy to implement, it provides a very high level of security. According to this approach, a sequence of operations applied to a message ($M$) yields the encrypted message ($M_E$). In that series of operations, the one with the most important role is operation 6, which involves a random binary sequence (RBS) generated by using the Hybrid Random Number Generator (HRNG) or the Mathematical Random Number Generator (MRNG). A sequence of anti-operations applied to MEM_EME makes it possible to recover MMM.

A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences... more A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences of bases of human DNA. The results obtained are displayed using the Square Wave Transform (SWT), an SWM tool. It is hypothesized that the results of this analysis can be of interest, in certain cases, to understand the functional role of some of those sequences. Preliminary data which make this hypothesis plausible are presented.

Preprints, 2024

A presentation is provided of a structural approach for the concurrent teaching of introductory p... more A presentation is provided of a structural approach for the concurrent teaching of introductory propositional calculus and set theory. The existence of isomorphism is shown between each law (or tautology) of propositional calculus and the form of a corresponding set which is equal to the universal set U considered.

bioRxiv, 2023

A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences... more A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences of bases of human DNA. The results obtained are displayed using the Square Wave Transform (SWT), an SWM tool. It is hypothesized that the results of this analysis can be of interest, in certain cases, to understand the functional role of some of those sequences. Preliminary data which make this hypothesis plausible are presented.

How to cite Complete issue More information about this article Journal's homepage in redalyc... more How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System

A review is presented of the correspondence existing in both classical bivalent logic (BL) and ca... more A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the equality of a) a set whose structure is isomorphic to the law considered in propositional calculus and b) the universal set. In addition to the operations of CFL considered previously by the authors, initial attention is given to the operations with infinite sets by considering two of them: the union of sets and the intersection of sets. Attention is also given to how propositional calculus in BL can be considered a particular case of propositional calculus in CFL, and how the theory of classical sets can be considered a particular case of the theory of fuzzy sets according to CFL.

ScienceOpen Preprints, 2023

A review is presented of the correspondence existing in both classical bivalent logic (BL) and ca... more A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the equality of a) a set whose structure is isomorphic to the law considered in propositional calculus and b) the universal set. In addition to the operations of CFL considered previously by the authors, initial attention is given to the operations with infinite sets by considering two of them: the union of sets and the intersection of sets. Attention is also given to how propositional calculus in BL can be considered a particular case of propositional calculus in CFL, and how the theory of classical sets can be considered a particular case of the theory of fuzzy sets according to CFL.

The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously... more The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT is used to analyze a sequence of samples (that is, of measured values) taken from an electroencephalographic recording. A computational tool, available at

Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the valid... more Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the validity of categorical syllogisms, and are used here for the analysis of diverse categorical syllogisms. As a preliminary example of a possible generalization of the use of inclusion diagrams, consideration is given also to an argument that includes more than two premises and more than three terms, the classic major, middle and minor terms in categorical syllogisms.

A description is provided of a method – the Set Equality Method (SEM) – to determine the validity... more A description is provided of a method – the Set Equality Method (SEM) – to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered – that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In s...

This is a variation of a previously presented method [1] for characterizing the shapes of plane f... more This is a variation of a previously presented method [1] for characterizing the shapes of plane figures. In addition to retaining the advantages of the original method, this variant includes one more: It is no longer necessary to halt a (simulated) diffusion process during the transient stage; that is, before arriving at an equilibrium. On the contrary, the longer the process takes, the more noticeable the difference becomes between the concave parts and the convex parts of the contours of the figures analyzed. Key words: shape characterization, contours of plane figures, diffusion process, concav-ities, convexities.

A presentation is provided of a method — the Membership Table Method (MTM) — to determine the val... more A presentation is provided of a method — the Membership Table Method (MTM) — to determine the validity of categorical syllogisms. This method makes it possible for each syllogism to be assigned a specific set. If this set is equal to the universal set U, then the categorical syllogism considered is valid, and if that set is not equal to U, then that categorical syllogism is not valid. In other words, any categorical syllogism is valid if and only if its respective set, according to the MTM, is equal to the universal set U. The conclusion of a valid categorical syllogism whose premises are true is true.

Revista de Matemática: Teoría y Aplicaciones, 2009

The notions “regularity index” and “randomness index” previously introduced for binary strings (2... more The notions “regularity index” and “randomness index” previously introduced for binary strings (2-ary) have been modified slightly and generalized for m-ary strings (m = 2, 3, 4, . . .). These notions are complementary and the regular/random dichotomy has been replaced by a gradation of values of regularity and of randomness. With this approach, the more regular an m-ary string, the less random it is, and vice versa. The distributions of frequencies of different length strings —2-ary and 3-ary strings— according to their indices of randomness, are shown by histograms.

The Square Wave Method (SWM), previously introduced for the analysis of signals and images, is pr... more The Square Wave Method (SWM), previously introduced for the analysis of signals and images, is presented here as a mathematical tool suitable for the analysis of time series and signals. To show the potential that the SWM has to analyze many different types of time series, the results of the analysis of a time series composed of a sequence of 10,000 numerical values are presented here. These values were generated by using the Mathematical Random Number Generator (MRNG).

Zenodo, 2022

A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validi... more A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered -- that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In some cases, as will be specified, it is possible to provide a second test for the validity of a syllogism whose validity was already proven, thus providing information about the logical form of categorical syllogisms.

This is a variation of a previously presented method [1] for characterizing the shapes of plane f... more This is a variation of a previously presented method [1] for characterizing the shapes of plane figures. In addition to retaining the advantages of the original method, this variant includes one more: it is no longer necessary to halt a (simulated) diusion process during the transient stage; that is, before arriving at an equilibrium. On the contrary, the longer the process takes, the more noticeable the dierence becomes between the concave parts and the convex parts of the contours of the figures analyzed.

Uniciencia, 2016

We present a new combinatorial approach to compute the transition probability corresponding to an... more We present a new combinatorial approach to compute the transition probability corresponding to an arbitrary pair of positions of a particle which follows a random walk on an n-dimensional lattice.The formulas presented here differ in form from the ones previously obtained for the same problem with another approach. Obviously the same numerical results follow from either one of these two approaches.

Revista de Matemática: Teoría y Aplicaciones, 2008

The “Square-Wave Method” (SWM) presented here is a new method for the systematic analysis of sign... more The “Square-Wave Method” (SWM) presented here is a new method for the systematic analysis of signals – either locally or globally – depending on only one variable (time). The SWM is based on a technique (previously described elsewhere) for the representation of this type of signals using a sum of trains of square waves. The SWM is applied here to several analytically characterized signals and to an audio signal.

ArXiv, 2018

A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although i... more A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although it is very simple, and easy to implement, it provides a very high level of security. According to this approach, a sequence of operations applied to a message ($M$) yields the encrypted message ($M_E$). In that series of operations, the one with the most important role is operation 6, which involves a random binary sequence (RBS) generated by using the Hybrid Random Number Generator (HRNG) or the Mathematical Random Number Generator (MRNG). A sequence of anti-operations applied to MEM_EME makes it possible to recover MMM.