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1. Sentential logics based on k-cyclic modal pseudocomplemented De Morgan algebras

Author

Figallo-Orellano, Aldo, Perez-Gaspar, Miguel, and Ramirez-Contreras, Juan Manuel

Subjects
Mathematics - Logic
Abstract

The study of the theory of operators over modal pseudocomplemented De Morgan algebras was begun in the papers [15] and [16]. In this paper, we introduce and study the class of modal pseudocomplemented De Morgan algebras enriched by an automorphism k-periodic (or Ck-algebras) where k is a positive integer; for k = 2 the class coincides with the one studied in [15] where the automorphism works as a new unary operator. In the first place, we prove the class Ck-algebras is a semisimple variety and we determine the generating algebras. Afterwards, we calculate the cardinality of the free Ck-algebra with n generator. After the algebraic study, we built two sentential logics that have as algebraic counterpart the class of Ck-algebras that we denote L

Published
2021

2. A fuzzy description logic based IoT framework: Formal verification and end user programming.

Author

Pérez-Gaspar, Miguel, Gomez, Javier, Bárcenas, Everardo, and Garcia, Francisco

Abstract

The Internet of Things (IoT) has become one of the most popular technologies in recent years. Advances in computing capabilities, hardware accessibility, and wireless connectivity make possible communication between people, processes, and devices for all kinds of applications and industries. However, the deployment of this technology is confined almost entirely to tech companies, leaving end users with only access to specific functionalities. This paper presents a framework that allows users with no technical knowledge to build their own IoT applications according to their needs. To this end, a framework consisting of two building blocks is presented. A friendly interface block lets users tell the system what to do using simple operating rules such as "if the temperature is cold, turn on the heater." On the other hand, a fuzzy logic reasoner block built by experts translates the ambiguity of human language to specific actions to the actuators, such as "call the police." The proposed system can also detect and inform the user if the inserted rules have inconsistencies in real time. Moreover, a formal model is introduced, based on fuzzy description logic, for the consistency of IoT systems. Finally, this paper presents various experiments using a fuzzy logic reasoner to show the viability of the proposed framework using a smart-home IoT security system as an example. [ABSTRACT FROM AUTHOR]

Published
2024
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8. Un estudio de la lógica CG´3

Author

Pérez Gaspar, Miguel, Villa Hernández, David, and Arrazola Ramírez, José Ramón Enrique

Subjects
Kripke, Saul A., 1940, CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA, Lógica simbólica y matemática, Física matemática, Lógica matemática no clásica, Inconsistencia (Lógica), Semántica--Modelos matemáticos, Teoría de campos (Física)
Abstract

"Un punto de partida fundamental para ese proyecto, no obstante, y el análisis del desarrollo lógico-formal y conceptual de la ley lógica, conocida por su adagio latino, ex falso sequitur quodlibet, la cual establece que se puede admitir lícitamente cualquier conclusión mediante inconsistencia o contradicción lógica. Esta ley lógica funciona como divisor de aguas y codifica la cláusula fundamental del fenómeno lógico de la trivialización formal. De hecho, es válida en la Lógica Clásica y en la Intuicionista. No es válida, en general en cualquier clase de lógicas paraconsistentes. De su importancia como indicador inicial de posturas lógico-teóricas de carácter paraconsistente; que es una piedra de toque, esa regla es decisiva en la identificación de autores que fueron favorables o desfavorables a un enfoque que hoy puede ser considerado paraconsistente, ya sea en un sentido amplio o en un sentido estricto [18]. El objetivo principal de esta tesis es buscar una semántica de tipo Kripke y una axiomatización tipo Hilbert para la Lógica Paraconsistente CG3."

Published
2018

9. Kripke-type Semantics for [formula omitted].

Author

Borja Macías, Verónica and Pérez-Gaspar, Miguel

Subjects
KRIPKE semantics, FUZZY logic, MATHEMATICAL logic, MATHEMATICAL analysis, MANY-valued logic, NONCLASSICAL mathematical logic
Abstract

In Osorio et al. [Revisiting Z. Notre Dame Journal of Formal Logic , 55(1):129–155, 2014] introduced a paraconsistent three-valued logic, the logic CG 3 ′ which was named after the logic G 3 ′ due to the close relation between them. Authors defined CG 3 ′ via the three-valued matrix that defines G 3 ′ but changing the set of designated truth values. In this article we present a brief study of the Kripke-type semantics for some logics related with CG 3 ′ before constructing a Kripke-type semantics for it. [ABSTRACT FROM AUTHOR]

Published
2016
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