Lo que sigue es un listado de las asignaturas que imparto o he impartido en cursos anteriores durantes los últimos años.

Máster en Lógica y Filosofía de la Ciencia:

1. Metalógica I: Completud y sus Consecuencias
2. Lógicas de Orden Superior

Máster en Sistemas Inteligentes:

• Lógicas para la Red Semántica

Grado en Filosofía/Licenciatura Filosofía:

1. Lógica I
2. Lógica II
3. Aplicaciones de la Lógica
4. Historia y Filosofía de la Lógica
5. Extensiones y Aplicaciones de la Lógica
6. Teoría de Modelos
7. Seminarios de Lógica
8. Teoría de Conjuntos

Informática:

1. Lógica Matemática
2. Lógicas para la Informática y la Inteligencia Artificial

Últimos proyectos financiados

Intensional Logic as a Unifier: Logic, Language and Philosophy. (FFI2017-82554)

MICINN. Investigadoras responsables. María G. Manzano Arjona y María A. Huertyas Sánchez. Duración prevista: hasta: diciembre 2019.

SUMMARY: The research program to be developed in this project complements our previous research project: Hybrid Intensional Logic. We have defined several systems of intensional logic from a formal point of view; namely, Hybrid Type Theory (HTT), Equational Hybrid Propositional Type Theory (EHPTT) and Intensional Hybrid Type Theory (IHTT).
During the elaboration of the previous project we were aware of the fact that our systems were trying to solve a variety of problems that arise not only in humanities but also in science. Moreover, we now believe that intensionality can serve as a unifying tool from a logical perspective as well as from a linguistic and philosophical one. That is the main objective of this research project.

Logic:
We will define translations between the logical systems we have developed in the previous project to a common logical framework.
In the same line, the logical systems we have defined, HTT, EHPTT, etc. combine features of a variety of existing logical systems. Since Combined Logic is a well-known research branch that studies and classifies combined systems, we would like to investigate where to place ours.

Language and Philosophy:
In the existing logical literature most of the examples in natural language contain descriptions but the formal development of descriptions is not satisfactory. What we plan to do is to try to establish links with the research that is taking place in philosophy of language and to unify results obtained in both branches of our area. 
Most of the issues treated in intensional logic have their roots in philosophy. A look of the history reveals that modal notions (like necessity or possibility) as well as the distinctions between de re and de dicto reading of sentences are present all over. 
The treatment of the identity concept and its distinction from the also binary relation of equal denotation between terms of the formal language can also be analyzed from a philosophical perspective. In the previous project we treated the issue from a technical point of view but now we would like to carry out a historical revision to see how both treatments converge.
In particular, we were surprised by the the philosophical concept of nominalism. The models we have created in our completeness proofs need only terms of the language and maximal consistent sets of sentences with particular extra properties. We wonder if, following ideas of Leon Henkin, we can dispense with sets and relations in the definition of models by using sets of formulas instead and limit the existing objects to individuals. When modal, hybrid and intensional logics are taken into account this view gains force as it is in consonance with Carnap’s view of worlds as maximal consistent sets of sentences.
The problem of intensionality in the modal realm is further accentuated when epistemic, doxastic, or imaginary entities are considered. For example, several epistemic agents in the same system may be assigning different references to the same term or to two terms denoting the same entity. We would like to address the problem of intensionality beyond individuals, whether real or fictitious, in the context of the logic of fiction.

Pedagogy:
Finally, our long experience on teaching reveals that first-order or higher order non-classical logics are rarely teached and we limit ourselves to propositional non-classical logics. We would like to elaborate easy, attractive and simplified systems to be used in our logic courses in philosophy

Hybrid Intensional Logic (FFI2013-47126-P)

MICINN. Investigador responsable. Duración prevista: hasta: 2016.

SUMMARY: Intensional Logic as understood here is a research program based upon the broad presupposition that so-called “intensional contexts” in natural language can be explained semantically by the idea of multiple reference. The inspiration for the semantic theories to be developed in this project is diverse, coming from linguistics, traditional philosophy, philosophical logic, philosophy of science, but also from computer science and mathematical logic.

The general goal of this project is to investigate how far the combination of type theoretic machinery with hybrid logic can solve historical and contemporary problems (both philosophical and technical) in intensional logic, and to try and solve them in a simple, general, easy-to-use, framework.  This main goal has the following subgoals:

• To systematically study and classify existing intensional logic systems and their problems. Both philosophical and technical issues will need to be considered.
• To explore historical aspects of intensional logic. 
• To construct and explore various hybrid (typed) intensional logics that address expressivity and completeness gaps in current intensional logic. To explore, when appropriate, computational aspects of the new systems.
• To emphasize the educational aspect of this work, particularly e-learning educational aspects. We intend to introduce “pedagogical” versions of intensional logics, maintain and improve branches of the summa logica portal (http://logicae.usal.es ) and to  develope specific material for e-learning that meet current standards of interactivity.

Nociones de Completud (FFI2009-09345)

MICINN. Investigador responsable. Duración prevista: hasta: 2012.

SUMMARY: To reconcile the syntactic and semantic presentations of consequence is at the core of any logic.  This same idea can also be understood as a balancing act, between the expressive capacity of a formal language and the computational power of a particular presentation.

The goal of this project is to investigate these fundamental issues.  In particular, we have organized the work in the following three main lines:

• To investigate pure and applied logics, classic and non classic, focusing on algebraic, description and hybrid logics; aiming at, whenever possible, studying both first order and higher order versions. The common thread to investigate these formal languages is the completeness proof; starting with the pre-existing proofs for each system, and relating them to the expressive power of the logic. The study will also include incompleteness proofs. The first step is to obtain a “catalogue” of different completeness / incompleteness proofs, to study their similarities and differences. We will then analyse each proof aiming to understand when each different proof can be applied, and which are the exact information that each proof gives us about the logic.
• To investigate historical aspects of completeness.  We will take as central referent point Henkin's completeness proof, his doctoral thesis and his articles from 1949 and 1950.  Then investigate previous proofs, and the evolution of completeness theory since then.
• To include also pedagogical aspects, in particular concerning e-learning.  We want to use the notion of completeness to explain central ideas of logic in class.  We plan to extend the already existing digital library (Summa Logicae, http://logicae.usal.es) with texts and exercises concerning completeness; and we will develop new educational software.

Alumnos que finalizaron su tesis en este programa bajo mi dirección:

• Gabriela Hernández Deciderio, Capacidades de los sistemas lógicos formales: El caso de algunos sistemas lógicos clásicos y de lógica libre
• Manuel Crescencio Moreno Gómez, Intensions, Types and Existence
• Elías Fuentes Guillén. The Germanic Development of the Pre-Modern Notion of Number. From c. 1750 to Bolzano’s Rein analytischer Beweis

Alumnos que realizan actualmente la tesis de doctorado en este programa bajo mi dirección:

• Cuitláhuac Rodríguez Campos
• José Javier González López
• Julián Mauricio Valdés Toro
• Alfonso Cabanzo

Alumnos que realizaron el trabajo fin de máster bajo mi dirección:

• Luis Urtubey. Completud e Interpolación: un Enfoque a partir de la Generalización del Método de Constantes de Henkin
• Claudio Fuentes. Espacios de Filosofía en la Representación de Sistemas de Información: del Conocimiento Pragmático a la Construcción de Ontologías Formales
• Thomaida Andoni. Hybrid and Description Logic.
• Lluis Homen. TOPICS IN PROGRAMMING LANGUAGES, a Philosophical Analysis through the case of Prolog
• Manuel Crescencio Moreno. Los argumentos ontológicos clásicos
• Joan Casas Roma.  Lógica Temporal: perspectiva histórica y relación con los flujos del tiempo.
• Juan Uclés. Tools for Teaching Logic.
• Sofía Cárdenas Cortés. El Concepto de expresividad en Lógica.
• Pedro González Nuñez. Teoría de Tipos Parcial Híbrida
• José Javier González López. El Teorema de Lówenheim-Skolem: Conexiones y Consecuencias
• Samuel Cuello Muñoz. La aritmética de Peano y la Lógica de segundo orden.
• Daira Pinto Prieto. Modal Reduction Principles Across Relational Semantics.