The Marlo diagram can operate with an unlimited number of terms and is a powerful tool for the didactics of logic that could become a new model of the constitutive processes of reasoning. The diagram reconciles the Aristotelian logic of the middle term and the mathematical rigour through the generation of a network system that seeks to explain how cognitive systems organize information to anticipate and communicate their expectations.

Logical tree diagrams

In Marlo’s Diagram, it is possible to work with several terms.  Nowadays, it may develop the “first-orden-logic”: propositional and predicates logic. Diagrams are created when trying to add the ability of expressing implicit possibilities to the Venn’s diagrams and recombine their DNA with the connective network models. In López Aznar (2017), logic connectives are described, ↔,→,∨, ⊻, as the elimination of the different disjunctive issues that can be equally expressed either in the tree diagram or in the Marlo’s Diagram.

Keywords: diagrammatic reasoning, visualization, cognitive science.


1. The laws of thought and classes of reasoning

leyes activacion nodos EN INGLES

tipos de razonamiento INGLES

2  Logical connective in the logical tree diagrams

Cognitive systems encode their expectations in a communicable way. Based on experience, they establish what presences or absences are reasonable to expect based on others, and if it is reasonable to expect them in all or any occasions. Cognitive systems must use codes that allow them to communicate (more or less explicitly), on one hand, the sample space of all possibilities in play and, on the other hand, which of those possibilities should be eliminated before deciding what fits better the actual case.A declarative proposition expresses, in an explicit way, to what extent it is reasonable to expect B basing on A. If heeding the quantification of predicate, it also communicates, in an implicit way, to what extent it is reasonable to expect A on the basis of B.

Classical connectives can be represented in the Marlo’s Diagram by basing on the definitions that can be found in Frege’s Begriffsschrift. Each connective, except for conjunction, is defined by the possibilities that eliminates. This process allows to easily overcome the difficulty to express an exclusive disjunction ⊻ or a biconditional connective (iff) in network model. Symbolically, a variable is considered as universal when is represented by the subscript “x” and, when no such subscript appears, that variable is considered as particular. therefore, the subscript x means in Marlo’s diagram the same as the conditional in classical logic.

ImprimirModels of beliefs not only inform what things are or are not. In order to facilitate the decision-making process, cognitive systems also communicate to each other information about subjective certainty. With this subjective certainty, it can be foreseen the presence/absence of each type of object of the universe of discourse, for example “abc”, or the presence/absence of any of the partial perspectives of those objects, such as “ab, ac, bc, a, b, c”.  We distinguish:

3. Square of opposition

tabla de oposicion del juicio ingles.jpg

4. Alfa system

sistema alfa 1 en ingles

5. Exercises solved by diagrammatic reasoning

5.1 Propositional calculus.

Example 1

LÃfiGICA DE PREDICADOS

Example 2LÃfiGICA DE PREDICADOS

Example 3LÃfiGICA DE PREDICADOS

Example 4LÃfiGICA DE PREDICADOS

Example 5LÃfiGICA DE PREDICADOS

Example 6LÃfiGICA DE PREDICADOS

Example 7LÃfiGICA DE PREDICADOS

Example 8LÃfiGICA DE PREDICADOS

5.2 first-order logic

Example of Syllogism solved by visual reasoningLÃfiGICA DE PREDICADOS

Example of problem of first-order logic  with several terms solved by visual reasoning

LÃfiGICA DE PREDICADOS

Bibliography:

López Aznar, M.B. “Redes de expectativas lógico matemáticas, una herramienta para el desarrollo del razonamiento. En Federación Española de Asociaciones de Profesores de Matemáticas: Actas del VIII Congreso Iberoamericano de Educación Matemática. Del 10 al 14 de Julio. Madrid. 2017. pp 283-293. ISBN: 978-84-945722-3-4

López Aznar, M.B. (2018): El Diagrama de Marlo, una alternativa para trabajar la inteligencia lógico matemática. En Federación Española de Asociaciones de Profesores de Matemáticas: Actas del VIII Congreso Iberoamericano de Educación Matemática, del 10 al 14 de Julio. Madrid 2017. pp 202-211. ISBN: 978-84-945722-3-4

López Aznar, M.B.: Redes de expectativas Marlo: el conjunto como base de la inferencia. In Actas II Congreso Internacional de la Red española de Filosofía. Vol. VII. pp. 9-24, Madrid (2017a).

López Aznar, M.B.: Ser y estar en las redes de conocimiento: Resolución de problemas lógico matemáticos.: In Actas II Congreso Internacional de la Red española de Filosofía. Vol. VII, pp. 25-39, Madrid (2017b).

López Aznar, M. B. (2016). Innovación en didáctica de la lógica: el Diagrama de Marlo. En Rutas didácticas y de investigación en lógica, argumentación y pensamiento crítico. pp 105-154. Mijangos Martínez, T.; México: Academia Mexicana de la Lógica AC. Libro electrónico.

López Aznar, M.B. (2016). Lógica de predicados en el diagrama de Marlo, cuando razonar se convierte en un juego de niños. En: GARCÍA NORRO,J.J.; INGALA GÓMEZ, E.; ORDEN JIMÉNEZ, R.F. (coords.). Diotima o de la dificultad de enseñar filosofía. p 335-356. Madrid: Escolar y Mayo.

López Aznar, M.B. (2016). Estructura formal de los sistemas cognitivos desde el diagrama de Marlo. En ESTYLF 2016. XVIII Congreso Español sobre tecnologías y Lógicas fuzzy. Libro de resúmenes. pp 108, 109. alcaide Cristina. Donostia-San Sebastián.

López Aznar, M.B. (2015). Adiós a bArbArA y Venn. Lógica de predicados en el diagrama. Paideia. Revista de Filosofía y didáctica filosófica número 102. pp 35-52.

López Aznar, M. B.: Cálculo lógico de modelos proposicionales: La revolución del silogismo en el diagrama de Marlo. Círculo Rojo. El Ejido (2014).

 

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