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Rubén de la Peña Ramos Lógicas para la Inf. y la I.A.
© 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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Contenidos Introducción Syntax Prove! Compare!
Detalles de Implementación Conclusiones Enlaces © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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1. Introducción © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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1. Introducción (i) ¿Qué es Easy Logic? Objetivo
“Interfaz web interactiva para demostradores de teoremas” (Fernando Soler Toscano et al.) Objetivo Dadas unas premisas y una conclusión: Mostrar los pasos seguidos para probar la conclusión a partir de las premisas Mostrar un contra-ejemplo © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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1. Introducción (ii) Procedimiento de Cálculo Disponibles:
Tablas de verdad. Normalización Tableaux Semánticos Deducción Natural Cálculo de Secuentes © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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1. Introducción (iii) http://easylogic.yi.org
© 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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2. Syntax © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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2. Syntax (i) Conectivas Lógicas Orden de Preferencia
Negación: -a Doble Negación: -(-a) Conjunción: a & b Disyunción: a v b Condicional: a=>b Bicondicional: a<=>b Orden de Preferencia a v b & c a v ( b & c ) Asociatividad a & b & c ( a & b ) & c a => b => c a => ( b => c ) Variables Proposicionales Letras / Combinaciones de letras ( salvo “v”) © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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2. Syntax (ii) Ejemplo Premisas: a b, c Conclusión: b
© 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! (i) Premises Conclusion Select a Calculus Syntactic Tree
Premisas de la fórmula a probar Conclusion Conclusión de la fórmula a probar Select a Calculus Procedimiento de cálculo a utilizar Syntactic Tree Árbol sintáctico de la fórmula © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! (ii) © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! (iii) Procedimientos de Cálculo: CASO A: { a b, a} b
Tablas de verdad. Normalización Tableaux Semánticos Deducción Natural Cálculo de Secuentes CASO A: { a b, a} b CASO B: { a b, a} b © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Tablas de Verdad (i)
“Un razonamiento con premisas p1 … pn y conclusión c es correcto si p1 … pn → c es siempre evaluado a 1 (Se debe considerar cada posible valoración).” © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Tablas de Verdad (ii)
CASO A © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Tablas de Verdad (iii)
CASO B © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Normalización (i)
“Un razonamiento con premisas p1 … pn y conclusión c es correcto si la forma normal conjuntiva (CNF) de ( p1 ∧ … ∧ pn ) → c tiene literales complementarios en cada disyunción.” © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Normalización (ii)
CASO A © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Normalización (iii)
CASO B © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Tableaux Sem. (i)
“Un razonamiento con premisas p1 … pn y conclusión c es correcto si el tableaux de { p1, … ,pn, ¬c } es cerrado, es decir, cada rama acaba en ” © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Tableaux Sem. (ii)
CASO A © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Tableaux Sem. (iii)
CASO B © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Deducción Natural (i)
“Un razonamiento con premisas p1 … pn y conclusión c es correcto si partiendo del conjunto de premisas p1 … pn podemos llegar a c mediante la aplicación de una serie de reglas.” © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Deducción Natural (ii)
CASO A © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Deducción Natural (iii)
CASO B © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Cálculo Secuentes (i)
“(O cálculo de consecuencias lógicas) Un razonamiento con premisas p1 … pn y conclusión c es correcto si se puede demostrar el secuente: ( p1 ∧ … ∧ pn ) → c , lo que implica que el árbol de prueba esté completo (todas las ramas acaben con un axioma).” © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Cálculo Secuentes (ii)
CASO A © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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3. Prove! – Cálculo Secuentes (iii)
CASO B © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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4. Compare! © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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4. Compare! (i) © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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4. Compare! (ii) CASO A © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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4. Compare! (iii) CASO B © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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5. Implementación © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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5. Implementación Estructura de Easy Logic
© 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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6. Conclusiones © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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6. Conclusiones Aplicaciones Limitaciones
Usuarios Noveles: Herramienta de Aprendizaje Usuarios Avanzados: Excelente Complemento Limitaciones Solo soporta Lógica Proposicional Solventable Participación Usuarios © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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7. Enlaces © 2004 Microsoft Corporation. All rights reserved.
This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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7. Enlaces http://easylogic.yi.org/ ¡Fundamental!
Departamento de Filosofía y Lógica y Filosofía de la Ciencia de la Universidad de Sevilla. Introducción a la deducción natural. Cálculo de secuentes (en inglés). © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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¿ Preguntas ? Gracias © 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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Rubén de la Peña Ramos Lógicas para la Inf. y la I.A.
© 2004 Microsoft Corporation. All rights reserved. This presentation is for informational purposes only. Microsoft makes no warranties, express or implied, in this summary.
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