An Implementation of Propositional Logic Resolution Applying a Novel Specific Algebra

 

Eduardo Zurek¹, Mayra Zurbaran², Margarita Gamarra³, and Pedro Wightman⁴

 

¹ Research in Robotics and Intelligent Systems group at the Universidad del Norte, Barranquilla, Colombia (e-mail: ezurek@uninorte.edu.co).

² GReCIS group at Universidad del Norte, Barranquilla, Colombia (e-mail: mzurbaran@uninorte.edu.co).

³ IET group, Department of Electronic and Telecommunication Engineering, Universidad Autónoma del Caribe, Barranquilla, Colombia (e-mail: margarita.gamarra@edu.co).

⁴ GReCIS group at the Universidad del Norte, Barranquilla, Colombia (e-mail: pwightman@uninorte.edu.co).

 

Manuscript received on February 25, 2015
Accepted for publication on June 23, 2015
Published on October 15, 2015

 

Abstract

This paper presents a methodology for evaluating propositional logic satisfiability using resolution-refutation. The method applies a strategy based on an algebra developed by the authors that estimates the possible outcomes of the expression and generates a logic value for refuting or accepting the satisfiability of the argument.

Key words: Algebraic logic, propositional logic, resolution-refutation, tableau.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

REFERENCES

[1] J. T. Palma Méndez and R. L. Marín Morales, Inteligencia artificial: técnicas, métodos y aplicaciones. Aravaca: McGraw-Hill Interamericana de España, 2008.         [ Links ]

[2] R. Jansana, "Propositional consequence relations and algebraic logic," in The Stanford Encyclopedia of Philosophy, 2011.         [ Links ]

[3] M. D'Agostino and D. M. Gabbay, Handbook of tableau methods. Springer, 1999.         [ Links ]

[4] I. Niemela, "Implementing circumscription using a tableau method," in ECAI, 1996, pp. 80-84.         [ Links ]

[5] P. Wolper, "The tableau method for temporal logic: An overview," Logique et Analyse, vol. 28, no. 110-111, pp. 119-136, 1985.         [ Links ]

[6] T. A. Junttila and I. Niemela, "Towards an efficient tableau method for Boolean circuit satisfiability checking," in Computational Logic - CL 2000, Springer, 2000, pp. 553-567.         [ Links ]

[7] M. Y. Vardi, "Boolean satisfiability: Theory and engineering," Commun. ACM, vol. 57, no. 3, pp. 5, 2014.         [ Links ]

[8] "Propositional Logic | Internet Encyclopedia of Philosophy".         [ Links ]

[9] P. D. Magnus, "An Introduction to formal logic," University at Albany: State University of New York, 2008.         [ Links ]

[10] A. J. A. Robinson and A. Voronkov, Handbook of Automated Reasoning. Elsevier, 2001.         [ Links ]

[11] H. K. Büning and T. Lettmann, Propositional Logic: Deduction and Algorithms. Cambridge University Press, 1999.         [ Links ]

[12] "MATLAB-The language of technical computing." [Online]. Available: http://www.mathworks.com/products/matlab/. [Accessed: 23-Jan-2015]         [ Links ].

[13] L. F. del Cerro, D. Fauthoux, O. Gasquet, A. Herzig, D. Longin, and F. Massacci, "Lotrec: The generic tableau prover for modal and description logics," in Automated Reasoning, Springer, 2001, pp. 453-458.         [ Links ]

[14] "Java Software Oracle." [Online]. Available: https://www.oracle.com/java/index.html. [Accessed: 23-Jan-2015]         [ Links ].