Paraconsistent Multivalued Logic and Coincidentia Oppositorum: Evaluation with Complex Numbers

Usó-Doménech J.L.¹, Nescolarde-Selva J.^1, , Pérez-Gonzaga S.¹ and M. J Sabán²

¹Department of Applied Mathematics, University of Alicante, Alicante, Spain

²Department of Philosophy, University Rey Juan Carlos, Madrid, Spain

Cite this paper:
Usó-Doménech J.L., Nescolarde-Selva J., Pérez-Gonzaga S. and M. J Sabán. Paraconsistent Multivalued Logic and Coincidentia Oppositorum: Evaluation with Complex Numbers. American Journal of Systems and Software. 2015; 3(1):1-12. doi: 10.12691/ajss-3-1-1

Abstract

Paraconsistent logic admits that the contradiction can be true. Let p be the truth values and P be a proposition. In paraconsistent logic the truth values of contradiction is . This equation has no real roots but admits complex roots . This is the result which leads to develop a multivalued logic to complex truth values. The sum of truth values being isomorphic to the vector of the plane, it is natural to relate the function V to the metric of the vector space R². We will adopt as valuations the norms of vectors. The main objective of this paper is to establish a theory of truth-value evaluation for paraconsistent logics with the goal of using in analyzing ideological, mythical, religious and mystic belief systems.

Keywords:
belief systems circle of truth coincidentia oppositorum contradiction complex number denier logic coordinations paraconsistency propositions truth values

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