92 Int. J. Reasoning-based Intelligent Systems, Vol. 1, Nos. 1/2, 2009 Copyright © 2009 Inderscience Enterprises Ltd. The development of paraconsistent annotated logic programs Kazumi Nakamatsu* School of Human Science and Environment, University of Hyogo, 1-1-12, Shinzaike-honcho, Himeji, 670-0092, Japan E-mail: nakamatu@shse.u-hyogo.ac.jp *Corresponding author Jair Minoro Abe Graduate Program in Production Engineering, ICET, Paulista University, and Institute For Advanced Studies, Department of Computer Science, University of Sao Paulo, Rua Dr. Bacelar, 1.212, São Paulo, SP, CEP 4026-002, Brazil E-mail: jairabe@uol.com.br Abstract: We have developed paraconsistent annotated logic programs called Extended Vector Annotated Logic Program with Strong Negation (EVALPSN) and applied it to various intelligent control and safety verification. We have also developed EVALPSN to deal with before-after (bf) relation between time intervals and applied it to process order control. The developed EVALPSN is called bf-EVALPSN. In this paper, we review the process of the development of EVALPSN and bf-EVALPSN and introduce the details of EVALPSN defeasible deontic reasoning. Keywords: paraconsistent logic; annotated logic; logic program; defeasible deontic reasoning; before-after relation. Reference to this paper should be made as follows: Nakamatsu, K. and Abe, J.M. (2009), ‘The development of paraconsistent annotated logic programs’, Int. J. Reasoning-based Intelligent Systems, Vol. 1, Nos. 1/2, pp.92–112. Biographical notes: Kazumi Nakamatsu is a Professor at School of Human Sciences and Environment at the University of Hyogo, Japan. He completed his PhD from Kyushu University, Fukuoka in 1999. Since 1992, he has been researching in application of paraconsistent logic programs. J.M. Abe received his Doctoral degree from University of Sao Paulo in 1992. He is currently a Full Professor at the Graduate Program in Production Engineering, Paulista University and a Coordinator of the logic and science theory area of Institute for Advanced Studies, University of Sao Paulo. His current research interest include paraconsistent annotated logic and application in AI, automation and robotics, biomedicine and production engineering. 1 Introduction The main purpose of paraconsistent logic is to deal with inconsistency in a framework of consistent logical systems. It has been almost six decades since the first paraconsistent logical system was proposed by Jaskowski (1948). It was four decades later that a family of paraconsistent logic called annotated logics was proposed in da Costa et al. (1989) and Subrahmanian (1987). They can deal with inconsistency with many truth values called annotation that should be attached to each atomic formula, although their semantics is basically two-valued. The paraconsistent annotated logic was developed from the viewpoint of logic programming, aiming at application to computer science such as the semantics for knowledge bases in Blair and Subrahmanian (1989), Kifer and Subrahmanian (1992) and Subrahmanian (1994). Furthermore, in order to deal with inconsistency and non-monotonic reasoning in a framework of annotated logic programming, the paraconsistent annotated logic program