Constructive Discursive Logic: Paraconsistency in Constructivism Seiki Akama, Jair Minoro Abe and Kazumi Nakamatsu Abstract We propose a constructive discursive logic with strong negation CDLSN based on Nelson’s constructive logic N  as a constructive version of Jaśkowski’s discursive logic. In CDLSN, discursive negation is defined similar to intuitionistic negation and discursive implication is defined as material implication using dis- cursive negation. We give an axiomatic system and Kripke semantics with a completeness proof. We also discuss some possible applications of CDLSN for common-sense reasoning. Keywords Jaśkowski  Constructive discursive logic  Common-sense reasoning 1 Introduction Jaśkowski proposed discursive logic (or discussive logic) in 1948. It is the first formal paraconsistent logic which is classified as a non-adjunctive system; see Jaśkowski [10]. The gist of discursive logic is to consider the nature of our ordinary discourse. In a discourse, there are several participants who have some information, beliefs, and such. In this regard, truth is formalized by means of the sum of opinions supplied by participants. Even if each participant has consistent information, some participant could be inconsistent with other participants. S. Akama (&) 1-20-1 Higashi-Yurigaoka, Asao-Ku, Kawasaki 215-0012, Japan e-mail: akama@jcom.home.ne.jp J.M. Abe Paulista University, São Paulo, Brazil e-mail: jairabe@uol.com.br K. Nakamatsu University of Hyogo, Himeji, Japan e-mail: nakamatsu@shse.u-hyogo.ac.jp © Springer International Publishing Switzerland 2015 J.M. Abe (ed.), Paraconsistent Intelligent-Based Systems, Intelligent Systems Reference Library 94, DOI 10.1007/978-3-319-19722-7_2 23