Paraconsistent conjectural deduction based on logical entropy measures. I: \(C\)-systems as non-standard inference framework. (English) Zbl 1185.03046
Summary: A conjectural inference is proposed, aimed at producing conjectural theorems from formal conjectures assumed as axioms, as well as admitting contradictory statements as conjectural theorems. To this end, we employ Paraconsistent Informational Logic, which provides a formal setting where the notion of conjecture formulated by an epistemic agent can be defined. The paraconsistent systems on which conjectural deduction is based are sequent formulations of the \(C\)-systems presented by W. A. Carnielli and J. Marcos [“A taxonomy of \(C\)-systems”, in: W. A. Carnielli et al. (eds.), Paraconsistency. The logical way to the inconsistent. Proceedings of the 2nd world congress on paraconsistency, WCP 2000, in honor of Newton da Costa on the occasion of his 70th birthday, São Paulo, Brazil, May 12–19, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 228, 1–94 (2002; Zbl 1036.03022)]. Thus, conjectural deduction may also be considered to be a tool for investigating the properties of paraconsistency in general.
MSC:
| 03B53 | Paraconsistent logics |
Citations:
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