Conflict without contradiction: paraconsistency and axiomatizable conflict toleration hierarchies in Evidence Logic

Don Faust



Evidence Logic (EL) goes beyond Classical Logic (CL) in its primitive expressivity by including both confirmatory and refutatory predications, additionally equipped with evidence level annotations. Previous work has characterized the Boolean Sentence Algebras (BSAs) of the monadic, functional, and undecidable varieties of EL [4], [5]. From the perspective that our knowledge of the world is often less-than-certain, that is to say “evidential”, application-wise EL is conceptually antecedent to CL and provides a broad foundational framework wherein axiomatizable extensions reach out to a number of the more domain-specific recent constructions of logics for the representation and processing of uncertainty in Artificial Intelligence (AI). In this paper we analyze EL from this point of view in sections 1 and 2. In Section 3 the relationship between this work and issues in paraconsistency is briefly explored.

Full Text:



Dempster, A., “Upper and lower probabilities induced by a multivalued mapping”, Annals Of Mathematical Statistics 388 (1967), 325–339.

Dempster, A., “A generalization of Bayesian inference”, J. Royal Statistical Society 30 (series B) (1968).

Faust, D., “The Boolean algebra of formulas of first-order logic”, Annals of Mathematical Logic 23 (1982), 27–53. (MR 84f:03007)

Faust, D., “The concept of evidence”, Inter. J. of Intelligent Systems 15 (2000), 477–493.

Faust, D., “The concept of evidence” (abstract), Journal of Symbolic Logic 59 (1994), 347–348.

Faust, D., “Aspects of negation related to evidential conflict”, submitted.

Faust, D., “Evidence and negation” (abstract), Bulletin of Symbolic Logic 3 (1997), p. 364.

Faust, D., “The concept of negation”, Logic and Logical Philosophy 5 (1998), 35–48.

Faust, D., “Evidence Logic” (abstract), Bulletin of Symbolic Logic vol. 4 (1998), p. 86.

Faust, D., “Conflict without contradiction: noncontradiction as a scientific modus operandi”, paper read at the World Congress of Philosphy, Boston (1998), available at

Popper, K., The Logic of Scientific Discovery, Harper, New York, 1965.

Priest, G., “What not? A defence of the dialetheic theory of negation”, to appear in Negation, D. Gabby & H. Wansing (ed.), published by Kluwer.

Quinlan, J., “Inferno: a cautious approach to uncertain inference”, Computer Journal 26 (1983), 255–269.

Russell, B., “Vagueness”, Australian Journal of Philosophy and Psychology 1 (1923), 84–92.

Shafer, G., A Mathematical Theory of Evidence, Princeton University Press, 1976.

Smiley, T., and G. Priest, “Can contradictions be true?”, Proceedings of the Aristotelian Society, Suppl. vol. 67 (1993), 17–54.

Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism