Where the truth lies: a paraconsistent approach to Bayesian epistemology


  • Walter Carnielli
  • Juliana Bueno-Soler


Bayesian epistemology has close connections to inductive reasoning, accepting the view that inductive inferences should be analyzed in terms of epistemic probabilities. An important precept of Bayesian epistemology is the dynamics of belief change, with change in belief resulting from updating procedures based on new evidence.

The inductive relations between evidence E and hypotheses or theories H are essential, particularly the notions of plausibility, confirmation, and acceptability, which are critical but subject to several difficulties. As a non-deductive process, Bayesian reasoning
cannot itself be subjected to strict deductive logic, but it can take advantage of an enabling logical environment. The present paper
proposes that paraconsistent and paracomplete logics can be helpful for some questions of Bayesian epistemology, even to the point of being relevant in developing a legitimate paraconsistent Bayesian epistemology. By developing a novel probability theory based on the Logic of Evidence and Truth (LETF ), a logic that deals with evidence for or against a judgment, including contradictory or missing
evidence, we allow for the possibility of quantifying the degree of evidence attributed to a proposition through novel probability

We illustrate, through examples, some ways to address challenging problems in the area by using paraconsistent and paracomplete
paradigms. This topic is of significant interest not only in the philosophy of science but also in Artificial Intelligence and other emerging trends such as probabilistic networks and related models.

Acknowledgements: The authors thank Branden Fitelson, Tikhon Pshenitsyn, Stanislav Speranski, Julio Stern, and three anonymous referees for useful criticisms, suggestions, and com- ments on this article. This research is supported by the FAPESP Thematic Project
2020/16353-3 and by the National Council for Scientific and Technological Development (CNPq, Brazil), research grants 311433/2019-9, 303780/2022-3 and 408040/2021-1.

Keywords: Probability theories; Bayesian epistemology; Inductive reasoning; Conditionaliza- tion; Evidence; Paraconsistency; Paracompleteness.


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