Presumptive Reasoning in a Paraconsistent Setting

Sabine Frittella, Daniil Kozhemiachenko, Bart Verheij

We explore presumptive reasoning in the paraconsistent case. Specifically, we provide semantics for non-trivial reasoning with presumptive arguments with contradictory assumptions or conclusions. We adapt the case models proposed by Verheij [25, 26] and define the paraconsistent analogues of the three types of validity defined therein: coherent, presumptively valid, and conclusive ones. To formalise the reasoning, we define case models that use BD△, an expansion of the Belnap–Dunn logic with the Baaz Delta operator. We also show how to recover presumptive reasoning in the original, classical context from our paraconsistent version of case models. Finally, we construct a two-layered logic over BD△ and biG (an expansion of Gödel logic with a coimplication) and obtain a faithful translation of presumptive arguments into formulas.

The paper was presented by Daniil Kozhemiachenko at the TARK 2023 conference in Oxford.

The proceedings version of the paper has DOI 10.4204/EPTCS.379.19.

EPTCS provides information about the paper at

A preprint version was posted on arXiv at

Manuscript (in PDF-format)

Frittella, S., Kozhemiachenko, D., & Verheij, B. (2023). Presumptive Reasoning in a Paraconsistent Setting. Theoretical Aspects of Rationality and Knowledge 2023 (TARK 2023). EPTCS 379 (ed. Verbrugge, R.). 244-233.

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