A Simple Paraconsistent Logic without Addition

doi:10.1007/s10992-025-09827-1

A Simple Paraconsistent Logic without Addition

2026-01-01

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Philipp Mayr *

DOI：10.1007/s10992-025-09827-1

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This paper develops a logic that invalidates Ex Contradictione Quodlibet but delivers a package of other results that are unusual for a paraconsistent logic. In particular, it validates Disjunctive Syllogism. But it also is structurally classical, meaning that its consequence relation is reflexive, monotonic, and transitive. As a trade-off it will invalidate the Law of Addition which allows us to infer a disjunction from one of its disjuncts. The logic will also allow for certain logical theorems such as instances of the Law of the Excluded Middle and the Law of Non-Contradiction. This logic is captured with both a natural proof system and a simple modal model theory, showing the relevant completeness theorem. I discuss adding a conditional operator and briefly explore routes for responding to worries about some less intuitive results of the logic such as the logical invalidity of modus tollens.

Keywords:

Paraconsistent logic

Inferentialism

Disjunction

Relevance

A Simple Paraconsistent Logic without Addition

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