Modal (logic) paraconsistency

Philippe Besnard*, Paul Wong

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

2 Citations (Scopus)


According to the standard definition, a logic is said to be paraconsistent if it fails the (so-called) rule of ex falso: i.e., α, ¬α ∀ β.Thus, paraconsistency captures an important sense in which a logic is inconsistency-tolerant, namely when arbitrary inference is prohibited in the presence of inconsistencies. We investigate a family of notions of paraconsistency within the context of modal logics. An illustration comes from an epistemic version of the lottery paradox showing how important it sometimes is to distinguish between ordinary and higher order beliefs: A logic may fail to tolerate inconsistent beliefs at a given level while tolerating inconsistent beliefs across different levels. We identify a few properties arising from some well-known modal theorems and inference rules in order to classify modal logics according to their capacity to tolerate modalized inconsistencies. In doing so, we show various relationships among these logics.

Original languageEnglish
Pages (from-to)540-551
Number of pages12
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publication statusPublished - 2003
Externally publishedYes
Event7th European Conference, ECSQARU 2003 - Aalborg, Denmark
Duration: 2 Jul 20035 Jul 2003


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