Non-Normal Worlds and Representation

Francesco Berto

Research output: Chapter in Book/Report/Conference proceedingChapter


World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic coun- terexamples to such irrelevant entailments as (A ¿ ¬A) ¿ B, A ¿ (B¿¬B), or A ¿ (B ¿ B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic side, with a representation operator, (R), and on the semantic side, with particularly anarchic non-normal worlds. This combination easily invalidates unwelcome “logical omniscience” inferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment (R) in order to express more vertebrate kinds of conceivability.
Original languageEnglish
Title of host publicationThe Logica Yearbook 2011
EditorsMichal Pelis, Vit Puncochar
Place of PublicationLondon
PublisherCollege Publications
Number of pages16
ISBN (Print)978-1-84890-071-4
Publication statusPublished - 23 May 2012

Publication series

NameThe Logica Yearbook
PublisherCollege Publications


  • Epistemic logic
  • Non-normal worlds
  • Modal Logic


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