It ain't necessarily so: Basic sequent systems for negative modalities

Ori Lahav, João Marcos, Yoni Zohar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We look at non-classical negations and their corresponding adjustment connectives from a modal viewpoint, over complete distributive lattices, and apply a very general mechanism in order to offer adequate analytic proof systems to logics that are based on them. Defining non-classical negations within usual modal semantics automatically allows one to treat equivalent formulas as synonymous, and to have a natural justification for a global version of the contraposition rule. From that perspective, our study offers a particularly useful environment in which negative modalities and their companions may be used for dealing with inconsistency and indeterminacy. After investigating modal logics based on arbitrary frames, we extend the results to serial frames, reflexive frames, functional frames, and symmetric frames. In each case we also investigate when and how classical negation may thereby be defined.

Original languageEnglish
Title of host publicationAdvances in Modal Logic, AiML 2016
EditorsStephane Demri, Lev Beklemishev, Andras Mate
Number of pages20
ISBN (Electronic)9781848902015
StatePublished - 2016
Externally publishedYes
Event11th Conference on Advances in Modal Logic, AiML 2016 - Budapest, Hungary
Duration: 30 Aug 20162 Sep 2016

Publication series

NameAdvances in Modal Logic


Conference11th Conference on Advances in Modal Logic, AiML 2016


  • Analyticity
  • Cut-admissibility
  • Negative modalities
  • Sequent systems

All Science Journal Classification (ASJC) codes

  • Logic
  • Computational Theory and Mathematics
  • Computational Mathematics


Dive into the research topics of 'It ain't necessarily so: Basic sequent systems for negative modalities'. Together they form a unique fingerprint.

Cite this