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On Conditionals

14 pagesPublished: December 18, 2015


We discuss the evaluation of conditionals. Under classical logic a conditional of the form "A implies B" is semantically equivalent to "not A or B". However, psychological experiments have repeatedly shown that this is not how humans understand and use conditionals.
We introduce an innovative abstract reduction system under the three-valued Łukasiewicz logic and the weak completion semantics, that allows us to reason abductively and by revision with respect to conditionals, in three values. We discuss the strategy of minimal revision followed by abduction and discuss two notions of relevance.
Psychological experiments will need to ascertain if these strategies and notions, or a variant of them, correspond to how humans reason with conditionals.

Keyphrases: conditionals, logic programming, non-monotonic reasoning

In: Georg Gottlob, Geoff Sutcliffe and Andrei Voronkov (editors). GCAI 2015. Global Conference on Artificial Intelligence, vol 36, pages 79--92

BibTeX entry
  author    = {Emmanuelle-Anna Dietz and Steffen H\textbackslash{}"olldobler and Lu\textbackslash{}'is Moniz Pereira},
  title     = {On Conditionals},
  booktitle = {GCAI 2015. Global Conference on Artificial Intelligence},
  editor    = {Georg Gottlob and Geoff Sutcliffe and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {36},
  pages     = {79--92},
  year      = {2015},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/7p4b}}
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