Default Modal Systems as Algebraic Updates

V. Cassano, R. Fervari, C. Areces, and P. Castro. Default Modal Systems as Algebraic Updates. In M. Martins and I. Sedlár, editors, Dynamic Logic. New Trends and Applications - Third International Workshop, DaL\'i 2020, Prague, Czech Republic, October 9-10, 2020, Revised Selected Papers, Lecture Notes in Computer Science, pp. 103–119, Springer, 2020.

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Abstract

Default Logic refers to a family of formalisms designed to carry out non-monotonic reasoning over a monotonic logic (in general, Classical First-Order or Propositional Logic). Traditionally, default logics have been dened and dealt with via syntactic consequence relations. Here, we introduce a family of default logics dened over modal logics. First, we present these default logics syntactically. Then, we elaborate on an algebraic counterpart. We do the latter by extending the notion of a modal algebra to acommodate for the main elements of default logics: defaults and extensions. Our algebraic treatment of default logics concludes with an algebraic completeness result. To our knowledge, our approach is novel, and it lays the groundwork for studying default logics from a dynamic logic perspective.

BibTeX

@InCollection{CassanoFAC20,
  author =       "V. Cassano and R. Fervari and C. Areces and P.
                 Castro",
  booktitle =    "Dynamic Logic. New Trends and Applications - Third
                 International Workshop, DaL{\'i} 2020, Prague, Czech
                 Republic, October 9-10, 2020, Revised Selected Papers",
  title =        "Default Modal Systems as Algebraic Updates",
  year =         "2020",
  editor =       "M. Martins and I. Sedl{\'a}r",
  pages =        "103--119",
  publisher =    "Springer",
  series =       "Lecture Notes in Computer Science",
  volume =       "12569",
  abstract =     "Default Logic refers to a family of formalisms
                 designed to carry out non-monotonic reasoning over a
                 monotonic logic (in general, Classical First-Order or
                 Propositional Logic). Traditionally, default logics
                 have been dened and dealt with via syntactic
                 consequence relations. Here, we introduce a family of
                 default logics dened over modal logics. First, we
                 present these default logics syntactically. Then, we
                 elaborate on an algebraic counterpart. We do the latter
                 by extending the notion of a modal algebra to
                 acommodate for the main elements of default logics:
                 defaults and extensions. Our algebraic treatment of
                 default logics concludes with an algebraic completeness
                 result. To our knowledge, our approach is novel, and it
                 lays the groundwork for studying default logics from a
                 dynamic logic perspective.",
  bibsource =    "dblp computer science bibliography, https://dblp.org",
  biburl =       "https://dblp.org/rec/conf/dali/CassanoFAC20.bib",
  doi =          "10.1007/978-3-030-65840-3\_7",
  timestamp =    "Wed, 21 Apr 2021 08:53:38 +0200",
  URL =          "https://doi.org/10.1007/978-3-030-65840-3\_7",
  ISBN =         "978-3-030-65840-3",
}