An algebraic approach for action based default reasoning

P. Castro, V. Cassano, R. Fervari, and C. Areces. An algebraic approach for action based default reasoning. Electronic Proceedings in Theoretical Computer Science, pp. 91–105, 2019. Proceedings 7th Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2019, Toulouse, France, 17-19 July 2019

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Abstract

Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous computing systems where decisions must be taken in the presence of an incomplete set of norms regulating a particular scenario. Combining default and deontic reasoning over actions allows us to formally reason about such assumptions. With this in mind, we propose a logical formalism for default reasoning over a deontic action logic. The novelty of our approach is twofold. First, our formalism for default reasoning deals with actions and action operators, and it is based on the deontic action logic originally proposed by Segerberg in [27]. Second, inspired by Segerberg's approach, we use tools coming from the theory of Boolean Algebra. These tools allow us to extend Segerberg's algebraic completeness result to the setting of Default Logics.

BibTeX

@Article{Castro2019,
  author =       "P. Castro and V. Cassano and R. Fervari and C.
                 Areces",
  note =         "Proceedings 7th Conference on Theoretical Aspects of
                 Rationality and Knowledge, {TARK} 2019, Toulouse,
                 France, 17-19 July 2019",
  journal =      "Electronic Proceedings in Theoretical Computer
                 Science",
  title =        "An algebraic approach for action based default
                 reasoning",
  year =         "2019",
  ISSN =         "2075-2180",
  pages =        "91--105",
  abstract =     "Often, we assume that an action is permitted simply
                 because it is not explicitly forbidden; or, similarly,
                 that an action is forbidden simply because it is not
                 explicitly permitted. This kind of assumptions appear,
                 e.g., in autonomous computing systems where decisions
                 must be taken in the presence of an incomplete set of
                 norms regulating a particular scenario. Combining
                 default and deontic reasoning over actions allows us to
                 formally reason about such assumptions. With this in
                 mind, we propose a logical formalism for default
                 reasoning over a deontic action logic. The novelty of
                 our approach is twofold. First, our formalism for
                 default reasoning deals with actions and action
                 operators, and it is based on the deontic action logic
                 originally proposed by Segerberg in [27]. Second,
                 inspired by Segerberg's approach, we use tools coming
                 from the theory of Boolean Algebra. These tools allow
                 us to extend Segerberg's algebraic completeness result
                 to the setting of Default Logics.",
  bibsource =    "dblp computer science bibliography, https://dblp.org",
  biburl =       "https://dblp.org/rec/journals/corr/abs-1907-09124.bib",
  doi =          "10.4204/EPTCS.297.7",
  timestamp =    "Tue, 08 Oct 2019 13:24:16 +0200",
  URL =          "https://doi.org/10.4204/EPTCS.297.7",
}