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@PHDTHESIS{Liu:856068,
      author       = {Liu, Daxin},
      othercontributors = {Lakemeyer, Gerhard and Belle, Vaishak},
      title        = {{P}rojection in a probabilistic epistemic logic and its
                      application to belief-based program verification},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2022-10632},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2022},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University 2023; Dissertation, RWTH Aachen University, 2022},
      abstract     = {Rich representation of knowledge and actions has been a
                      goal that many AI researchers pursue. Among all proposals,
                      perhaps, the situation calculus by Reiter is the most widely
                      studied, where actions are treated as logical terms and the
                      agent’s knowledge is represented by logical formulas. The
                      language has been extended to incorporate many features like
                      time, concurrency, procedures, Most recently, Belle and
                      Lakemeyer proposed a modal logic DS which deals with degrees
                      of belief and noisy sensing. The logic has many appealing
                      properties like full introspection, however, it also has
                      some shortcomings. Perhaps the main one is the lack of
                      expressiveness when it comes to degrees of belief.
                      Currently, the language allows expressing degrees of belief
                      only as constants making it impossible to express belief
                      distribution. Another important problem is that it lacks
                      projection reasoning mechanisms. Projection is the task to
                      determine whether a query about the future is entailed by an
                      initial knowledge base. Two solutions of projection exist
                      regression and progression. While regression transfers the
                      query about the future into a query about the initial state
                      and evaluates it there, progression transfers the whole
                      initial knowledge base into a future one.In this thesis, we
                      first lift the expressiveness of the logic DS by modifying
                      both the syntax and semantics. Moreover, we investigate the
                      projection problem in DS. In particular, we propose a
                      regression operator which can handle querieswith nested
                      beliefs and beliefs with quantifying-in. For progression, we
                      show that classical progression is first-order definable for
                      a fragment of the logic and provide our solution for the
                      progression of belief in terms of only-believing after
                      actions. Moreover, we exploit how to apply the proposed
                      methods in a more practical scenario: on the verification of
                      belief programs, a probabilistic extension of Golog
                      programs, where every action and sensing could be noisy and
                      every test refers to the agent’s subjective beliefs. We
                      show that the verification problem is undecidable even in
                      very restrictive settings. We also show a special case where
                      the problem is decidable.},
      cin          = {121920 / 120000 / 080060},
      ddc          = {004},
      cid          = {$I:(DE-82)121920_20140620$ / $I:(DE-82)120000_20140620$ /
                      $I:(DE-82)080060_20170720$},
      pnm          = {GRK 2236 - UNRAVEL - UNcertainty and Randomness in
                      Algorithms, VErification, and Logic (282652900) / TAILOR -
                      Foundations of Trustworthy AI - Integrating Reasoning,
                      Learning and Optimization (952215)},
      pid          = {G:(GEPRIS)282652900 / G:(EU-Grant)952215},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2022-10632},
      url          = {https://publications.rwth-aachen.de/record/856068},
}