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Logic of Discovery in Uncertain Situations– Deciding Algorithms

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Knowledge-Based Intelligent Information and Engineering Systems (KES 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4693))

Abstract

We study a logic LDU (logic of Discovery in Uncertain Situations) generated in a semantic way as the set of all formulas valid in Krike/Hintikka models, which are models of linear discrete time with time clusters imitating possible uncertain states. The possibility of discovery and uncertain necessity of discovery are modeled by modal operations. The logic LDU differs from all standard normal and non-normal modal logics because the modalities ate not mutually expressible in standard way. We discuss properties of this logic, i.e. study its fragments, compare LDU with well known modal logics and study the main question about decidability of this logic. We propose an algorithm recognizing theorems of LDU (so we show that LDU is decidable), which is based on verification of validity of special normal reduced forms of rules in models of quadratic polynomial size in the testing rules.

This research is supported by Engineering and Physical Sciences Research Council (EPSRC), U.K., grant EP/F014406/1.

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Author information

Authors and Affiliations

  1. Department of Computing and Mathematics, Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester M1 5GD, U.K.

    V. Rybakov

Authors
  1. V. Rybakov
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Editor information

Editors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, Via Comelico 39/41, 20135, Milano, Italy

    Bruno Apolloni

  2. Centre for SMART Systems, School of Engineering, University of Brighton, BN2 4GJ, Brighton, UK

    Robert J. Howlett

  3. Knowledge-Based Intelligent Engineering Systems Centre, University of South Australia, Mawson Lakes, SA 5095, Adelaide, Australia

    Lakhmi Jain

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Rybakov, V. (2007). Logic of Discovery in Uncertain Situations– Deciding Algorithms. In: Apolloni, B., Howlett, R.J., Jain, L. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2007. Lecture Notes in Computer Science(), vol 4693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74827-4_119

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  • DOI: https://doi.org/10.1007/978-3-540-74827-4_119

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74826-7

  • Online ISBN: 978-3-540-74827-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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