On Real-Valued Evaluation of Propositional Formulas

  • Aleksandar Perović
  • Dragan Doder
  • Zoran Ognjanović
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7153)

Abstract

Arguably, [0,1]-valued evaluation of formulas is dominant form of representation of uncertainty, believes, preferences and so on despite some theoretical issues - most notable one is incompleteness of any unrestricted finitary formalization. We offer an infinitary propositional logic (formulas remain finite strings of symbols, but we use infinitary inference rules with countably many premises, primarily in order to address the incompleteness issue) which is expressible enough to capture finitely additive probabilistic evaluations, some special cases of truth functionality (evaluations in Lukasiewicz, product, Gödel and \(\L\mathrm\Pi\frac{1}{2}\) logics) and the usual comparison of such evaluations. The main technical result is the proof of completeness theorem (every consistent set of formulas is satisfiable).

Keywords

Fuzzy Logic Inference Rule Propositional Formula Completeness Theorem Possibility Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Aleksandar Perović
    • 1
  • Dragan Doder
    • 2
  • Zoran Ognjanović
    • 3
  1. 1.Faculty of Transportation and Traffic EngineeringUniversity of BelgradeSerbia
  2. 2.Faculty of Mechanical EngineeringUniversity of BelgradeSerbia
  3. 3.Mathematical Institute of Serbian Academy of Sciences and ArtsSerbia

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