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Probabilistic Reasoning About Simply Typed Lambda Terms

  • Silvia Ghilezan
  • Jelena Ivetić
  • Simona Kašterović
  • Zoran Ognjanović
  • Nenad Savić
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10703)

Abstract

Reasoning with uncertainty has gained an important role in computer science, artificial intelligence and cognitive science. These applications urge for development of formal models which capture reasoning of probabilistic features. We propose a formal model for reasoning about probabilities of simply typed lambda terms. We present its syntax, Kripke-style semantics and axiomatic system. The main results are the corresponding soundness and strong completeness, which rely on two key facts: the completeness of simple type assignment and the existence of a maximal consistent extension of a consistent set.

Keywords

Simply typed lambda calculus Probabilistic logic Soundness Strong completeness 

Notes

Acknowledgements

This work was supported by the SNSF project 200021_165549 Justifications and non-classical reasoning, and by the Serbian Ministry of Education, Science and Technological Development through projects ON174026, III 044006 and ON174008.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Silvia Ghilezan
    • 1
    • 2
  • Jelena Ivetić
    • 1
  • Simona Kašterović
    • 1
  • Zoran Ognjanović
    • 2
  • Nenad Savić
    • 3
  1. 1.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia
  2. 2.Mathematical Institute SANUBelgradeSerbia
  3. 3.Institute of Computer ScienceUniversity of BernBernSwitzerland

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