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Author: Dušan Guller

Affiliation: Alexander Dubček University of Trenčín, Slovak Republic

Keyword(s): Goedel Logic : Resolution : Many-valued Logics : Automated Deduction

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Computational Intelligence ; Fuzzy Systems ; Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic ; Soft Computing

Abstract: We have generalised the well-known hyperresolution principle to the first-order G¨odel logic for the general case. This paper is a continuation of our work. We propose a modification of the hyperresolution calculus suitable for automated deduction with explicit partial truth. We expand the first-order G¨odel logic by a countable set of intermediate truth constants ¯ c, c 2 (0;1). Our approach is based on translation of a formula to an equivalent satisfiable finite order clausal theory, consisting of order clauses. An order clause is a finite set of order literals of the form e1  e2 where  is a connective either P or . P and  are interpreted by the equality and standard strict linear order on [0;1], respectively. We shall investigate the so-called canonical standard completeness, where the semantics of the first-order G¨odel logic is given by the standard G-algebra and truth constants are interpreted by themselves. The modified hyperresolution calculus is refutation sound and comp lete for a countable order clausal theory under certain condition for suprema and infima of sets of the truth constants occurring in the theory. (More)

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Paper citation in several formats:
Guller, D. (2014). An Order Hyperresolution Calculus for Gödel Logic with Truth Constants. In Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA; ISBN 978-989-758-053-6, SciTePress, pages 37-52. DOI: 10.5220/0005073700370052

@conference{fcta14,
author={Dušan Guller.},
title={An Order Hyperresolution Calculus for Gödel Logic with Truth Constants},
booktitle={Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA},
year={2014},
pages={37-52},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005073700370052},
isbn={978-989-758-053-6},
}

TY - CONF

JO - Proceedings of the International Conference on Fuzzy Computation Theory and Applications (IJCCI 2014) - FCTA
TI - An Order Hyperresolution Calculus for Gödel Logic with Truth Constants
SN - 978-989-758-053-6
AU - Guller, D.
PY - 2014
SP - 37
EP - 52
DO - 10.5220/0005073700370052
PB - SciTePress

- Science and Technology Publications, Lda.
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