An Order Hyperresolution Calculus for Gödel Logic with Truth Constants

Dušan Guller

2014

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 complete for a countable order clausal theory under certain condition for suprema and infima of sets of the truth constants occurring in the theory.

Paper Citation

in Harvard Style

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 - Volume 1: FCTA, (IJCCI 2014) ISBN 978-989-758-053-6, pages 37-52. DOI: 10.5220/0005073700370052

in Bibtex Style

@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 - Volume 1: FCTA, (IJCCI 2014)},
year={2014},
pages={37-52},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005073700370052},
isbn={978-989-758-053-6},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Fuzzy Computation Theory and Applications - Volume 1: FCTA, (IJCCI 2014)
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