A DPLL PROCEDURE FOR THE PROPOSITIONAL GÖDEL LOGIC

Dušan Guller

2010

Abstract

In the paper, we investigate the satisfiability and validity problems of a formula in the propositional Gödel logic. Our approach is based on the translation of a formula to an equivalent CNF one which contains literals of the augmented form: either a or a→b or (a→b)→b, where a, b are propositional atoms or the propositional constants 0, 1. A CNF formula is further translated to an equisatisfiable finite order clausal theory which consists of order clauses, finite sets of order literals of the forms a ≖ b or a ≺ b. ≖ and ≺ are interpreted by the equality and strict linear order on [0,1], respectively. A variant of the DPLL procedure for deciding the satisfiability of a finite order clausal theory is proposed. The DPLL procedure is proved to be refutation sound and complete. Finally, we reduce the validity problem of a formula (tautology checking) to the unsatisfiability of a finite order clausal theory.

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Paper Citation


in Harvard Style

Guller D. (2010). A DPLL PROCEDURE FOR THE PROPOSITIONAL GÖDEL LOGIC . In Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010) ISBN 978-989-8425-32-4, pages 31-42. DOI: 10.5220/0003061700310042


in Bibtex Style

@conference{icfc10,
author={Dušan Guller},
title={A DPLL PROCEDURE FOR THE PROPOSITIONAL GÖDEL LOGIC},
booktitle={Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010)},
year={2010},
pages={31-42},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003061700310042},
isbn={978-989-8425-32-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Fuzzy Computation and 2nd International Conference on Neural Computation - Volume 1: ICFC, (IJCCI 2010)
TI - A DPLL PROCEDURE FOR THE PROPOSITIONAL GÖDEL LOGIC
SN - 978-989-8425-32-4
AU - Guller D.
PY - 2010
SP - 31
EP - 42
DO - 10.5220/0003061700310042