# A DPLL PROCEDURE FOR THE PROPOSITIONAL GÖDEL LOGIC

### Dušan Guller

#### 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