# A DPLL Procedure for the Propositional Product Logic

### Dušan Guller

#### Abstract

In the paper, we investigate the deduction problem of a formula from a finite theory in the propositional Product logic from a perspective of automated deduction.Our approach is based on the 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 $\varepsilon_1\diamond \varepsilon_2$ where $\varepsilon_i$ is either a conjunction of propositional atoms or the propositional constant $\gz$ (false) or $\gu$ (true), and $\diamond$ is a connective either $<$ or $=$. $<$ and $=$ are interpreted by the equality and standard strict linear order on $[0,1]$, respectively. A variant of the DPLL procedure, operating over order clausal theories, is proposed. The DPLL procedure is proved to be refutation sound and complete for finite order clausal theories.

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#### in Harvard Style

Guller D. (2013). A DPLL Procedure for the Propositional Product Logic . In Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013) ISBN 978-989-8565-77-8, pages 213-224. DOI: 10.5220/0004557402130224

#### in Bibtex Style

@conference{fcta13,
author={Dušan Guller},
title={A DPLL Procedure for the Propositional Product Logic},
booktitle={Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013)},
year={2013},
pages={213-224},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004557402130224},
isbn={978-989-8565-77-8},
}

#### in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (IJCCI 2013)
TI - A DPLL Procedure for the Propositional Product Logic
SN - 978-989-8565-77-8
AU - Guller D.
PY - 2013
SP - 213
EP - 224
DO - 10.5220/0004557402130224