# On Enumerating All the Minimal Models for Particular CNF Formula Classes

### Yakoub Salhi

#### Abstract

In this work, we propose approaches for enumerating all the minimal models for two particular classes of CNF formulæ. The first class is that of PN formulæ which are defined as CNF formulæ where each clause is either positive or negative, whereas the second class is that of PH formulæ in which each clause is either positive or a Horn clause. We first provide an approach for enumerating all the minimal models in the case of PN formulæ that is based on the use of an algorithm for generating the minimal transversals of a hypergraph. We also propose a SAT-based encoding for solving the same problem. Then, we provide a characterization of the minimal models in the case of PH formulæ, which allows us to use our approaches in the case of PN formulæ for solving the problem of minimal model enumeration for PH formulæ. Finally, we describe an application in datamining of the problem of enumerating the minimal models in the case of PN formulæ.

Download#### Paper Citation

#### in Harvard Style

Salhi Y. (2019). **On Enumerating All the Minimal Models for Particular CNF Formula Classes**.In *Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-350-6, pages 403-410. DOI: 10.5220/0007257104030410

#### in Bibtex Style

@conference{icaart19,

author={Yakoub Salhi},

title={On Enumerating All the Minimal Models for Particular CNF Formula Classes},

booktitle={Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2019},

pages={403-410},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007257104030410},

isbn={978-989-758-350-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - On Enumerating All the Minimal Models for Particular CNF Formula Classes

SN - 978-989-758-350-6

AU - Salhi Y.

PY - 2019

SP - 403

EP - 410

DO - 10.5220/0007257104030410