# Solving Fuzzy Answer Set Programs in Product Logic

### Ivor Uhliarik

#### Abstract

In recent years, foundations have been laid for a turn in logic programming paradigms in continuous domains. Fuzzy answer set programming (FASP) has emerged as a combination of a tool for non-monotonic reasoning and solving combinatorial problems (ASP) and a knowledge representation formalism that allows for modeling partial truth (fuzzy logic). There have been various attempts at designing a solver for FASP, but they either make use of transformations into optimization programs with scaling problems, operate only on finite-valued Łukasiewicz logic, or yield only approximate answer sets. Moreover, there has been no research focused on the product logic semantics in FASP. In this work we investigate the methods used in state-of-the-art classical ASP solvers with the aim of designing a FASP solver for product propositional logic. In particular, we base our approach on the conversion into fuzzy SAT (satisfiability problem) and the fuzzy generalization of the DPLL algorithm. Since both Łukasiewicz and (extended) Gödel logic can be embedded into product logic, the resulting system should be able to operate on all three logics uniformly.

Download#### Paper Citation

#### in Harvard Style

Uhliarik I. (2017). **Solving Fuzzy Answer Set Programs in Product Logic**.In *Proceedings of the 9th International Joint Conference on Computational Intelligence - Volume 1: IJCCI,* ISBN 978-989-758-274-5, pages 367-372. DOI: 10.5220/0006518303670372

#### in Bibtex Style

@conference{ijcci17,

author={Ivor Uhliarik},

title={Solving Fuzzy Answer Set Programs in Product Logic},

booktitle={Proceedings of the 9th International Joint Conference on Computational Intelligence - Volume 1: IJCCI,},

year={2017},

pages={367-372},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006518303670372},

isbn={978-989-758-274-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Joint Conference on Computational Intelligence - Volume 1: IJCCI,

TI - Solving Fuzzy Answer Set Programs in Product Logic

SN - 978-989-758-274-5

AU - Uhliarik I.

PY - 2017

SP - 367

EP - 372

DO - 10.5220/0006518303670372