### Abstract

In this paper, α-paramodulation and α-GH paramodulation methods are proposed for handling logical formulae with equality in a lattice-valued logic L
_{n}F(X) , which has unique ability for representing and reasoning uncertain information from a logical point of view. As an extension of the work of He et al. (in: 2015 10th international conference on intelligent systems and knowledge engineering (ISKE), pp 18–20. IEEE, 2015; Uncertainty modelling in knowledge engineering and decision making: proceedings of the 12th international FLINS conference, pp 477–482. World Scientific, 2016), a new form of α-equality axioms set is proposed. The equivalence between α-equality axioms set and E
_{α}-interpretation in L
_{n}F(X) with an appropriate level is also established, which may provide a key foundation for equality reasoning in lattice-valued logic. Based on its equivalence, E
_{α}-unsatisfiability equivalent transformation is given. Furthermore, α-paramodulation and its restricted method (i.e., α-GH paramodulation) are given. The soundness and completeness of the proposed methods are also examined.

Original language | English |
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Journal | Soft Computing |

Early online date | 15 Jul 2020 |

DOIs | |

Publication status | E-pub ahead of print - 15 Jul 2020 |

### Keywords

- Equality
- Lattice-valued logic
- α-Equality axioms
- α-GH paramodulation
- α-Paramodulation

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## Cite this

_{n}F(X) with equality.

*Soft Computing*. https://doi.org/10.1007/s00500-020-05136-8