Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics

WANG Jun-tao; WANG Mei; SHE Yan-hong

doi:10.12263/DZXB.20210267

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Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics

PAPERS | 更新时间：2025-12-08

- Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics
- ACTA ELECTRONICA SINICA Vol. 51, Issue 4, Pages: 956-964(2023)
- 作者机构：
  
  1.西安石油大学理学院，陕西西安 710065
  2.陕西科技大学电气与控制工程学院，陕西西安 710021
- 作者简介：
- 基金信息：
  
  Foundation Item(s):　National Natural Science Foundation of China(12001423;61976244;12171294);Natural Science Foundation of Shaanxi Province(2020JQ-762;2021JQ-580);Natural Science Foundation of Education Committee of Shannxi Province(20JK0626)
- DOI：10.12263/DZXB.20210267
  CLC： O155;
- Received：22 February 2021，
  
  Revised：2021-12-06，
  
  Published：25 April 2023
- 稿件说明：
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王军涛,王梅,折延宏.一元子结构谓词逻辑中相似的代数语义[J].电子学报,2023,51(04):956-964.

WANG Jun-tao,WANG Mei,SHE Yan-hong.Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics[J].ACTA ELECTRONICA SINICA,2023,51(04):956-964.
王军涛,王梅,折延宏.一元子结构谓词逻辑中相似的代数语义[J].电子学报,2023,51(04):956-964. DOI： 10.12263/DZXB.20210267.

WANG Jun-tao,WANG Mei,SHE Yan-hong.Algebraic Semantics of Similarity in Monadic Substructural Predicate Logics[J].ACTA ELECTRONICA SINICA,2023,51(04):956-964. DOI： 10.12263/DZXB.20210267.

摘要

借助一元模糊谓词逻辑与S5型模糊模态逻辑的等价性，建立了一元子结构谓词逻辑中相似联结词的代数语义，引入了相似一元剩余格，并研究了其基本的代数性质.其次，研究了相似一元剩余格上的相似滤子，刻画了可表示的相似一元剩余格. 最后，引入了相似一元剩余格对应的逻辑系统，证明了其完备性定理，并解决了其最小半线性扩张问题.

Abstract

Using the equivalence between monadic fuzzy predicate logics and S5 type fuzzy modal logic

the algebraic semantics of similarity in monadic substructural predicate logics are introduced

the resulting class of algebras called similarity monadic residuated lattices

and their basic algebraic properties are studied. Secondly

the similarity filters of similarity monadic residuated lattices are introduced

and representable similarity monadic residuated lattices are characterized by using them. Finally

the logic system corresponding to similarity monadic residuated lattices is established

and its minimum semilinear extension and completeness are studied.

关键词

Keywords

references

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