Algebraic Study of Substructural Fuzzy Epistemic Logics

This paper generalizes the notion of monadic residuated lattices to that of pseudo monadic residuated lattices. As monadic residuated lattices serve as algebraic models of modal logic S5(FLew ), we propose pseudo monadic resid- uated lattices as algebraic models of modal system KD45(FLew ). The main contributions of this paper are as follows: 1) we discuss the relationship be- tween pseudo monadic residuated lattices and other pseudo monadic algebraic structures, showing that it is a natural generalization of pseudo monadic BL- algebras, Bi-modal Gödel algebras and pseudo monadic algebras; 2) We provide a comprehensive characterization of pseudo monadic residuated lattices by con- sidering them as pairs of residuated lattices (L, B), where B represents a special case of a relatively complete subalgebra of L known as c-relatively complete. Furthermore, we establish a necessary and sufficient condition for a subalgebra to be c-relatively complete.

Authors

• Yongwei Yang
• Yijun Li

Keywords

• residuated lattice
• epistemic logics
• pseudo monadic residuated lattices
• relatively complete