Similarity MTL-algebras and Their Corresponding Logics
Jun Tao Wang, Arsham Borumand Saeid and Peng Fei He
In this paper, we expand MTL with a binary connective whose algebraic counterpart is a binary operator playing the role of similarity. Then, we prove the corresponding completeness theorem and show that the expanded logic is a conservative extension of MTLvt. Finally, we study the algebraic semantics of this logic, similarity MTL-algebras, together with its corresponding filters. In particular, we characterize representable similarity MTL-algebras and discuss the relationship between very true MTL-algebras and similarity MTL-algebras.
Keywords: MTL-algebra, similarity, very true, representation, completeness.
2010 MSC: 06D35, 06B99