Similarity triangle logic

Abstract

The present study aimed to propose the similarity triangle algebra and prove the completeness of the similarity triangle logic. The similarity was defined on triangle algebra. Similarity triangle algebra is a triangle algebra endowed with a binary operation S, which verifies specific additional properties. These properties and a class of all the similarity triangle algebras form a variety which were assessed as well. In addition, the similarity IVRL-filters (S-IVRL-filters) were investigated and introduced in the similarity triangle algebras, and the similarity triangle logic $$(\mathcal {STL})$$ was presented, which is a system of several-valued logic capturing the tautologies of similarity triangle algebras to prove the completeness theorem. According to the results, $$\mathcal {STL}$$ is a conservative extension of triangle logic ( $$\mathcal {TL}$$ ).