In this paper we deal with some fuzzy logics and their equivalent algebraic semantics. After introducing new constructions for left-continuous t-norms, we define the concept of rotation logic as the assertional logic of a variety of -algebras generated by t-norm algebras of a certain type; next we prove which algebraic models of those logics come from the algebraic construction of generalized rotation. In the final sections we show other examples and applications of the construction, focusing on the variety of -algebras.
Agliano', P., Ugolini, S. (2020). Rotation Logics. FUZZY SETS AND SYSTEMS, 388, 1-25 [10.1016/j.fss.2019.07.015].
Rotation Logics
Agliano' P.
;
2020-01-01
Abstract
In this paper we deal with some fuzzy logics and their equivalent algebraic semantics. After introducing new constructions for left-continuous t-norms, we define the concept of rotation logic as the assertional logic of a variety of -algebras generated by t-norm algebras of a certain type; next we prove which algebraic models of those logics come from the algebraic construction of generalized rotation. In the final sections we show other examples and applications of the construction, focusing on the variety of -algebras.
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https://hdl.handle.net/11365/1078848