States of finite GBL-algebras with monoidal sum

详细信息    查看全文

• 作者：Tommaso Flaminio ^{tommaso.flaminio@uninsubria.it} ; Brunella Gerla ^{brunella.gerla@uninsubria.it} ; Francesco Marigo ; ^{francesco.marigo@uninsubria.it}
• 关键词：Residuated lattices ; GBL-algebras ; Weighted posets ; States
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：33-52
• 全文大小：385 K
• 卷排序：311

文摘

Generalized BL-algebras, i.e. divisible residuated lattices, provide the semantics for a generalization of Basic Logic where the axiom of prelinearity does not hold. Informally, GBL-algebras generalize Heyting algebras in a similar way as MV-algebras generalize Boolean algebras. We introduce the operation of sum in finite GBL-algebras and we axiomatize the obtained finite structures, called GBL⊕GBL⊕-algebras. We hence define states of GBL⊕GBL⊕-algebras, extending MV-algebraic states, and we prove that they are determined by their restriction on the Heyting skeleton. Extremal states are also characterized in terms of densities concentrated in a unique join-prime idempotent.