2024/08/25 by Sayantan Roy, Roy, Sayantan, Sankha S. Basu +3
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2408.13769
openalex publication_date 2024/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we try to formulate a definition of ''many-valued logical structure''. For this, we embark on a deeper study of Suszko's Thesis (ST) and show that the truth or falsity of ST depends, at least, on the precise notion of semantics. We propose two different notions of semantics and three different notions of entailment. The first one helps us formulate a precise definition of inferentially many-valued logical structures. The second and the third help us to generalise Suszko Reduction and provide adequate bivalent semantics for monotonic and a couple of nonmonotonic logical structures. All these lead us to a closer examination of the played by language/metalanguage hierarchy vis-á-vis ST. We conclude that many-valued logical structures can be obtained if the bivalence of all the higher-order metalogics of the logic under consideration is discarded, building formal bridges between the theory of graded consequence and the theory of many-valued logical structures, culminating in generalisations of Suszko's Thesis.