Displaying similar documents to “Polyadic algebras over nonclassical logics”

Equality Logic

Shokoofeh Ghorbani (2020)

Bulletin of the Section of Logic

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In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear) equality∆-algebras and investigate some related properties. Also, we study ∆-deductive...

Putting together Lukasiewicz and product logics.

Francesc Esteva, Lluis Godo (1999)

Mathware and Soft Computing

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In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law. ...

Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study

Bart Jacobs (2010)

RAIRO - Theoretical Informatics and Applications

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This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean...