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A Proof Calculus for Automated Deduction in Propositional Product Logic
MathematicsPropositional product logic belongs to the basic fuzzy logics with continuous t-norms using the product t-norm (defined as the ordinary product of real numbers) on the unit interval [0,1].
Dušan Guller
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On Product Logic with Truth-constants [PDF]
Journal of Logic and Computation, 2006 Product Logic Π is an axiomatic extension of Hájek's Basic Fuzzy Logic BL coping with the 1-tautologies when the strong conjunction & and implication → are interpreted by the product of reals in [0, 1] and its residuum respectively. In this paper we investigate expansions of Product Logic by adding into the language a countable set of truth-constants ...
Petr Savický +4 more
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Maximal Theories of Product Logic
Lecture Notes in Computer Science, 2023 Product logic is one of the main fuzzy logics arising from a continuous t-norm, and its equivalent algebraic semantics is the variety of product algebras. In this contribution, we study maximal filters of product algebras, and their relation with product hoops. The latter constitute the variety of 0-free subreducts of product algebras.
Sara Ugolini, Ugolini Sara
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Bulletin of the Section of Logic, 2020 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.
Shokoofeh Ghorbani
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Engineering the Stability of Nanozyme-Catalyzed Product for Colorimetric Logic Gate Operations
Molecules, 2021 Recently, the design and development of nanozyme-based logic gates have received much attention. In this work, by engineering the stability of the nanozyme-catalyzed product, we demonstrated that the chromogenic system of 3, 3′, 5, 5 ...
Lianlian Fu +4 more
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A Note on Drastic Product Logic [PDF]
, 2014 The drastic product $*_D$ is known to be the smallest $t$-norm, since $x *_D y = 0$ whenever $x, y < 1$. This $t$-norm is not left-continuous, and hence it does not admit a residuum. So, there are no drastic product $t$-norm based many-valued logics, in the sense of [EG01].
S. Aguzzoli, M. Bianchi, D. Valota
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