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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/231562
Beyond Degrees of Truth and the Axiomatization of Superintuitionistic Prime Mixed Models
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Introduction
This thesis can be divided into two main parts.
In the first part, after two chapters of overview of preliminary knowledge, we introduce a new family of logics, which we call order-based logics, and provide a Hilbert-style presentation for them. These logics are obtained by taking the axioms of a logic associated with a variety of bounded integral commutative residuated lattices and replacing the usual rule of modus ponens with a restricted version thereof. The motivation for introducing these systems is to study weaker counterparts of the well-known logics preserving degrees of truth associated with varieties of (bounded) integral commutative residuated lattices.
The resulting systems form a family of paraconsistent logics for which we provide a natural matrix semantics. We also determine their position within the Leibniz and Frege hierarchies. In particular, we show that all order-based logics are fully selfextensional, while none of them is protoalgebraic and, all of them fail to be (fully) Fregean. Furthermore, we prove that the order-based logic associated with classical logic coincides with a language reduct of the well-known paraconsistent logic D2. As a consequence, this logic admits an interpretation into the global modal logic S5 as well as the local modal logic T via what Priest calls the Jaśkowski move in [11]. This result serves as the main motivation for the second part of the thesis.
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Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona. Curs: 2025-2026. Tutor: Gispert, Joan, 1961-
Matèries (anglès)
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ASENSIO GARCÍA, Miguel. Beyond Degrees of Truth and the Axiomatization of Superintuitionistic Prime Mixed Models. [consulted: 24 of September of 2026]. Available at: https://hdl.handle.net/2445/231562