Gispert Brasó, JoanGastón Codony, Andrea2021-05-052021-05-052020-06-21https://hdl.handle.net/2445/177032Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Joan Gispert Brasó[en] The truth-functional interpretation of classical implication gives rise to relevance paradoxes, since it doesn't adequately model our usual understanding of a valid implication, which assumes the antecedent is relevant to the truth of the consequent. This work gives an overview of the system $\mathbf{R}$ of relevance logic, which aims to avoid said paradoxes. We present the logic $\mathbf{R}$ with a Hilbert calculus and then prove the Variable-sharing Theorem. We also give an equivalent algebraic semantics for $\mathbf{R}$ and a semantics for its first-degree entailment fragment.68 p.application/pdfengcc-by-nc-nd (c) Andrea Gastón Codony, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Lògica matemàticaTreballs de fi de grauLògica algebraicaMathematical logicBachelor's thesesAlgebraic logicinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess