Some Logics in the Vicinity of Interpretability Logics

• Autores: Celani, Sergio Arturo
• Año de publicación: 2023
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: INTERPRETABILITY LOGIC,; KRIPKE FRAMES; NEIGHBOURHOOD FRAMES; VELTMAN SEMANTICS
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

In this paper we shall define semantically some families of propositional modal logics related to the interpretability logic IL. We will introduce the logics BIL and BIL+ in the propositional language with a modal operator □ and a binary operator ⇒ such that BIL ⊆ BIL+ ⊆ IL. The logic BIL is generated by the relational structures ⟨X, R, N⟩, called basic frames, where ⟨X, R⟩ is a Kripke frame and ⟨X, N⟩ is a neighborhood frame. We will prove that the logic BIL+ is generated by the basic frames where the binary relation R is definable by the neighborhood relation N and, therefore, the neighborhood semantics is suitable to study the logic BIL+ and its extensions. We shall also study some axiomatic extensions of BIL and we will prove that these extensions are sound and complete with respect to a certain classes of basic frames. Finally, we prove that the logic BIL+ and some of its extensions are complete respect with the class of neighborhood frames.
Fil: Celani, Sergio Arturo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina