- Tytuł:
- Some Logics in the Vicinity of Interpretability Logics
- Autorzy:
- Celani, Sergio A.
- Powiązania:
- https://bibliotekanauki.pl/articles/43188883.pdf
- Data publikacji:
- 2024
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
interpretability logic
Kripke frames
neighbourhood frames
Veltman semantics - Opis:
- In this paper we shall define semantically some families of propositional modal logics related to the interpretability logic \(\mathbf{IL}\). We will introduce the logics \(\mathbf{BIL}\) and \(\mathbf{BIL}^{+}\) in the propositional language with a modal operator \(\square\) and a binary operator \(\Rightarrow\) such that \(\mathbf{BIL}\subseteq\mathbf{BIL}^{+}\subseteq\mathbf{IL}\). The logic \(\mathbf{BIL}\) is generated by the relational structures \(\left<X,R,N\right>\), called basic frames, where \(\left<X,R\right>\) is a Kripke frame and \(\left<X,N\right>\) is a neighborhood frame. We will prove that the logic \(\mathbf{BIL}^{+}\) 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 \(\mathbf{BIL}^{+}\) and its extensions. We shall also study some axiomatic extensions of \(\mathsf{\mathbf{BIL}}\) 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 \(\mathbf{BIL}^{+}\) and some of its extensions are complete respect with the class of neighborhood frames.
- Źródło:
-
Bulletin of the Section of Logic; 2024, 53, 2; 173-193
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł