Autor: Celani, Sergio A. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A Semantic Analysis of some Distributive Logics with Negation
Autorzy:: Celani, Sergio A.
Powiązania:: https://bibliotekanauki.pl/articles/1368625.pdf
Data publikacji:: 2013
Wydawca:: Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Opis:: In this paper we shall study some extensions of the semilattice based deductive systems $S$ (N) and $S$ (N, 1), where N is the variety of bounded distributive lattices with a negation operator. We shall prove that $S$ (N) and $S$ (N, 1) are the deductive systems generated by the local consequence relation and the global consequence relation associated with ¬-frames, respectively. Using algebraic and relational methods we will prove that $S$ (N) and some of its extensions are canonical and frame complete.
Źródło:: Reports on Mathematical Logic; 2013, 48; 81-100
0137-2904
2084-2589
Pojawia się w:: Reports on Mathematical Logic
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

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

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Skocz do pozycji: 3.

Tytuł:: Hilbert algebras with a necessity modal operator
Autorzy:: Celani, Sergio A.
Montangie, Daniela
Powiązania:: https://bibliotekanauki.pl/articles/1368664.pdf
Data publikacji:: 2014
Wydawca:: Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Opis:: We introduce the variety of Hilbert algebras with a modal operator $\square$, called $H\square$-algebras. The variety of $H\square$-algebras is the algebraic counterpart of the $\{ \rightarrow, \square \}$-fragment of the intuitionitic modal logic $\bb{IntK}_square$. We will study the theory of representation and we will give a topological duality for the variety of $\square$, called $H\square$-algebras. We are going to use these results to prove that the basic implicative modal logic $\bb{IntK}_square^rightarrow$ and some axiomatic extensions are canonical. We shall also to determine the simple and subdirectly irreducible algebras in some subvarieties of $H\square$-algebras.
Źródło:: Reports on Mathematical Logic; 2014, 49; 47-77
0137-2904
2084-2589
Pojawia się w:: Reports on Mathematical Logic
Dostawca treści:: Biblioteka Nauki

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