Zobrazeno 1 - 10
of 170
pro vyhledávání: '"03F45"'
Autor:
Beklemishev, Lev D., Wang, Yunsong
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for the complete
Externí odkaz:
http://arxiv.org/abs/2407.10190
Autor:
Holliday, Wesley H.
In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can b
Externí odkaz:
http://arxiv.org/abs/2405.06852
Autor:
Visser, Albert, Litak, Tadeusz
We study the principle phi implies box phi, known as `Strength' or `the Completeness Principle', over the constructive version of L\"ob's Logic. We consider this principle both for the modal language with the necessity operator and for the modal lang
Externí odkaz:
http://arxiv.org/abs/2404.11969
Autor:
Beklemishev, Lev D.
We show that the polymodal provability logic GLP, in a language with at least two modalities and one variable, has nullary unification type. More specifically, we show that the formula [1]p does not have maximal unifiers, and exhibit an infinite comp
Externí odkaz:
http://arxiv.org/abs/2404.04893
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely:
Externí odkaz:
http://arxiv.org/abs/2402.10494
Autor:
Saveliev, Denis I.
We consider a certain class of infinitary rules of inference, called here restriction rules, using of which allows us to deduce complete theories of given models. The first instance of such rules was the $\omega$-rule introduced by Hilbert, and gener
Externí odkaz:
http://arxiv.org/abs/2312.06626
We say that a Kripke model is a GL-model if the accessibility relation $\prec$ is transitive and converse well-founded. We say that a Kripke model is a D-model if it is obtained by attaching infinitely many worlds $t_1, t_2, \ldots$, and $t_\omega$ t
Externí odkaz:
http://arxiv.org/abs/2310.16369
Autor:
Okawa, Yuya, Kurahashi, Taishi
We study the modal completeness and the finite frame property of several sublogics of the logic $\mathbf{IL}$ of interpretability with respect to Visser frames, which are also called simplified Veltman frames. Among other things, we prove that the lo
Externí odkaz:
http://arxiv.org/abs/2211.15919
This paper presents a new uniform method for studying modal companions of superintuitionistic deductive systems and related notions, based on the machinery of stable canonical rules. Using our method, we obtain an alternative proof of the Blok-Esakia
Externí odkaz:
http://arxiv.org/abs/2206.08863
Autor:
Okawa, Yuya
De Rijke introduced a unary interpretability logic $\mathbf{il}$, and proved that $\mathbf{il}$ is the unary counterpart of the binary interpretability logic $\mathbf{IL}$. In this paper, we find the unary counterparts of the sublogics of $\mathbf{IL
Externí odkaz:
http://arxiv.org/abs/2206.03677