相关论文: Topological completeness of logics above S4
Unbounded {\L}ukasiewicz logic is a substructural logic that combines features of infinite-valued {\L}ukasiewicz logic with those of abelian logic. The logic is finitely strongly complete w.r.t.~the additive $\ell$-group on the reals…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and possibility as "in some forcing extension". In this modal…
We show in ZFC that the existence of completely separable maximal almost disjoint families of subsets of $\omega$ implies that the modal logic S4.1.2 is complete with respect to the \v{C}ech-Stone compactification of the natural numbers,…
For each natural number $n$ we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than $n$ and no strictly ascending chains. The case $n=0$ is the G\"odel-L\"ob…
We investigate a recent proposal for modal hypersequent calculi. The interpretation of relational hypersequents incorporates an accessibility relation along the hypersequent. These systems give the same interpretation of hypersequents as…
A logic $L$ is called tabular if it is the logic of some finite frame and $L$ is pretabular if it is not tabular while all of its proper consistent extensions are tabular. In this work, we study pretabular tense logics in the lattice…
In the present paper, we continue the research in \cite{Zh21c} to develop the Sahlqvist-type completeness theory for hybrid logic with satisfaction operators and downarrow binders $\mathcal{L}(@, \downarrow)$. We define the class of…
We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
The modal systems S1--S3 were introduced by C. I. Lewis as logics for strict implication. While there are Kripke semantics for S2 and S3, there is no known natural semantics for S1. We extend S1 by a Substitution Principle SP which…
The logico-algebraic study of Lewis's hierarchy of variably strict conditional logics has been essentially unexplored, hindering our understanding of their mathematical foundations, and the connections with other logical systems. This work…
A topological space is \emph{hereditarily $k$-irresolvable} if none of its subspaces can be partitioned into $k$ dense subsets, We use this notion to provide a topological semantics for a sequence of modal logics whose $n$-th member…
Dynamic topological logic (DTL) is a polymodal logic designed for reasoning about {\em dynamic topological systems. These are pairs (X,f), where X is a topological space and f:X->X is continuous. DTL uses a language L which combines the…
We determine the ZF-provable modal logic of the modality $\Box_{\mathrm{sym}}$, where $\Box_{\mathrm{sym}}\varphi$ means '$\varphi$ holds in every finite symmetry-preserving iteration' of the symmetric method. We prove that the exact logic…
Positive modal algebras are the positive-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover,…
In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
BS4 is a natural Belnapian conservative extension of Lewis modal system S4 via strong negation. In [24] it was proved that the translation TB that naturally generalises the Godel-Tarski translation T embeds faithfully Nelsons logic N4 into…
A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either…