Related papers: Characterising Modal Formulas with Examples
This paper contributes to the theory of the modal $\mu$-calculus by proving some model-theoretic results. More in particular, we discuss a number of semantic properties pertaining to formulas of the modal $\mu$-calculus. For each of these…
The paper proves finite model property and decidability for a family of modal logics. A binary relation $R$ is called pretransitive, if $R^*=\cup_{i\leq m} R^i$ for some $m\geq 0$, where $R^*$ is the transitive reflexive closure of $R$. By…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We study modal separability for fixpoint formulae: given two mutually exclusive fixpoint formulae $\varphi,\varphi'$, decide whether there is a modal formula $\psi$ that separates them, that is, that satisfies…
We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the…
We give a construction of a large first-order definable family of subrings of finitely generated fields $K$ of any characteristic. We deduce that for any such $K$ there exists a first-order sentence $\varphi_K$ characterising $K$ in the…
A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have…
We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the size of the world, and the permitted substitution instances.…
This paper establishes model-theoretic properties of $\mathrm{FOE}^{\infty}$, a variation of monadic first-order logic that features the generalised quantifier $\exists^\infty$ (`there are infinitely many'). We provide syntactically defined…
We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…
Modal separability for modal fixpoint formulae is the problem to decide for two given modal fixpoint formulae $\varphi,\varphi'$ whether there is a modal formula $\psi$ that separates them, in the sense that $\varphi\models\psi$ and…
Formal languages are in the core of models of computation and their behavior. A rich family of models for many classes of languages have been widely studied. Hyperproperties lift conventional trace-based languages from a set of execution…
Modal automata are a classic formal model for component-based systems that comes equipped with a rich specification theory supporting abstraction, refinement and compositional reasoning. In recent years, quantitative variants of modal…
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we…
A formal framework is given for the characterizability of a class of belief revision operators, defined using minimization over a class of partial preorders, by postulates. It is shown that for partial orders characterizability implies a…
It is known that a finite group with an automorphism $\varphi$ of coprime order has a soluble radical of $(|\varphi|,|C_G(\varphi)|)$-bounded Fitting height and index. We extend this classic result as follows. Let $f(x) = a_0 + a_1 \cdot x…
In Outline of a Theory of Truth, Kripke introduces some of the central concepts of the logical study of truth and paradox. He informally defines some of these -- such as groundedness and paradoxicality -- using modal locutions. We introduce…
We investigate the relationship between recursive enumerability and elementary frame definability in first-order predicate modal logic. On the one hand, it is well-known that every first-order predicate modal logic complete with respect to…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…