Related papers: Characterising Modal Formulas with Examples
A normal modal logic is pretransitive, if the modality corresponding to the transitive closure of an accessibility relation is expressible in it. In the present work we establish the finite model property for pretransitive generalizations…
Some aspects of the physical nature of language are discussed. In particular, physical models of language must exist that are efficiently implementable. The existence requirement is essential because without physical models no communication…
This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…
The main result of this paper is to prove the existence of a finite basis in the description logic ${\cal ALC}$. We show that the set of General Concept Inclusions (GCIs) holding in a finite model has always a finite basis, i.e. these GCIs…
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…
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…
This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with…
Grammatical features across human languages show intriguing correlations often attributed to learning biases in humans. However, empirical evidence has been limited to experiments with highly simplified artificial languages, and whether…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
A systematic way of defining variants of a modeling language is useful for adapting the language to domain or project specific needs. Variants can be obtained by adapting the syntax or semantics of the language. In this paper, we take a…
We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for…
We present a taxonomy of the variability mechanisms offered by modeling languages. The definition of a formal language encompasses a syntax and a semantic domain as well as the mapping that relates them, thus language variabilities are…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
We consider a class of systems over finite alphabets with linear internal dynamics, finite-valued control inputs and finitely quantized outputs. We motivate the need for a new notion of observability and propose three new notions of output…
We introduce the finite-horizon first-order rank profile of a language $L \subseteq \Sigma^*$: the least quantifier rank needed by an $\mathrm{FO}[<]$ sentence to classify membership in $L$ correctly on all words of length at most $n$. The…
While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…
Linguistic variables represent crisp information in a form and precision appropriate for the problem. For example, to answer the question "How are you?" one may say "I am fine." the linguistic variables like "fine", so common in everyday…
We consider the problem of explaining the temporal behavior of black-box systems using human-interpretable models. To this end, based on recent research trends, we rely on the fundamental yet interpretable models of deterministic finite…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for…