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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…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
Most parameterized complexity classes are defined in terms of a parameterized version of the Boolean satisfiability problem (the so-called weighted satisfiability problem). For example, Downey and Fellow's W-hierarchy is of this form. But…
We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…
Van Glabbeek's linear time-branching time spectrum is one of the most relevant work on comparative study on process semantics, in which semantics are partially ordered by their discrimination power. In this paper we bring forward a…
A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models:…
The condition of parameter identifiability is essential for the consistency of all estimators and is often challenging to prove. As a consequence, this condition is often assumed for simplicity although this may not be straightforward to…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
This paper involves generalizing the Goldblatt-Thomason and the Lindstr\"om characterization theorems to first-order modal logic.
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
Computer systems can be found everywhere: in space, in our homes, in our cars, in our pockets, and sometimes even in our own bodies. For concerns of safety, economy, and convenience, it is important that such systems work correctly.…
Modal description logics feature modalities that capture dependence of knowledge on parameters such as time, place, or the information state of agents. E.g., the logic S5-ALC combines the standard description logic ALC with an S5-modality…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
This article establishes general conditions for posterior consistency of Bayesian finite mixture models with a prior on the number of components. That is, we provide sufficient conditions under which the posterior concentrates on…
Fine's influential Canonicity Theorem states that if a modal logic is determined by a first-order definable class of Kripke frames, then it is valid in its canonical frames. This article reviews the background and context of this result,…
We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing primal and dual quantitative sufficient and necessary…
In the last decades much research effort has been devoted to extending the success of model checking from the traditional field of finite state machines and various versions of temporal logics to suitable subclasses of context-free…
We show that first-order formulae are concise in acylindrically hyperbolic groups and certain extensions thereof. We study further classes of groups, including Burnside groups, icc groups, groups with the `Big Powers' condition, torus knot…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…