We propose a description language capturing a simple but central aspect of the possible “lives” (the behavior) of a database application, namely the ability for the relations to grow, shrink, or keep the same size. We first consider arbitrary behaviors and investigate the basic properties of such descriptions. We characterize consistency, redundancy, and subsumption, and show that every behavior has a unique minimal complete description. We then consider the problem of computing the minimal complete description of a given database application. We model such applications as collections of procedures, specified by update programs based on relational algebra. The general problem is undecidable, even for an application consisting of a single procedure with a single update language statement. We also identify decidable cases and provide partial complexity characterisations.
Argumentation frameworks (AFs) provide a central formalism for abstract argumentation, representing arguments and their interactions as attack graphs and serving as reasoning engines across diverse domains. One of their main strengths lies in their ability to support explanations. However, their usefulness can be limited by size and structural complexity, which can hinder understanding. To address this challenge, we investigate simplification techniques for AFs, with particular emphasis on clustering-based abstraction. By grouping arguments into clusters and interpreting attacks accordingly, clustered AFs provide reduced representations that preserve essential argumentative properties while hiding redundant details. We study formal underpinnings for clustering on AFs in particular combined with other simplification techniques, and analyze their effects on main argumentation semantics, and explore conditions under which simplifications remain faithful and avoid spurious results. Our approach positions clustering as a principled method of abstraction and highlights its potential for enhancing explainability in argumentation.
We study two approximate variants of inclusion atoms and examine the axiomatization and computational complexity of their implication problems. The approximate variants allow for some imperfection in a team (corresponding to a unirelational database), and differ in how this degree is measured. One considers the error relative to the size of the team, while the other applies a fixed threshold independent of size. We obtain complete axiomatizations for both under some arity restrictions. In particular, restricted to unary atoms, the implication problem for each approximate variant is decidable in polynomial time.
In this paper we investigate splitting notions for conditional belief bases that allow us to localize reasoning and computations to only the relevant parts of a belief base. The focus of our investigations lies on splitting notions for c-representations, which are special kinds of Spohn’s ranking models for belief bases and which can be specified via a constraint satisfaction problem. We extend the notion of constraint splittings for c-representations to conditional constraint splittings, covering also cases where the subbases may share conditionals. Inspired by conditional syntax splittings, we identify the subclass of safe conditional constraint splittings, allowing us to solve the constraint systems of the subbases independently from each other. We elaborate the relationships of constraint and safe conditional constraint splittings to safe and generalized safe conditional syntax splittings and also to safe covers, which have been proposed for localized computation of c-representations. Additionally, we generalize solution splittings for c-representations to safe conditional c-solution splittings and show how they relate to conditional constraint splittings.
In this paper we bring together qualitative temporal reasoning and planning in order to pave the way for a new approach to planning and temporal planning. Both fields are concerned with arrangement problems of temporal intervals. We present a method to construct qualitative temporal reasoning tasks from planning problems, effectively reducing a class of planning tasks to qualitative temporal reasoning. The construction proposed in this paper enables additional temporal planning constraints to be considered, thereby making the method applicable to both classical planning and temporal planning.
