Problem
Research questions and friction points this paper is trying to address.
Approximate Functional Dependencies
Implication Problem
Axiomatisation
Model Checking Complexity
Approximate Functional Dependencies---Implication Problem Revisited
🤖 AI Summary
This study addresses the incompleteness of inference rules and the computational complexity of model checking for approximate functional dependencies by integrating team logic, axiomatic methods, and complexity analysis. By exposing semantic deficiencies in existing axiom systems and identifying previously uncaptured semantic entailments, this work refines the underlying theoretical framework. Key contributions include proving the general incompleteness of current axiom systems, establishing completeness for unary dependencies, and precisely characterizing the computational complexity of model checking. These findings bridge critical theoretical gaps, providing a robust foundation for logical reasoning and algorithmic analysis concerning approximate functional dependencies. Ultimately, this research advances the formal understanding of dependency theory within team semantics while clarifying the computational boundaries of verification tasks in this domain.
📝 Abstract
Functional dependencies are an important and well-studied class of database constraints that correspond to a notion expressed by dependence atoms in team logic. In practice, data often contain errors, so in some cases it might be useful to allow the database to have a small number of tuples that violate the desired dependency. Väänänen (2017) studied the axiomatisation of a notion of approximate dependence that specifies for each dependence atom how much of the database can be disregarded. We demonstrate that the interaction of approximate dependence atoms is more complicated than previously thought in the sense that there is a semantic consequence that is not captured by the inference rules introduced before. We show that Väänänen's axiomatisation is still complete in the restricted case of unary dependencies. We also consider the complexity of model checking for approximate dependence: it is NP-complete for disjunctions of two atoms and LOGSPACE-hard for individual atoms.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Approximate Functional Dependencies
Axiomatisation
Implication Problem
Model Checking Complexity
Team Logic
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