arXiv subjects

Matilda Häggblom

Publications and source records attributed to Matilda Häggblom.

7 recordsLinked to original sources

arXiv2026

Approximate Functional Dependencies---Implication Problem Revisited

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.

cs.LO↗

arXiv2026

Capturing dual team properties with inclusion atoms

We introduce propositional team-based logics expressively complete for (quasi) downward and (quasi) upward closed properties in a syntactically dual way, by using variants of the inclusion atom. In particular, the variants of the primitive inclusion atoms used in the (quasi) upward closed setting have equivalent formulas using variants of the might modality. The duality is visible in the logics' normal forms, mirroring the duality between the (quasi) upward and downward closed settings, where the quasi variants take special care of the empty and full team. Furthermore, we defined sound and complete natural deduction systems for each logic.

math.LO↗

arXiv2026

Expressibility and inexpressibility in propositional team logics

We develop dimension theoretic methods for propositional team based logics. Such quantitative methods were defined for team based first-order logic in a recent paper by Hella, Luosto and the third author and were used to obtain strong hierarchy results in the first-order logic context. We show that in propositional logic and in several important cases, a team theoretical atom can be expressed in terms of atoms of lower arity. We estimate the `price' of such a reduction of arity, i.e. how much more complicated the new expression is. Our estimates involve as parameters the arity of the atoms involved, as well as the number of times the atom occurs in a formula. We also consider new variants of atoms and propositional operations, inspired by our work. We believe that our quantitative analysis leads to a deeper understanding of the scope and limits of propositional team based logic.

math.LO↗

arXiv2025

Inclusion with repetitions and Boolean constants -- implication problems revisited

Inclusion dependencies form one of the most widely used dependency classes. We extend existing results on the axiomatization and computational complexity of their implication problem to two extended variants. We present an alternative completeness proof for standard inclusion dependencies and extend it to inclusion dependencies with repetitions that can express equalities between attributes. The proof uses only two values, enabling us to work in the Boolean setting. Furthermore, we study inclusion dependencies with Boolean constants, provide a complete axiomatization and show that no such system is k-ary. Additionally, the decision problems for both extended versions remain PSPACE-complete. The extended inclusion dependencies examined are common in team semantics, which serves as the formal framework for the results.

cs.LO↗

arXiv2025

Axiomatizing approximate inclusion

We introduce two approximate variants of inclusion dependencies and examine the axiomatization and computational complexity of their implication problems. The approximate variants allow for some imperfection in the database and differ in how this degree is measured. One considers the error relative to the database size, 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 inclusion dependencies, the implication problem for each approximate variant is decidable in PTIME. We formalise the results using team semantics, where a team corresponds to a uni-relational database.

cs.LO↗

arXiv2025

Axiomatizing modal inclusion logic and its variants

We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof system, and use the normal form to prove completeness of the axiomatization. Complete axiomatizations are also provided for two other extensions of modal logic with the same expressive power as modal inclusion logic: one augmented with a might operator and the other with a single-world variant of the might operator.

math.LO↗

arXiv2024

Axiomatization of approximate exclusion

We define and axiomatize approximate exclusion atoms in the team semantic setting. A team is a set of assignments, which can be seen as a mathematical model of a uni-relational database, and we say that an approximate exclusion atom is satisfied in a team if the corresponding usual exclusion atom is satisfied in a large enough subteam. We consider the implication problem for approximate exclusion atoms and show that it is axiomatizable for consequences with a degree of approximation that is not too large. We prove the completeness theorem for usual exclusion atoms, which is currently missing from the literature, and generalize it to approximate exclusion atoms. We also provide a polynomial time algorithm for the implication problems. The results also apply to exclusion dependencies in database theory.

cs.LO↗