6 research outputs found
Characterizing Quantifier Extensions of Dependence Logic
We characterize the expressive power of extensions of Dependence Logic and
Independence Logic by monotone generalized quantifiers in terms of quantifier
extensions of existential second-order logic.Comment: 9 page
A Fragment of Dependence Logic Capturing Polynomial Time
In this paper we study the expressive power of Horn-formulae in dependence
logic and show that they can express NP-complete problems. Therefore we define
an even smaller fragment D-Horn* and show that over finite successor structures
it captures the complexity class P of all sets decidable in polynomial time.
Furthermore we study the question which of our results can ge generalized to
the case of open formulae of D-Horn* and so-called downwards monotone
polynomial time properties of teams
Characterizing downwards closed, strongly first order, relativizable dependencies
In Team Semantics, a dependency notion is strongly first order if every
sentence of the logic obtained by adding the corresponding atoms to First Order
Logic is equivalent to some first order sentence. In this work it is shown that
all nontrivial dependency atoms that are strongly first order, downwards
closed, and relativizable (in the sense that the relativizations of the
corresponding atoms with respect to some unary predicate are expressible in
terms of them) are definable in terms of constancy atoms.
Additionally, it is shown that any strongly first order dependency is safe
for any family of downwards closed dependencies, in the sense that every
sentence of the logic obtained by adding to First Order Logic both the strongly
first order dependency and the downwards closed dependencies is equivalent to
some sentence of the logic obtained by adding only the downwards closed
dependencies
Dependence logic with a majority quantifier ∗
We study the extension of dependence logic D by a majority quantifier M over finite structures. We show that the resulting logic is equi-expressive with the extension of second-order logic by second-order majority quantifiers of all arities. Our results imply that, from the point of view of descriptive complexity theory, D(M) captures the complexity class counting hierarchy