13 research outputs found
Some observations about generalized quantifiers in logics of imperfect information
We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engstrom. comparing them with a more general, higher order definition of team quantifier. We show that Engstrom's definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engstrom's quantifiers only range over the latter. We further argue that Engstrom's definitions are just embeddings of the first-order generalized quantifiers into team semantics. and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engstrom's quantifiers.Peer reviewe
First-Order Model Checking on Generalisations of Pushdown Graphs
We study the first-order model checking problem on two generalisations of
pushdown graphs. The first class is the class of nested pushdown trees. The
other is the class of collapsible pushdown graphs. Our main results are the
following. First-order logic with reachability is uniformly decidable on nested
pushdown trees. Considering first-order logic without reachability, we prove
decidability in doubly exponential alternating time with linearly many
alternations. First-order logic with regular reachability predicates is
uniformly decidable on level 2 collapsible pushdown graphs. Moreover, nested
pushdown trees are first-order interpretable in collapsible pushdown graphs of
level 2. This interpretation can be extended to an interpretation of the class
of higher-order nested pushdown trees in the collapsible pushdown graph
hierarchy. We prove that the second level of this new hierarchy of nested trees
has decidable first-order model checking. Our decidability result for
collapsible pushdown graph relies on the fact that level 2 collapsible pushdown
graphs are uniform tree-automatic. Our last result concerns tree-automatic
structures in general. We prove that first-order logic extended by Ramsey
quantifiers is decidable on all tree-automatic structures.Comment: phd thesis, 255 page
Lindström Quantifiers and Leaf Language Definability
We show that examinations of the expressive power of logical formulae enriched by Lindström quantifiers over ordered finite structures have a well-studied complexity-theoretic counterpart: the leaf language approach to define complexity classes. Model classes of formulae with Lindström quantifiers are nothing else than leaf language definable sets. Along the way we tighten the best up to now known leaf language characterization of the classes of the polynomial time hierarchy and give a new model-theoretic characterization of PSPACE
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum