Adding Transitivity and Counting to the Fluted Fragment

We study the impact of adding both counting quantifiers and a single transitive relation to the fluted fragment - a fragment of first-order logic originating in the work of W.V.O. Quine. The resulting formalism can be viewed as a multi-variable, non-guarded extension of certain systems of description logic featuring number restrictions and transitive roles, but lacking role-inverses. We establish the finite model property for our logic, and show that the satisfiability problem for its k-variable sub-fragment is in (k+1)-NExpTime. We also derive ExpSpace-hardness of the satisfiability problem for the two-variable, fluted fragment with one transitive relation (but without counting quantifiers), and prove that, when a second transitive relation is allowed, both the satisfiability and the finite satisfiability problems for the two-variable fluted fragment with counting quantifiers become undecidable

One-Dimensional Fragment Over Words and Trees

One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a complete classification of the complexity of its satisfiability problem for various navigational signatures and comparing its expressive power with other important formalisms. These include the two-variable fragment with counting and the unary negation fragment.Peer reviewe

Homogeneity and Homogenizability: Hard Problems for the Logic SNP

We show that the question whether a given SNP sentence defines a homogenizable class of finite structures is undecidable, even if the sentence comes from the connected Datalog fragment and uses at most binary relation symbols. As a byproduct of our proof, we also get the undecidability of some other properties for Datalog programs, e.g., whether they can be rewritten in MMSNP, whether they solve some finite-domain CSP, or whether they define the age of a reduct of a homogeneous Ramsey structure in a finite relational signature. We subsequently show that the closely related problem of testing the amalgamation property for finitely bounded classes is EXPSPACE-hard or PSPACE-hard, depending on whether the input is specified by a universal sentence or a set of forbidden substructures.Comment: 34 pages, 3 figure

When Can We Answer Queries Using Result-Bounded Data Interfaces?

We consider answering queries where the underlying data is available only over limited interfaces which provide lookup access to the tuples matching a given binding, but possibly restricting the number of output tuples returned. Interfaces imposing such "result bounds" are common in accessing data via the web. Given a query over a set of relations as well as some integrity constraints that relate the queried relations to the data sources, we examine the problem of deciding if the query is answerable over the interfaces; that is, whether there exists a plan that returns all answers to the query, assuming the source data satisfies the integrity constraints. The first component of our analysis of answerability is a reduction to a query containment problem with constraints. The second component is a set of "schema simplification" theorems capturing limitations on how interfaces with result bounds can be useful to obtain complete answers to queries. These results also help to show decidability for the containment problem that captures answerability, for many classes of constraints. The final component in our analysis of answerability is a "linearization" method, showing that query containment with certain guarded dependencies -- including those that emerge from answerability problems -- can be reduced to query containment for a well-behaved class of linear dependencies. Putting these components together, we get a detailed picture of how to check answerability over result-bounded services.Comment: 45 pages, 2 tables, 43 references. Complete version with proofs of the PODS'18 paper. The main text of this paper is almost identical to the PODS'18 except that we have fixed some small mistakes. Relative to the earlier arXiv version, many errors were corrected, and some terminology has change