Related papers: Conservative Extensions for Existential Rules
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…
We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if…
Access limitations are restrictions in the way in which the tuples of a relation can be accessed. Under access limitations, query answering becomes more complex than in the traditional case, with no guarantee that the answer tuples that can…
We consider an extension of linear-time temporal logic (LTL) with both local and remote data constraints interpreted over a concrete domain. This extension is a natural extension of constraint LTL and the Temporal Logic of Repeating Values,…
Moving beyond the dualistic view in AI where agent and environment are separated incurs new challenges for decision making, as calculation of expected utility is no longer straightforward. The non-dualistic decision theory literature is…
Extensions (entropies) play a central role in the theory of hyperbolic conservation laws by providing intrinsic selection criteria for weak solutions. For a given hyperbolic system u_t+f(u)_x=0, a standard approach is to analyze directly…
This paper discusses the decidability of node query preservation problems for XML document transformations. We assume a transformation given by a deterministic linear top-down data tree transducer (abbreviated as DLT^V) and an n-ary query…
Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink;…
Conjunctive queries select and are expected to return certain tuples from a relational database. We study the potentially easier problem of counting all selected tuples, rather than enumerating them. In particular, we are interested in the…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
The conservative sequence of a set $A$ under a transformation $T$ is the set of all $n \in \mathbb{Z}$ such that $T^n A \cap A \not = \varnothing$. By studying these sequences, we prove that given any countable collection of nonsingular…
The satisfiability and finite satisfiability problems for the two-variable guarded fragment of first-order logic with counting quantifiers, a database, and path-functional dependencies are both ExpTime-complete.
We consider two basic problems of algebraic topology, the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity. The extension problem is the following: Given…
The Guarded Fragment (GF) is a well-established decidable fragment of first-order logic. We study an extension of GF with nested equivalence relations, namely a family of distinguished binary predicates $E_1, E_2, \dots$ interpreted as…
Datalog+/- is a Datalog-based language family enhanced with existential quantification in rule heads, equalities and negative constraints. Query answering over databases with respect to a Datalog+/- theory is generally undecidable, however…
Probabilistic databases (PDBs) are probability spaces over database instances. They provide a framework for handling uncertainty in databases, as occurs due to data integration, noisy data, data from unreliable sources or randomized…
The chase is a widely implemented approach to reason with tuple-generating dependencies (tgds), used in data exchange, data integration, and ontology-based query answering. However, it is merely a semi-decision procedure, which may fail to…
We prove some general theorems for preserving Dependent Choice when taking symmetric extensions, some of which are unwritten folklore results. We apply these to various constructions to obtain various simple consistency proofs.
We study reductions that limit the extreme adaptivity of Turing reductions. In particular, we study reductions that make a rapid, structured progression through the set to which they are reducing: Each query is strictly longer (shorter)…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…