Related papers: Optimally Rewriting Formulas and Database Queries:…
Interpretability is often pointed out as a key requirement for trustworthy machine learning. However, learning and releasing models that are inherently interpretable leaks information regarding the underlying training data. As such…
It is often stated that human languages, as other biological systems, are shaped by cost-cutting pressures but, to what extent? Attempts to quantify the degree of optimality of languages by means of an optimality score have been scarce and…
Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive…
We introduce a general abstract framework for database repairs, where the repair notions are defined using formal logic. We distinguish between integrity constraints and so-called query constraints. The former are used to model consistency…
A class of relational databases has low degree if for all $\delta>0$, all but finitely many databases in the class have degree at most $n^{\delta}$, where $n$ is the size of the database. Typical examples are databases of bounded degree or…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
Semiring semantics evaluates logical statements by values in some commutative semiring K. Random semiring interpretations, induced by a probability distribution on K, generalise random structures, and we investigate here the question of how…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
Database theory is exciting because it studies highly general and practically useful abstractions. Conjunctive query (CQ) evaluation is a prime example: it simultaneously generalizes graph pattern matching, constraint satisfaction, and…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In…
Answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs) are arguably among the most fundamental tasks in Computer Science. They are classical NP-complete problems. Consequently, the search for tractable…
In this paper, we study the sampling problem for first-order logic proposed recently by Wang et al. -- how to efficiently sample a model of a given first-order sentence on a finite domain? We extend their result for the…
Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time…
Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the…
We present a new efficient method for approximate search in electronic lexica. Given an input string (the pattern) and a similarity threshold, the algorithm retrieves all entries of the lexicon that are sufficiently similar to the pattern.…
For the whole class of linear term rewriting systems, we define \emph{bottom-up rewriting} which is a restriction of the usual notion of rewriting. We show that bottom-up rewriting effectively inverse-preserves recognizability and analyze…
In several different applications, including data transformation and entity resolution, rules are used to capture aspects of knowledge about the application at hand. Often, a large set of such rules is generated automatically or…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to…