Related papers: Fixpoint Semantics and Optimization of Recursive D…
This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator…
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…
Datalog reasoning based on the semina\"ive evaluation strategy evaluates rules using traditional join plans, which often leads to redundancy and inefficiency in practice, especially when the rules are complex. Hypertree decompositions help…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Most work on query optimization has concentrated on loop-free queries. However, data science and machine learning workloads today typically involve recursive or iterative computation. In this work, we propose a novel framework for…
Datalog is a powerful yet elegant language that allows expressing recursive computation. Although Datalog evaluation has been extensively studied in the literature, so far, only loose upper bounds are known on how fast a Datalog program can…
Motivated by applications in declarative data analysis, we study $\mathit{Datalog}_{\mathbb{Z}}$---an extension of positive Datalog with arithmetic functions over integers. This language is known to be undecidable, so we propose two…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
This short paper describes a simple and intuitive Prolog program, a metainterpreter, that computes the bottom up meaning of a simple positive Horn clause definition. It involves a simple transformation of the object program rules into…
Arguing for the need to combine declarative and probabilistic programming, B\'ar\'any et al. (TODS 2017) recently introduced a probabilistic extension of Datalog as a "purely declarative probabilistic programming language." We revisit this…
In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent…
We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of…
The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(|At(P)|size(P))…
Many modern solvers and program analyzers rely on non-monotone reasoning (e.g. negation-as-failure, speculative updates, backtracking) for which classical monotone fixed-point methods do not apply. The general problem of finding the fixed…
Big data programming frameworks have become increasingly important for the development of applications for which performance and scalability are critical. In those complex frameworks, optimizing code by hand is hard and time-consuming,…
Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although correntropy has been used with complex data, no theoretical study was pursued…
We present a recursive formulation of the Horn algorithm for deciding the satisfiability of propositional clauses. The usual presentations in imperative pseudo-code are informal and not suitable for simple proofs of its main properties. By…
Semantic operators have increasingly become integrated within data systems to enable processing data using Large Language Models (LLMs). Despite significant recent effort in improving these operators, their accuracy is limited due to a…
In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative…
The logic of hybrid MKNF (minimal knowledge and negation as failure) is a powerful knowledge representation language that elegantly pairs ASP (answer set programming) with ontologies. Disjunctive rules are a desirable extension to normal…