Related papers: Foundations of Declarative Data Analysis Using Lim…
Given an argumentation framework AF, we introduce a mapping function that constructs a disjunctive logic program P, such that the preferred extensions of AF correspond to the stable models of P, after intersecting each stable model with the…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
In the context of ontology-mediated querying with description logics (DLs), we study the data complexity of queries in which selected predicates can be closed (OMQCs). We provide a non-uniform analysis, aiming at a classification of the…
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…
The problem of learning logical rules from examples arises in diverse fields, including program synthesis, logic programming, and machine learning. Existing approaches either involve solving computationally difficult combinatorial problems,…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
We introduce derivation depth-a computable metric of the reasoning effort needed to answer a query based on a given set of premises. We model information as a two-layered structure linking abstract knowledge with physical carriers, and…
We study the program complexity of datalog on both finite and infinite linear orders. Our main result states that on all linear orders with at least two elements, the nonemptiness problem for datalog is EXPTIME-complete. While containment…
We present a method for computing stable models of normal logic programs, i.e., logic programs extended with negation, in the presence of predicates with arbitrary terms. Such programs need not have a finite grounding, so traditional…
Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…
We propose a novel framework for ontology-based access to temporal log data using a datalog extension datalogMTL of a Horn fragment of the metric temporal logic MTL. We show that datalogMTL is ExpSpace-complete even with punctual intervals,…
A very desirable Datalog extension investigated by many researchers in the last thirty years consists in allowing the use of the basic SQL aggregates min, max, count and sum in recursive rules. In this paper, we propose a simple…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Large language models have shown unprecedented abilities in generating linguistically coherent and syntactically correct natural language output. However, they often return incorrect and inconsistent answers to input questions. Due to the…
The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and…