Related papers: Disjunctive Logic Programs with Inheritance
This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel…
Disjunctive Logic Programming (\DLP) is an advanced formalism for Knowledge Representation and Reasoning (KRR). \DLP is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is…
Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows for expressing every property of finite structures that is decidable in the complexity class SigmaP2 (= NP^NP). Despite this high expressiveness, there are some…
DLV is an efficient logic programming and non-monotonic reasoning (LPNMR) system with advanced knowledge representation mechanisms and interfaces to classic relational database systems. Its core language is disjunctive datalog…
We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
One approach to explaining the hierarchical levels of understanding within a machine learning model is the symbolic method of inductive logic programming (ILP), which is data efficient and capable of learning first-order logic rules that…
Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where…
Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…
We propose a novel paradigm for solving Inductive Logic Programming (ILP) problems via deep recurrent neural networks. This proposed ILP solver is designed based on differentiable implementation of the deduction via forward chaining. In…
This paper focuses on the expressive power of disjunctive and normal logic programs under the stable model semantics over finite, infinite, or arbitrary structures. A translation from disjunctive logic programs into normal logic programs is…
Pre-trained large language models (LMs) struggle to perform logical reasoning reliably despite advances in scale and compositionality. In this work, we tackle this challenge through the lens of symbolic programming. We propose DSR-LM, a…
Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming…
We present trichotomy results characterizing the complexity of reasoning with disjunctive logic programs. To this end, we introduce a certain definition schema for classes of programs based on a set of allowed arities of rules. We show that…
W.C. Rounds and G.-Q. Zhang (2001) have proposed to study a form of disjunctive logic programming generalized to algebraic domains. This system allows reasoning with information which is hierarchically structured and forms a (suitable)…
With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the…
Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which…
Acquiring factual knowledge with Pretrained Language Models (PLMs) has attracted increasing attention, showing promising performance in many knowledge-intensive tasks. Their good performance has led the community to believe that the models…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…