Related papers: Disjunctive Datalog with Existential Quantifiers: …
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…
Multi-document Multi-entity Question Answering inherently demands models to track implicit logic between multiple entities across scattered documents. However, existing Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG)…
Database schema elements such as tables, views, triggers and functions are typically defined with many interrelationships. In order to support database users in understanding a given schema, a rule-based approach for analyzing the…
Building on previous work by Andr\'e Platzer, we present a formal language for Stochastic Differential Dynamic Logic, and define its semantics, axioms and inference rules. Compared to the previous effort, our account of the Stochastic…
Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…
The Web of Linked Data is composed of tons of RDF documents interlinked to each other forming a huge repository of distributed semantic data. Effectively querying this distributed data source is an important open problem in the Semantic Web…
In many engineering applications, processes must be followed precisely, making conformance checking between event logs and declarative process models crucial for ensuring adherence to desired behaviors. This is a critical area where…
We study rewritability of monadic disjunctive Datalog programs, (the complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and on conjunctive queries. We show that…
Distributed linguistic representations are powerful tools for modelling the uncertainty and complexity of preference information in linguistic decision making. To provide a comprehensive perspective on the development of distributed…
A range of methodologies and techniques are available to guide the design and implementation of language extensions and domain-specific languages. A simple yet powerful technique is based on source-to-source transformations interleaved…
Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Ontologies and automated reasoning are the building blocks of the Semantic Web initiative. Derivation rules can be included in an ontology to define derived concepts, based on base concepts. For example, rules allow to define the extension…
Several applications demand the timely detection of critical situations, such as threats to safety and transparency, over high-velocity streams of symbolic events. This demand has motivated the development of (i) event specification…
Commonsense reasoning has long been considered as one of the holy grails of artificial intelligence. Most of the recent progress in the field has been achieved by novel machine learning algorithms for natural language processing. However,…
Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds,…
Legislation can be viewed as a body of prescriptive rules expressed in natural language. The application of legislation to facts of a case we refer to as statutory reasoning, where those facts are also expressed in natural language.…
Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning…
Large language models have been used to translate natural language questions to SQL queries. Without hard constraints on syntax and database schema, they occasionally produce invalid queries that are not executable. These failures limit the…
Ontological query answering is the problem of answering queries in the presence of schema constraints representing the domain of interest. Datalog+/- is a common family of languages for schema constraints, including tuple-generating…