Related papers: Complexity of Arithmetic in Warded Datalog+-
Recent advances in Large Language Models have demonstrated their capabilities across a variety of tasks. However, automatically extracting implicit knowledge from natural language remains a significant challenge, as machines lack active…
Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
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,…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
This paper presents a novel framework for structured argumentation, named extend argumentative decision graph ($xADG$). It is an extension of argumentative decision graphs built upon Dung's abstract argumentation graphs. The $xADG$…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the…
Resolving complex information needs that come with multiple constraints should consider enforcing the logical operators encoded in the query (i.e., conjunction, disjunction, negation) on the candidate answer set. Current retrieval systems…
Logical rules are a popular knowledge representation language in many domains, representing background knowledge and encoding information that can be derived from given facts in a compact form. However, rule formulation is a complex process…
Non-classical logics are used in a wide spectrum of disciplines, including artificial intelligence, computer science, mathematics, and philosophy. The de-facto standard infrastructure for automated theorem proving, the TPTP World, currently…
To create usable and deployable Artificial Intelligence (AI) systems, there requires a level of assurance in performance under many different conditions. Many times, deployed machine learning systems will require more classic logic and…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
Logic programming languages present clear advantages in terms of declarativeness and conciseness. However, the ideas of logic programming have been met with resistance in other programming communities, and have not generally been adopted by…
Duplicates in data management are common and problematic. In this work, we present a translation of Datalog under bag semantics into a well-behaved extension of Datalog, the so-called {\em warded Datalog}$^\pm$, under set semantics. From a…
Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent,…
In this paper, we tackle the incremental maintenance of Datalog inference materialisation when the rule set can be updated. This is particularly relevant in the context of the Internet of Things and Edge computing where smart devices may…
Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…