Hybrid MKNF knowledge bases under the well-founded semantics integrate Description Logics with Logic Programming. However, they do not support classical negation in the rule component, limiting their ability to represent explicit negative knowledge. This limitation is particularly significant in safety-critical applications, where reasoning often requires explicit negative information rather than interpreting the absence of information as evidence of absence. To address this issue, we introduce an extension of Hybrid MKNF that supports classical negation in the rule component. We formally define the syntax and semantics of the extended language and present a general procedure for computing its well-founded model.
Chess is a two player strategic game that is embedded in classical AI culture as it was once the frontier for intelligent behaviour. There was the silent assumption that the advent of computer engines that play better than the best humans will extinguish interest in the game. How…
We present the interactions with an LLM (Large Language Model) aiming at proving that the square root of 2 is not a rational number in an LP (Logic Programming) context. We start from a few basic pure logic programming predicate definitions. We rely on the LPTP (Logic Program The…
In the field of Artificial Intelligence, an agent is a system which is able to autonomously make decisions in order to reach a desired goal. As these systems grow more prevalent in our day-to-day lives, there has been an increased need to add explainability features which can pro…
Inductive Logic Programming (ILP) originated within the Logic Programming community in the Nineties as a framework for combining symbolic learning with declarative knowledge representation. Nowadays, mature ILP frameworks exist and they are capable of learning complex, non-monoto…
Neurosymbolic (NeSy) systems integrate neural networks with logical reasoning to achieve both generalization and interpretability, but recent work has shown they are susceptible to shortcut reasoning behaviors. We propose a novel method using matrix-based differentiable logic pro…
Motivated by challenging modelling issues in the life sciences, we investigate the relationship between logic programming semantics and the eventual states of causal processes compatible with those logic programs. More precisely, we show that while stable models of positive logic…