Related papers: Extending SROIQ with Constraint Networks and Groun…
Developments in semantic web technologies have promoted ontological encoding of knowledge from diverse domains. However, modelling many practical domains requires more expressive representations schemes than what the standard description…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
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…
State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a…
The Semantic Web Rule Language (SWRL) is a direct extension of OWL 2 DL with a subset of RuleML, and it is designed to be the rule language of the Semantic Web. This paper explores the state-of-the-art of SWRL's expressiveness extensions…
We present a tool for modelling and reasoning with knowledge from various diverse (and possibly conflicting) viewpoints. The theoretical underpinnings are provided by enhancing base logics by standpoints according to a recently introduced…
This report extends the Spectral Neuro-Symbolic Reasoning (Spectral NSR) framework by introducing three semantically grounded enhancements: (1) transformer-based node merging using contextual embeddings (e.g., Sentence-BERT, SimCSE) to…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
To appear in Theory and Practice of Logic Programming (TPLP), 2008. We are researching the interaction between the rule and the ontology layers of the Semantic Web, by comparing two options: 1) using OWL and its rule extension SWRL to…
Reasoning in the Semantic Web (SW) commonly uses Description Logics (DL) via OWL2 DL ontologies, or SWRL for variables and Horn clauses. The Rule Interchange Format (RIF) offers more expressive rules but is defined outside RDF and rarely…
We propose a formal model of reasoning limitations in large neural net models for language, grounded in the depth of their neural architecture. By treating neural networks as linear operators over logic predicate space we show that each…
As the interest in the representation of context dependent knowledge in the Semantic Web has been recognized, a number of logic based solutions have been proposed in this regard. In our recent works, in response to this need, we presented…
Large Language Models (LLMs) excel at generating natural language answers, yet their outputs often remain unverifiable and difficult to trace. Knowledge Graphs (KGs) offer a complementary strength by representing entities and their…
Lehmann and Magidor's rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment…
Recent advances in large language models (LLMs) demonstrate their impressive reasoning capabilities. However, the reasoning confined to internal parametric space limits LLMs' access to real-time information and understanding of the physical…
This paper provides a self-contained first introduction to description logics (DLs). The main concepts and features are explained with examples before syntax and semantics of the DL SROIQ are defined in detail. Additional sections review…
We study extensions of expressive decidable fragments of first-order logic with circumscription, in particular the two-variable fragment FO$^2$, its extension C$^2$ with counting quantifiers, and the guarded fragment GF. We prove that if…
Inspired by the success of large language models, there is a trend toward developing graph foundation models to conduct diverse downstream tasks in various domains. However, current models often require extra fine-tuning to apply their…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
Recent progress in large language models (LLMs) has demonstrated the ability to learn and leverage Internet-scale knowledge through pre-training with autoregressive models. Unfortunately, applying such models to settings with embodied…