Related papers: FOLE: The First-order Logical Environment
Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
This paper discusses an axiomatic approach for the integration of ontologies, an approach that extends to first order logic a previous approach (Kent 2000) based on information flow. This axiomatic approach is represented in the Information…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
A converter from first-order modal logics to classical higher- order logic is presented. This tool enables the application of off-the-shelf higher-order theorem provers and model finders for reasoning within first- order modal logics. The…
Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model-value beyond mere comprehensible pictures. To…
One of the main obstacles for developing flexible AI systems is the split between data-based learners and model-based solvers. Solvers such as classical planners are very flexible and can deal with a variety of problem instances and goals…
Constraint propagation is one of the basic forms of inference in many logic-based reasoning systems. In this paper, we investigate constraint propagation for first-order logic (FO), a suitable language to express a wide variety of…
In this paper we introduce the olog, or ontology log, a category-theoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and cross-compared in ways that other KR models (such as…
In spite of the amazing results obtained by deep learning in many applications, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higher-level symbolic inference. Therefore, there is a…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…
We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…
Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model,…
The theory of distributed conceptual structures, as outlined in this paper, is concerned with the distribution and conception of knowledge. It rests upon two related theories, Information Flow and Formal Concept Analysis, which it seeks to…
Information extraction (IE) aims to produce structured information from an input text, e.g., Named Entity Recognition and Relation Extraction. Various attempts have been proposed for IE via feature engineering or deep learning. However,…
First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…