Related papers: Considerations on Everett J. Nelson's connexive lo…

Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…

Natural language definitions possess a recursive, self-explanatory semantic structure that can support representation learning methods able to preserve explicit conceptual relations and constraints in the latent space. This paper presents a…

With computers to handle more and more complicated things in variable environments, it becomes an urgent requirement that the artificial intelligence has the ability of automatic judging and deciding according to numerous specific…

Although Large Language Models (LLMs) have demonstrated impressive formal reasoning abilities, they often break down when problems require complex proof planning. One promising approach for improving LLM reasoning abilities involves…

Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to…

We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined…

We present a network model in which words over a specific alphabet, called {\it structures}, are associated to each node and undirected edges are added depending on some distance between different structures. It is shown that this model can…

For many standard models of random structure, first-order logic sentences exhibit a convergence phenomenon on random inputs. The most well-known example is for random graphs with constant edge probability, where the probabilities of…

The unification of symbolic reasoning and neural networks remains a central challenge in artificial intelligence. Symbolic systems offer reliability and interpretability but lack scalability, while neural networks provide learning…

This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called…

We investigate the problem of learning description logic ontologies from entailments via queries, using epistemic reasoning. We introduce a new learning model consisting of epistemic membership and example queries and show that polynomial…

In the last 20 years many proposals have been made to incorporate non-monotonic reasoning into description logics, ranging from approaches based on default logic and circumscription to those based on preferential semantics. In particular,…

We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…

Extracting relations is critical for knowledge base completion and construction in which distant supervised methods are widely used to extract relational facts automatically with the existing knowledge bases. However, the automatically…

Since the seminal paper by Tversky and Kahneman, the conjunction fallacy has been the subject of multiple debates and become a fundamental challenge for cognitive theories in decision-making. In this article, we take a rather uncommon…

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…

Document-level relation extraction requires integrating information within and across multiple sentences of a document and capturing complex interactions between inter-sentence entities. However, effective aggregation of relevant…

While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the…

We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of subsets of a given set is called here an "eventual family" if it is upper hereditary with…

The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of…