arXiv:2606. 15719v1 Announce Type: cross Abstract: This paper investigates the algebraic structure of Krom logic programs, consisting only of facts and rules with at most one body atom.
arXiv:2603. 13854v2 Announce Type: replace-cross Abstract: We introduce power term polynomial algebra, a representation language for Boolean formulae designed to bridge conjunctive normal form (CNF) and algebraic normal form (ANF).
arXiv:2608. 04945v1 Announce Type: cross Abstract: The emergence of the ISO standard GQL introduces a powerful query language extending first-order logic with controlled recursion, raising the question of its applicability to evaluation of ontology-mediated queries (OMQs).
arXiv:2608. 08118v1 Announce Type: new Abstract: There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators.
arXiv:2407. 15510v2 Announce Type: replace Abstract: Abstraction is key to human and artificial intelligence as it allows one to identify common structure in otherwise distinct objects or situations.
arXiv:2608. 13433v1 Announce Type: cross Abstract: Transformer-based language models are known to sometimes generalize to sequences longer than seen during training, but we lack a precise characterization of which tasks admit length generalization.
The emergence of the ISO standard GQL introduces a powerful query language extending first-order logic with controlled recursion, raising the question of its applicability to evaluation of ontology-mediated queries (OMQs). We focus on OMQs consisting of atomic queries over ontologies expressed in Horn-ALCHI, an expressive Description Logic that is not, in general, first-order rewritable.
arXiv:2607. 23500v1 Announce Type: cross Abstract: Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming.
arXiv:2606. 03655v1 Announce Type: new Abstract: Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al.
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
arXiv:2607. 21203v1 Announce Type: new Abstract: Description logic programs are a powerful formalism for combining rules with ontologies.
arXiv:2606. 17882v1 Announce Type: new Abstract: Bridges between graph neural networks (GNNs) and logical formalisms have been established by fixing architectural choices, such as the types of aggregation, combination, and activation functions.
arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.