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:2607. 09032v1 Announce Type: cross Abstract: Quantum logic is usually presented as a non-classical departure from ordinary reasoning forced on us by quantum mechanics, with classical logic kept as the secure starting point.
arXiv:2607. 06407v1 Announce Type: new Abstract: The XAI community has studied a wide range of queries and scores for explaining predictions of ML models.
arXiv:2608. 15143v1 Announce Type: new Abstract: Constraint solving is a declarative approach for solving combinatorial satisfaction and optimization problems.
arXiv:2604. 26976v2 Announce Type: replace-cross Abstract: We study the problem of fitting a description logic (DL) ontology to a given set of positive and negative examples that take the form of an ABox and a Boolean query.
arXiv:2607. 21203v1 Announce Type: new Abstract: Description logic programs are a powerful formalism for combining rules with ontologies.
arXiv:2607. 21199v1 Announce Type: cross Abstract: Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution.
arXiv:2601. 18747v2 Announce Type: replace-cross Abstract: Modern AI agents increasingly rely on search infrastructure to execute complex, neuro-symbolic reasoning workflows.
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.
Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies.
The paper presents three Isabelle/HOL embeddings of monadic second‑order logic (MSO): a deep embedding, a maximal‑shallow embedding, and a minimal‑shallow embedding that collapses formulas to bool. It introduces a two‑sorted substitution system that ensures capture‑avoiding substitution and proves the faithfulness of all embeddings. A fully mechanised two‑sorted downward Löwenheim‑Skolem theorem is established, showing that the minimal embedding recovers deep validity relative to countable assignments and aligns with both the general (Henkin‑style) and standard readings of MSO, while also demonstrating differences in classical MSO properties across the embeddings.
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
The paper presents a complete characterization of when two deep ReLU networks realize the same function, showing that this occurs iff one can be transformed into the other using a set of axioms from many‑valued logic. It introduces a symbolic calculus that maps networks to substitution graphs, proves a completeness theorem linking equivalent formulas, and provides an algorithm to reconstruct networks from these graphs. The framework yields a new compositional normal form for MV logic that preserves the algebraic structure of deep ReLU networks.