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: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).
The paper introduces the Quantum-Logic Tsetlin Machine (QL‑TM), a variant of Tsetlin Machines that replaces Boolean literals with quantum propositions represented by projectors while keeping the classical include/exclude automata. Clauses are limited to commuting measurement contexts and are activated through the Born probability of their joint projector, allowing an exact reduction to ordinary Boolean TM clauses in diagonal computational‑basis contexts. Experiments on Bell states, phase‑flip syndromes, stabilizer tasks, and noise‑robust settings demonstrate that correct non‑diagonal contexts recover physically meaningful clauses, whereas diagonal or wrong contexts lose phase or syndrome information, and the context‑budget results align with the predicted separability ladder.
arXiv:2609.14533v1 Announce Type: cross Abstract: Automated theorem proving seeks to use computational systems to prove or disprove mathematical and logical statements [1, 2]. It underpins a wide ran...
arXiv:2602.02940v2 Announce Type: replace-cross Abstract: Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model...
The paper derives an information‑theoretic bound for a shared‑state cognitive architecture that uses an auxiliary variable to mediate context. It shows that the residual dependence of observable behavior on context, given the shared state, is bounded by the information carried by the auxiliary variable and its conditional entropy. A recognition‑memory example illustrates how to compute and compare this bound across different representational choices, providing a framework for analyzing context‑memory‑control trade‑offs in cognitive models and artificial agents.
arXiv:2603. 20381v2 Announce Type: replace-cross Abstract: Understanding the fundamental mechanisms governing the production of meaning in the processing of natural language is critical for designing safe, thoughtful, engaging, and empowering human-agent interactions.
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.
arXiv:2606. 13811v1 Announce Type: cross Abstract: Can Large Language Models (LLMs) understand and reason about quantum operators?
The paper introduces QXymb, a framework for building observational declarative twins of quantum circuits, and presents its first complete order‑0 specialization, QILP‑0. QILP‑0 transforms observed circuit behavior into a finite multi‑valued propositional logic program by incrementally traversing a declared family of quantum observables, quantifying progress via reference‑relative coverage, and preserving observational semantics through deterministic mapping back to original observable columns. Validation on Bars & Stripes and MNIST quantum machine learning settings shows that the induced QILP‑0 theory achieves perfect, conflict‑free reconstruction of the discrete relations, with logical exactness separated from numerical and discretization uncertainties. whyItMatters":"The work demonstrates a method to construct exact observational declarative twins of quantum circuits, enabling precise logical reconstruction of quantum behavior independent of numerical uncertainties."
arXiv:2608. 14004v1 Announce Type: new Abstract: In-context learning is commonly formalized as inference from examples of a function.
arXiv:2609.36279v1 Announce Type: cross Abstract: The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's va...
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.