Analogical proportions link four items a, b, c, d by a relation stating that ``a is to b as c is to d", a, b, c, d being the formal representation of real world entities, ranging from simple numerical values to more complex structures such as profiles. Accordingly, $a, b, c, d$ could be atomic values like Boolean, nominal or numerical values, more generally vectors of such values, or even families of items represented by logical formulas.
Analogies are quaternary relations of the form "A is to B as C is to D". Among the various formalizations of analogical reasoning, proportional analogies provide an important axiomatic framework by characterizing valid analogies through a set of postulates.
arXiv:2608. 11724v1 Announce Type: new Abstract: Analogies are quaternary relations of the form "A is to B as C is to D".
arXiv:2606. 03245v1 Announce Type: cross Abstract: Concepts of calibration formalize the compatibility between probabilistic predictions and the respective outcomes.
arXiv:2609.09855v1 Announce Type: new Abstract: Although probabilistic statements are ubiquitous, foundational disagreements persist about their understanding, as exemplified by debates between Bayes...
arXiv:2608. 14220v1 Announce Type: new Abstract: Analogies are quaternary relations of the form "a is to b as c is to d", usually denoted a : b :: c : d.
arXiv:2606. 00102v1 Announce Type: new Abstract: Over the centuries, probability theory has grown from the calculus of games of chance into a central framework for reasoning under uncertainty.
The paper examines the geometry of semantic neighbourhood graphs as modal logic, translating this view into a statistical framework to differentiate human from AI-generated text. It models texts as worlds in a finite frame where accessibility is defined by the k‑nearest‑neighbour relation of transformer embeddings, and measures the frequencies of modal axioms (B, 4, 5, D) as validation degrees. A prompt‑balanced comparison shows consistently higher degrees for axioms 4 and 5 in AI‑generated corpora, and the study further introduces measures of groundedness and situatedness, recasting the analysis in a sequent‑style tableau setting. "whyItMatters":"The work provides a quantitative, modal‑logic‑based method to detect structural differences between human and machine‑generated text, offering a new lens for evaluating AI language models."
arXiv:2605. 05368v4 Announce Type: replace-cross Abstract: Information is one of the most widely-discussed concepts of the current era.
arXiv:2608.31120v1 Announce Type: new Abstract: The motivation for this paper is the investigation of the trade-offs implicit in probabilistic models used in machine learning. Models are often used t...
arXiv:2606. 17851v1 Announce Type: new Abstract: A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $\sigma$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases.
arXiv:2006. 04156v2 Announce Type: replace Abstract: Our inferences in the real world are rarely na\"ive - we acquire experiences through our lifetime that can help us more quickly understand the structure of something new.
Baobab compiles an OWL 2 DL (ΣROIQ) ontology with a finite ABox into a Sentential Decision Diagram (SDD), saturating a propositional core and instantiating remaining DL features over the active domain. The resulting evidence‑conditioned weighted model count trains a perception network to recognize real images under partial ABox supervision, enabling a CNN to recover latent ontology concepts that an independent perception would miss. When supervision allows multiple ontology‑consistent completions, Baobab’s mixture indexed by query justifications represents the calibrated posterior, achieving Bayes‑optimal performance on a real‑image MNIST task where single‑WMC and learned mixtures fail, thereby characterizing and mitigating reasoning shortcuts in a non‑Horn description logic.