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: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.
arXiv:2605. 05368v4 Announce Type: replace-cross Abstract: Information is one of the most widely-discussed concepts of the current era.
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.
arXiv:2608. 17741v1 Announce Type: new Abstract: OWL 2 DL ontologies, grounded in the description logic $\mathcal{SROIQ}$, express large knowledge bases in biomedicine and the Semantic Web.
arXiv:2511. 03000v2 Announce Type: replace-cross Abstract: Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations.
This paper addresses Carl Hempel's longstanding problem of statistical ambiguity in inductive-statistical inference, in which contradictory predictions are derived from statistical laws. To avoid such predictions, Carl Hempel proposed the Requirement of Maximal Specificity (RMS) for the statistical laws used in the inference.
arXiv:2606. 19626v1 Announce Type: new Abstract: Byte-Pair Encoding tokenization is statistically efficient for vocabulary compression, but semantically blind to structured technical entities, fragmenting physical quantities, numbers, units, and symbolic expressions into lexically arbitrary subwords.