arXiv:2608. 11724v1 Announce Type: new Abstract: Analogies are quaternary relations of the form "A is to B as C is to D".
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.
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.
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:2607. 20502v1 Announce Type: new Abstract: To allow for principled comparison between two probabilistic graphical models defined over non-identical variable sets, they have to be lifted to a common measurable space.
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. 07230v1 Announce Type: new Abstract: Probabilistic logic programming is a formalism of statistical relational artificial intelligence that supports causal queries, including interventions from outside the system.
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arXiv:2606. 03245v1 Announce Type: cross Abstract: Concepts of calibration formalize the compatibility between probabilistic predictions and the respective outcomes.
arXiv:2606. 21585v4 Announce Type: replace Abstract: A finite agent, a machine's digital twin or any bounded reasoner, infers a fixed and noisy world through finite sensors, so its coherent output is a belief: a probability density over states (the Bayes posterior).
arXiv:2503. 07811v3 Announce Type: replace-cross Abstract: The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science.