Related papers: Reasoning about embedded dependencies using inclus…
Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary)…
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…
We study various notions of dependency in semiring team semantics. Semiring teams are essentially database relations, where each tuple is annotated with some element from a positive semiring. We consider semiring generalizations of several…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
In Inverse subsumption for complete explanatory induction Yamamoto et al. investigate which inductive logic programming systems can learn a correct hypothesis $H$ by using the inverse subsumption instead of inverse entailment. We prove that…
During the last decade, entity embeddings have become ubiquitous in Artificial Intelligence. Such embeddings essentially serve as compact but semantically meaningful representations of the entities of interest. In most approaches, vectors…
This unpublished note is an alternate, shorter (and hopefully more readable) proof of the decidability of all minimal models. The decidability follows from a proof of the existence of a cellular term in each observational equivalence class…
The logic of Bunched Implications (BI) freely combines additive and multiplicative connectives, including implications; however, despite its well-studied proof theory, proof-search in BI has always been a difficult problem. The focusing…
Incomplete data are common in practical applications. Most predictive machine learning models do not handle missing values so they require some preprocessing. Although many algorithms are used for data imputation, we do not understand the…
We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Proofs (sequent calculus, natural deduction) and imperative algorithms (pseudocodes) are two well-known coexisting concepts. Then what is their relationship? Our answer is that \[ imperative\ algorithms\ =\ proofs\ with\ cuts \] This…
Like any field of empirical science, AI may be approached axiomatically. We formulate requirements for a general-purpose, human-level AI system in terms of postulates. We review the methodology of deep learning, examining the explicit and…
We construct a realizability model of linear dependent type theory from a linear combinatory algebra. Our model motivates a number of additions to the type theory. In particular, we add a universe with two decoding operations: one takes…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
We study the assessment of semiparametric and other highly-parametrised models from the perspective of foundational principles of parametric statistical inference. In doing so, we highlight the possibility of avoiding the usual…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…