Related papers: NNIL-formulas revisited: universal models and fini…
We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hypergraph version of the results from [L. Lov\'asz, B.…
Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is…
Neural models combining representation learning and reasoning in an end-to-end trainable manner are receiving increasing interest. However, their use is severely limited by their computational complexity, which renders them unusable on real…
We have proved that for any pattern p the tail recursive program model of naive pattern matching may be automatically specialized w.r.t. the pattern p to a specialized version of the so-called KMP-algorithm, using the Higman-Kruskal…
Our goal is a modern approach to answering questions via systematic reasoning where answers are supported by human interpretable proof trees grounded in an NL corpus of authoritative facts. Such a system would help alleviate the challenges…
Any representational enterprise must omit variation in order to function. NASA still uses Newtonian mechanics, though Einstein superseded Newton, and the standard picture of scientific progress cannot explain how. A description that omitted…
We introduce the notions of triviality and order-triviality for global invariant types in an arbitrary first-order theory and show that they are well behaved in the NIP context. We show that these two notions agree for invariant global…
Let L be a finite extension of Q_p and d a positive integer. A conjecture, due to C. Breuil and P. Schneider, says that the existence of invariant norms on certain locally algebraic representations of GL_{d+1}(L) should be equivalent to the…
Let K be an algebraically bounded structure and T be its theory. If T is model complete, then the theory of K endowed with a derivation, denoted by $T^{\delta}$, has a model completion. Additionally, we prove that if the theory T is…
Inductive Logic Programming (ILP) systems learn generalised, interpretable rules in a data-efficient manner utilising existing background knowledge. However, current ILP systems require training examples to be specified in a structured…
We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them,…
By a result of John Ball (1981), a locally orientation preserving Sobolev map is almost everywhere globally invertible whenever its boundary values admit a homeomorphic extension. As shown here for any dimension, the conclusions of Ball's…
We introduce Spectral NSR, a fully spectral neuro-symbolic reasoning framework that embeds logical rules as spectral templates and performs inference directly in the graph spectral domain. By leveraging graph signal processing (GSP) and…
In this paper we generalize the well known relation between Heyting algebras and Nelson algebras in the framework of subresiduated lattices. In order to make it possible, we introduce the variety of subresiduated Nelson algebras. The main…
The nonlocal bosonic theory obtained from integrating out all anticommuting and auxiliary variables in a globally supersymmetric theory is characterized by the Nicolai map. We present a universal formula for the latter in terms of an…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
Combining two results from machine learning theory we prove that a formula is NIP if and only if it satisfies uniform definability of types over finite sets (UDTFS). This settles a conjecture of Laskowski.
On taking a non-trivial and semi-transitive bi-relation constituted by two (hard and soft) binary relations, we report a (i) p-continuity assumption that guarantees the completeness and transitivity of its soft part, and a (ii)…
Although the standard cosmological model is capable of explaining most current observational data, it faces some theoretical and observational issues. This is the main motivation for exploring alternative cosmological models. In this paper,…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…