Related papers: Redundancy in Logic II: 2CNF and Horn Propositiona…

Hierarchical feature learning based on convolutional neural networks (CNN) has recently shown significant potential in various computer vision tasks. While allowing high-quality discriminative feature learning, the downside of CNNs is the…

We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven clause learning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL) deciding the…

In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…

We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…

We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…

Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to…

This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…

We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…

We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…

In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative…

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…

This paper aims to define, quantify, and analyze the feature complexity that is learned by a DNN. We propose a generic definition for the feature complexity. Given the feature of a certain layer in the DNN, our method disentangles feature…

We leverage diffusion models to study the robustness-performance tradeoff of robust classifiers. Our approach introduces a simple, pretrained diffusion method to generate low-norm counterfactual examples (CEs): semantically altered data…

In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…

Forgetting a specific belief revision episode may not erase information because the other revisions may provide or entail the same information. Whether it does was proved coNP-hard for sequences of two arbitrary lexicographic revisions or…

We present a novel view that unifies two frameworks that aim to solve sequential prediction problems: learning to search (L2S) and recurrent neural networks (RNN). We point out equivalences between elements of the two frameworks. By…

The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of…

Compositionality is one of the fundamental abilities of the human reasoning process, that allows to decompose a complex problem into simpler elements. Such property is crucial also for neural networks, especially when aiming for a more…