Related papers: Unification of Deterministic Higher-Order Patterns…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
The uniform boundary condition in a normed chain complex asks for a uniform linear bound on fillings of null-homologous cycles. For the $\ell^1$-norm on the singular chain complex, Matsumoto and Morita established a characterisation of the…
Finite determinacy for mappings has been classically thoroughly studied in numerous scenarios in the real- and complex-analytic category and in the differentiable case. It means that the map-germ is determined, up to a given equivalence…
In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f \colon X \to Y$ between $\operatorname{qcb}_0$-spaces one…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
This paper introduces a model theory for resolution on Higher Order Hereditarily Harrop formulae (HOHH), the logic underlying the Lambda-Prolog programming language, and proves soundness and completeness of resolution. The semantics and the…
We investigate lifted inference on ordered domains with predecessor relations, where the elements of the domain respect a total (cyclic) order, and every element has a distinct (clockwise) predecessor. Previous work has explored this…
Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects…
A common feature of recent unification-based grammar formalisms is that they give the user the ability to define his own structures. However, this possibility is mostly limited and does not include nonmonotonic operations. In this paper we…
The interplay between Machine Learning (ML) and Constrained Optimization (CO) has recently been the subject of increasing interest, leading to a new and prolific research area covering (e.g.) Decision Focused Learning and Constrained…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…
We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more…
We devise a unified framework for the design of canonization algorithms. Using hereditarily finite sets, we define a general notion of combinatorial objects that includes graphs, hypergraphs, relational structures, codes, permutation…
We introduce a new approach for establishing fixed-parameter tractability of problems parameterized above tight lower bounds. To illustrate the approach we consider three problems of this type of unknown complexity that were introduced by…
We propose an analysis of corrections which models some of the requirements corrections place on context. We then show that this analysis naturally extends to the interaction of corrections with pronominal anaphora on the one hand, and…
A unified approach to derive optimal finite differences is presented which combines three critical elements for numerical performance especially for multi-scale physical problems, namely, order of accuracy, spectral resolution and…
We formulate the machine unlearning problem as a general constrained optimization problem. It unifies the first-order methods from the approximate machine unlearning literature. This paper then introduces the concept of feasible updates as…