Related papers: On the convergence of reduction-based and model-ba…

Standard Bayesian inference can build models that combine information from various sources, but this inference may not be reliable if components of a model are misspecified. Cut inference, as a particular type of modularized Bayesian…

The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…

The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable…

Ill-founded (or non-wellfounded) proof systems have emerged as a natural framework for inductive and coinductive reasoning. In such systems, soundness relies on global correctness criteria, such as the progressivity condition. Ensuring that…

We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping…

Researchers have proposed a wide variety of model explanation approaches, but it remains unclear how most methods are related or when one method is preferable to another. We examine the literature and find that many methods are based on a…

We review a range of reduction methods that have been, or may be useful for connecting models of the Earth's climate system of differing complexity. We particularly focus on methods where rigorous reduction is possible. We aim to highlight…

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

This paper explores the connection between two central results in the proof theory of classical logic: Gentzen's cut-elimination for the sequent calculus and Herbrands "fundamental theorem". Starting from Miller's expansion-tree-proofs, a…

We provide a summary of the mathematical and computational techniques that have enabled learning reductions to effectively address a wide class of problems, and show that this approach to solving machine learning problems can be broadly…

Researchers have proposed a wide variety of model explanation approaches, but it remains unclear how most methods are related or when one method is preferable to another. We describe a new unified class of methods, removal-based…

Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction.

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…

This paper presents a proof-theoretic analysis of the modal $\mu$-calculus. More precisely, we prove a syntactic cut-elimination for the non-wellfounded modal $\mu$-calculus, using methods from linear logic and its exponential modalities.…

This paper is intended to provide an introduction to cut elimination which is accessible to a broad mathematical audience. Gentzen's cut elimination theorem is not as well known as it deserves to be, and it is tied to a lot of interesting…

Two moment-matching methods for model reduction of linear switched systems (LSSs) are presented. The methods are similar to the Krylov subspace methods used for moment matching for linear systems. The more general one of the two methods, is…

The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…

In this paper, we use a new method to prove cut-elimination of weak intuitionistic tense logic. This method focuses on splitting the contraction rule and cut rules. Further general theories and applications of this method shall be developed…

A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with…