Related papers: Natural Deduction and Normalization Proofs for the…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We report a four-years experiment in teaching reasoning to undergraduate students, ranging from weak to gifted, using Gentzen-Prawitz's style natural deduction. We argue that this pedagogical approach is a good alternative to the use of…
We study finite state transduction of automatic and morphic sequences. Dekking proved that morphic sequences are closed under transduction and in particular morphic images. We present a simple proof of this fact, and use the construction in…
In previous literature, backward error analysis was used to find ordinary differential equations (ODEs) approximating the gradient descent trajectory. It was found that finite step sizes implicitly regularize solutions because terms…
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…
Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation,…
We examine the reduction process of a system of second-order ordinary differential equations which is invariant under a Lie group action. With the aid of connection theory, we explain why the associated vector field decomposes in three…
The verification of reductions, representative subsets of interleavings, simplifies correctness proofs of parameterized concurrent programs. We introduce an expressive class of syntactic reductions, which we call natural reductions. Natural…
In the research on computational effects, defined algebraically, effect symbols are often expected to obey certain equations. If we orient these equations, we get a rewrite system, which may be an effective way of transforming or optimizing…
Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.
Unanticipated connections between different fragments of lambda calculus and different families of embedded graphs (a.k.a. "maps") motivate the problem of enumerating $\beta$-normal linear lambda terms. In this brief note, it is shown (by…
We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the…
We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is…
We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the "invariants by differentiation" property, and can hence be…
Designing and implementing typed programming languages is hard. Every new type system feature requires extending the metatheory and implementation, which are often complicated and fragile. To ease this process, we would like to provide…
In image processing, classical methods minimize a suitable functional that balances between computational feasibility (convexity of the functional is ideal) and suitable penalties reflecting the desired image decomposition. The fact that…
We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the…
Resolution and subtyping are two common mechanisms in programming languages. Resolution is used by features such as type classes or Scala-style implicits to synthesize values automatically from contextual type information. Subtyping is…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…