相关论文: A Topological Application of Labelled Natural Dedu…

This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…

We provide a simple linear time transformation from a directed or undirected graph with labeled edges to an unlabeled digraph, such that paths in the input graph in which no two consecutive edges have the same label correspond to paths in…

This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local…

We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in…

We introduced a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational…

We introduce a formalism to analyze partially defined functions between ordered sets. We show that our construction provides a uniform and conceptual approach to all the main definitions encountered in elementary real analysis including…

Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

We show that the proof-theoretic notion of logical preorder coincides with the process-theoretic notion of contextual preorder for a CCS-like calculus obtained from the formula-as-process interpretation of a fragment of linear logic. The…

In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system R is confluent if all its critical pairs are joinable and the critical pair steps are relatively terminating with respect to R. We further…

External labeling is frequently used for annotating features in graphical displays and visualizations, such as technical illustrations, anatomical drawings, or maps, with textual information. Such a labeling connects features within an…

Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…

Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…

Deduction modulo is a way to express a theory using computation rules instead of axioms. We present in this paper an extension of deduction modulo, called Polarized deduction modulo, where some rules can only be used at positive…

We propose a calculus of local equations over one-way computing patterns, which preserves interpretations, and allows the rewriting of any pattern to a standard form where entanglement is done first, then measurements, then local…

We show how polynomial path orders can be employed efficiently in conjunction with weak innermost dependency pairs to automatically certify polynomial runtime complexity of term rewrite systems and the polytime computability of the…

An algebraic telic problem is a decision problem in $\textsf{NP}_\mathbb{R}$ formalizing finite-time reachability questions for one-dimensional dynamical systems. We prove that the existence of "natural" mapping reductions between algebraic…

We give a new practical method for computing subvarieties of projective hypersurfaces. By computing the periods of a given hypersurface X, we find algebraic cohomology cycles on X. On well picked algebraic cycles, we can then recover the…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…