Related papers: Layer Systems for Proving Confluence

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…

A number of elements towards a classification of the quality of emergence in emergent collective systems are provided. By using those elements, several classes of emergent systems are exemplified, ranging from simple aggregations of simple…

This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…

Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…

This paper presents the methodology for the system requirements and architecture w.r.t. their decomposition and refinement. It also introduces ideas of refinement layers and of refinement-based verification.

We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…

We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be…

There exist a number of results proving that for certain classes of interacting particle systems in population genetics, mutual invadability of types implies coexistence. In this paper we prove a sort of converse statement for a class of…

Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…

We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…

We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations…

Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…

I study the modal theory of linear orders under embeddings, monotone maps, condensations, and end-extensions. I prove modality elimination for embeddings and monotone maps, show that condensations make scatteredness modally definable, and…

In type theories, universe hierarchies are commonly used to increase the expressive power of the theory while avoiding inconsistencies arising from size issues. There are numerous ways to specify universe hierarchies, and theories may…

Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network…

A coherent presentation of an n-category is a presentation by generators, relations and relations among relations. Confluent and terminating rewriting systems generate coherent presentations, whose relations among relations are defined by…

Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…