Related papers: Mathematical Structure of Syntactic Merge
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
As a natural basis of the Hopf algebra of quasisymmetric functions, monomial quasisymmetric functions are formal power series defined from compositions. The same definition applies to left weak compositions, while leads to divergence for…
Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of…
Most merging operators are defined by semantics methods which have very high computational complexity. In order to have operators with a lower computational complexity, some merging operators defined in a syntactical way have be proposed.…
The quasisymmetric functions, $QSym$, are generalized for a finite alphabet $A$ by the colored quasisymmetric functions, $QSym_A$, in partially commutative variables. Their dual, $NSym_A$, generalizes the noncommutative symmetric functions,…
We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which…
Informal mathematical text underpins real-world quantitative reasoning and communication. Developing sophisticated methods of retrieval and abstraction from this dual modality is crucial in the pursuit of the vision of automating discovery…
As first main contribution, this thesis characterises the PROP SVk of linear subspaces over a field k - an important domain of interpretation for circuit diagrams appearing in diverse research areas. We present by generators and equations…
The first contribution of this paper is the presentation of a Pavelka - like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (eg) and a new type of conjunction…
This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the…
Human language has a distinct systematic structure, where utterances break into individually meaningful words which are combined to form phrases. We show that natural-language-like systematicity arises in codes that are constrained by a…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
This paper describes a first step towards the definition of an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the…
This article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover…
In this talk, we show how the Connes-Kreimer Hopf algebra morphism can be extended when taking into account the wave-function renormalization. This leads us to a semi-direct product of invertible power series by formal diffeomorphisms.
In recent years a Hopf algebraic structure underlying the process of renormalization in quantum field theory was found. It led to a Birkhoff factorization for (regularized) Hopf algebra characters, i.e. for Feynman rules. In this work we…
Here we consider some well-known facts in syntax from a physics perspective, allowing us to establish equivalences between both fields with many consequences. Mainly, we observe that the operation MERGE, put forward by N. Chomsky in 1995,…
Syllables play an important role in speech synthesis, speech recognition, and spoken document retrieval. A novel, low cost, and language agnostic approach to dividing words into their corresponding syllables is presented. A hybrid genetic…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
We contruct here the Hopf algebra structure underlying the process of renormalization of non-commutative quantum field theory.