Related papers: Symbolic Languages and Ars Combinatoria
We present a unified framework for the declarative analysis of structured communications. By relying on a (timed) concurrent constraint programming language, we show that in addition to the usual operational techniques from process calculi,…
The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then…
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language…
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
I present the most fundamental features of an implemented system designed to manipulate representations of regular languages. The system is structured into two layers, allowing regular languages to be represented in an increasingly compact,…
Invitation to the statistical study of language: The topic of this presentation is the interdisciplinary nexus between linguistics and statistics. It targets linguists, for whom it may have a theoretical interest, or professionals that work…
NLP is deeply intertwined with the formal study of language, both conceptually and historically. Arguably, this connection goes all the way back to Chomsky's Syntactic Structures in 1957. It also still holds true today, with a strand of…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
This note clarifies the concept of syntax and semantics and their relationships. Today, a lot of confusion arises from the fact that the word "semantics" is used in different meanings. We discuss a general approach at defining semantics…
The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct…
"[M]athematicians care no more for logic than logicians for mathematics." Augustus de Morgan, 1868. Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional…
In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…
One hallmark of human language is its combinatoriality -- reusing a relatively small inventory of building blocks to create a far larger inventory of increasingly complex structures. In this paper, we explore the idea that combinatoriality…
Formal, Distributional, and Grounded theories of computational semantics each have their uses and their drawbacks. There has been a shift to ground models of language by adding visual knowledge, and there has been a call to enrich models of…
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…