Related papers: The Algebraic Structure of Morphosyntax
The syntactic Merge operation of the Minimalist Program in linguistics can be described mathematically in terms of Hopf algebras, with a formalism similar to the one arising in the physics of renormalization. This mathematical formulation…
We give an explicit construction of the generating set of a colored operad that implements theta theory in the mathematical model of Minimalism in generative linguistics, in the form of a coloring algorithm for syntactic objects. We show…
In this paper we present a lexicon-based approach to the problem of morphological processing. Full-form words, lemmas and grammatical tags are interconnected in a DAWG. Thus, the process of analysis/synthesis is reduced to a search in the…
We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector…
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…
We extend our formulation of Merge and Minimalism in terms of Hopf algebras to an algebraic model of a syntactic-semantic interface. We show that methods adopted in the formulation of renormalization (extraction of meaningful physical…
Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical…
Morphological segmentation has traditionally been modeled with non-hierarchical models, which yield flat segmentations as output. In many cases, however, proper morphological analysis requires hierarchical structure -- especially in the…
We provide a mathematical argument showing that, given a representation of lexical items as functions (wavelets, for instance) in some function space, it is possible to construct a faithful representation of arbitrary syntactic objects in…
In the modern language sciences, the core computational operation of syntax, 'Merge', is defined as an operation that combines two linguistic units (e.g., 'brown', 'cat') to form a categorized structure ('brown cat', a Noun Phrase). This…
Mathematical language in scientific communications and educational scenarios is important yet relatively understudied compared to natural languages. Recent works on mathematical language focus either on representing stand-alone mathematical…
We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up…
We show that head functions on syntactic objects extend the magma structure to a hypermagma, with the c-command relation compatible with the magma operation and the m-command relation with the hypermagma. We then show that the structure of…
The main ideas developed in this habilitation thesis consist in endowing combinatorial objects (words, permutations, trees, Young tableaux, etc.) with operations in order to construct algebraic structures. This process allows, by studying…
A general definition of mathematical morphology has been defined within the algebraic framework of complete lattice theory. In this framework, dealing with deterministic and increasing operators, a dilation (respectively an erosion) is an…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
The study of semantic relationships has revealed a close connection between these relationships and the morphological characteristics of a language. Morphology, as a subfield of linguistics, investigates the internal structure and formation…
Much like sentences are composed of words, words themselves are composed of smaller units. For example, the English word questionably can be analyzed as question+able+ly. However, this structural decomposition of the word does not directly…
Morpho-syntactic lexicons provide information about the morphological and syntactic roles of words in a language. Such lexicons are not available for all languages and even when available, their coverage can be limited. We present a…
Simon's factorization theorem is a celebrated tool in algebraic automata theory, providing bounded-depth decompositions of words with respect to morphisms into finite semigroups. We develop an analogue of Simon's theorem for \emph{forests}…