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In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…
Among the several findings deriving from the application of complex network formalism to the investigation of natural phenomena, the fact that linguistic constructions follow power laws presents special interest for its potential…
Sentence fusion is the task of joining related sentences into coherent text. Current training and evaluation schemes for this task are based on single reference ground-truths and do not account for valid fusion variants. We show that this…
Word embeddings predict a word from its neighbours by learning small, dense embedding vectors. In practice, this prediction corresponds to a semantic score given to the predicted word (or term weight). We present a novel model that, given a…
The words-as-classifiers model of grounded lexical semantics learns a semantic fitness score between physical entities and the words that are used to denote those entities. In this paper, we explore how such a model can incrementally…
Epistemic logics of intensional groups lift the assumption that membership in a group of agents is common knowledge. Instead of being represented directly as a set of agents, intensional groups are represented by a property that may change…
Nondeterministic weighted automata are finite automata with numerical weights on transitions. They define quantitative languages L that assign to each word w a real number L(w). The value of an infinite word w is computed as the maximal…
This paper has two parts. The main goal, carried out in Part I, is to survey some recent work by the authors in which "forced" grading constructions have played a significant role in the representation theory of semisimple algebraic groups…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
We further develop the theory of layered semigroups, as introduced by Farah, Hindman and McLeod, providing a general framework to prove Ramsey statements about such a semigroup $S$. By nonstandard and topological arguments, we show Ramsey…
Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
An established method for Word Sense Induction (WSI) uses a language model to predict probable substitutes for target words, and induces senses by clustering these resulting substitute vectors. We replace the ngram-based language model (LM)…
We present power low rank ensembles (PLRE), a flexible framework for n-gram language modeling where ensembles of low rank matrices and tensors are used to obtain smoothed probability estimates of words in context. Our method can be…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as…
In the last years renewed investigation of operator precedence languages (OPL) led to discover important properties thereof: OPL are closed with respect to all major operations, are characterized, besides the original grammar family, in…