A constructive proof of the Heine-Borel covering theorem for formal reals

The continuum is here presented as a formal space by means of a finitary inductive definition. In this setting a constructive proof of the Heine-Borel covering theorem is given

Glivenko sequent classes in the light of structural proof theory

Peer reviewe

The Poverty in USA: An In-Depth Analysis of the Last Two Decades

Poverty is a global problem that affects not only the undeveloped states but also the most developed ones. This research paper will analyze this problem in depth, trying to summarize several definitions, several causes that can lead to an increase in the poverty rate, and policies implemented by the government in order to reduce the total number of poor people. The author analyzed the poverty rate in each state of the United States from 1990 to 2019 using a panel data analysis. She found out that California is the state with the highest value of poor people in the U.S. The independent variables analyzed in this paper are the unemployment rate, personal income, total number of residents, total number of violent crimes, and Gini coefficient. At the end of our analysis, the author discovered that the total number of poor people is positively affected by population size, the total number of violent crimes, the Gini coefficient, and the unemployment rate (for relatively poor people only). In particular, the Gini coefficient has a standard error high, so it needs further studies. The last chapter will analyze the difference in poverty rate between the U.S. and Italy and possible causes that can explain the differences. The results show that the U.S. had a higher poverty rate than Italy from 1997 to 2019, and the author concludes with some suggestions to encourage further studies about the topic

Constructive Cut Elimination in Geometric Logic

Funding Information: Partially funded by the Academy of Finland, research project no. Publisher Copyright: © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.A constructivisation of the cut-elimination proof for sequent calculi for classical and intuitionistic infinitary logic with geometric rules - given in earlier work by the second author - is presented. This is achieved through a procedure in which the non-constructive transfinite induction on the commutative sum of ordinals is replaced by two instances of Brouwer's Bar Induction. Additionally, a proof of Barr's Theorem for geometric theories that uses only constructively acceptable proof-theoretical tools is obtained.Peer reviewe

Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics

International audienceThe preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness and completeness of PCL and its extensions with respect to this class of models are proved directly. Labelled sequent calculi for all logics of the family are then introduced. The cal-culi are modular and have standard proof-theoretical properties, the most important of which is admissibility of cut, that entails a syntactic proof of completeness of the calculi. By adopting a general strategy, root-first proof search terminates, thereby providing a decision procedure for PCL and its extensions. Finally, the semantic completeness of the calculi is established: from a finite branch in a failed proof attempt it is possible to extract a finite countermodel of the root sequent. The latter result gives a constructive proof of the finite model property of all the logics considered

Modal logic for induction

Peer reviewe

AlignAtt: Using Attention-based Audio-Translation Alignments as a Guide for Simultaneous Speech Translation

Attention is the core mechanism of today's most used architectures for natural language processing and has been analyzed from many perspectives, including its effectiveness for machine translation-related tasks. Among these studies, attention resulted to be a useful source of information to get insights about word alignment also when the input text is substituted with audio segments, as in the case of the speech translation (ST) task. In this paper, we propose AlignAtt, a novel policy for simultaneous ST (SimulST) that exploits the attention information to generate source-target alignments that guide the model during inference. Through experiments on the 8 language pairs of MuST-C v1.0, we show that AlignAtt outperforms previous state-of-the-art SimulST policies applied to offline-trained models with gains in terms of BLEU of 2 points and latency reductions ranging from 0.5s to 0.8s across the 8 languages.Comment: Accepted at Interspeech 202

Visualization: the missing factor in Simultaneous Speech Translation

Simultaneous speech translation (SimulST) is the task in which output generation has to be performed on partial, incremental speech input. In recent years, SimulST has become popular due to the spread of cross-lingual application scenarios, like international live conferences and streaming lectures, in which on-the-fly speech translation can facilitate users' access to audio-visual content. In this paper, we analyze the characteristics of the SimulST systems developed so far, discussing their strengths and weaknesses. We then concentrate on the evaluation framework required to properly assess systems' effectiveness. To this end, we raise the need for a broader performance analysis, also including the user experience standpoint. SimulST systems, indeed, should be evaluated not only in terms of quality/latency measures, but also via task-oriented metrics accounting, for instance, for the visualization strategy adopted. In light of this, we highlight which are the goals achieved by the community and what is still missing.Comment: Accepted at CLIC-it 202

The intensional side of algebraic-topological representation theorems

Stone representation theorems are a central ingredient in the metatheory of philosophical logics and are used to establish modal embedding results in a general but indirect and non-constructive way. Their use in logical embeddings will be reviewed and it will be shown how they can be circumvented in favour of direct and constructive arguments through the methods of analytic proof theory, and how the intensional part of the representation results can be recovered from the syntactic proof of those embeddings. Analytic methods will also be used to establish the embedding of subintuitionistic logics into the corresponding modal logics. Finally, proof-theoretic embeddings will be interpreted as a reduction of classes of word problems.Peer reviewe