Modalities in Substructural Logics: Theory, Methods and Applications

Project Information

MOSAIC

Grant agreement ID: 101007627

DOI

10.3030/101007627

Project closed

EC signature date 9 November 2020

Start date 1 September 2021

End date 30 April 2026

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 1 016 600,00

EU contribution

€ 1 016 600,00

Coordinated by

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS
Spain

Periodic Reporting for period 1 - MOSAIC (Modalities in Substructural Logics: Theory, Methods and Applications)

Reporting period: 2021-09-01 to 2024-04-30

Summary of the context and overall objectives of the project

Modal logics are a family of formal systems based on classical logic that improve its expressive power allowing to reason about modes of truth: epistemic, doxastic, temporal, normative, information updates, etc. Substructural logics are weaker deductive systems than classical logic that can account for notions of truth other than Boolean, such as constructive proofs and computation (intuitionistic logic), degrees of truth (fuzzy logics), local contradictions (paraconsistent logics), and others.

The objectives are:

(1) Putting forward a comprehensive and unifying logico-mathematical study of substructural modal logics, that is, substructural logics with modalities.

(2) Exploring the application of substructural modal logics outside the bounds of mathematical logic and, in particular, in the areas of knowledge representation; legal reasoning; data privacy and security; logical analysis of natural language.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

During the first year of the project, the involve community has been mainly investigating questions on Work Packages 4 (General Semantics and Axiomatization) and Work Package 7 (Logics for special reasoning models). Results on such argument have been published mainly in the proceedings of international conferences (4) and on international journals (3). Also, a book chapter will be published soon.
As for of publications in international journals, it is worth to remember that top journals in our area have a quite long revision process and, once accepted, a paper might take some months to be published either in its online or in its printed version. Despite this fact, the MOSAIC community manages to publish already 3 papers in international journals. As for conference proceedings, we have a total number of 4 publications, most of which in the main area of WPs 4 and 7. Quality indicators for publications: As for the international journals, the Annals of Pure and Applied Logic is one of the most renewed publication in our area. Also, Studia Logica and the Journal of Logic and Computation are considered top journals in the area of Logic. JELIA is a top conference in the area of Logic and Artificial Intelligence.

In September 2022 the MOSAIC kick off conference was organized in Paestum (Italy) and co-located with the international conference LATD 2022 (Logic, Algebra and Truth Degrees). The choice for a co-location will be explained in Section 2.1 below. This was the first event in which the whole community around the MOSAIC project met and we hence expect even stronger collaboration to start from now on. Around 70 scholars participated in the event.

Also in September 2022 the MOSAIC cofound summer school “Logics of the new AI spring” was organized in Como (Italy) in collaboration with the Como Lake School for Advanced Studies. The main organization of the school has been carried out by the CSIC together with the University of Milan, the latter being the Lead Beneficiary of WP2 (Schools and Training). Around 60 among PhD students and postdocs early stage researchers participated in the school. The summer school is linked to a Special Issue on “Logics for the new AI Spring”.
On September 2023 we cofound a summer school in South Africa together with our partner the University of Witwatersrand in Johannesburg.
Also we organize a workshop in Vienna (Austria), organized by the MOSAIC beneficiary Technische Universität Wien.

We are planning to co-locate the next major event together with the international conference AiML (Advances in Modal Logic) that will be held in Prague, and organized by the MOSAIC beneficiary Ustav informatiky (ICS-CAS), in 2024.

We add 4 new partners: University of Siena (Italy), University of Cagliari (Italy), University of Olomouc (Czech Republic) and the Jagiellonian University (Poland).

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

the scientific production produced by the community of the MOSAIC project, during the first 32 months of the action, have already published our results in:

- 24 articles have been published in peer-reviewed international journals
- 14 articles have been published in proceeding of peer-reviewed international conferences
- >100 communications at the international conferences and workshops organized and supported the project MOSAIC have been presented.

The special issue of the International Journal of Approximate Reasoning titled “Logics for the new AI spring”, linked to the summer school bringing the same name, has been published in February 2024 (https://www.sciencedirect.com/special-issue/10MRX9R3TGM)

Remarkably, a PhD candidate at the ILLC (University of Amsterdam) visited Chapman University in October 2023 thanks ot the MOSAIC project. During extensive working sessions a five decades old problem about decidability of the relevance logic S was solved. This has been an outstanding problem posed originally by Alasdair Urquhart - one of the founders of the area of substructural logic. The paper presenting this result has been published at the LICS conference, one of the most prestigious conferences on applications of logic in computer science.



We have extended 8 months to the first period in order to reach our goals in terms of secondments.

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