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Documents authored by Perini Brogi, Cosimo

Artifact
Software
DOI: 10.4230/artifacts.25484
HOLMS: A HOL Light Library for Modal Systems

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

Abstract
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Antonella Bilotta, Marco Maggesi, Cosimo Perini Brogi. HOLMS: A HOL Light Library for Modal Systems (Software, Source code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-25484,
   title = {{HOLMS: A HOL Light Library for Modal Systems}}, 
   author = {Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:36edca29f53f3fdd0a7fc675702990743eda4c8d}{\texttt{swh:1:dir:36edca29f53f3fdd0a7fc675702990743eda4c8d}} (visited on 2026-02-18)},
   url = {https://github.com/HOLMS-lib/HOLMS},
   doi = {10.4230/artifacts.25484},
}
Artifact
Software
DOI: 10.4230/artifacts.25485
Webpage of HOLMS: A HOL Light Library for Modal Systems

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

Abstract
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Antonella Bilotta, Marco Maggesi, Cosimo Perini Brogi. Webpage of HOLMS: A HOL Light Library for Modal Systems (Software, Project Documentation Website). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{holms-website,
   title = {{Webpage of HOLMS: A HOL Light Library for Modal Systems}}, 
   author = {Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
   note = {Software (visited on 2026-02-18)},
   url = {https://holms-lib.github.io/},
   doi = {10.4230/artifacts.25485},
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.18
A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We extend the existing HOL Light Library for Modal Systems (HOLMS) to support a modular implementation of modal reasoning within the HOL Light proof assistant. We deeply embed axiomatic calculi and relational semantics for seven normal modal logics (K, T, B, K4, S4, S5, GL) and formalise modal adequacy theorems for these systems. We then leverage those formalisations to implement a mechanism for automated reasoning via proof-search in the associated labelled sequent calculi, which we shallowly embed in HOL Light’s goal-stack mechanism. This way, we equip the general-purpose proof assistant with (semi)decision procedures for these logics that, in case of failure to construct a proof for the input formula, return a certified countermodel within the appropriate class for the logic under consideration. On the methodological side, we propose a precise measure of the modularity of our approach by systematically adopting Christopher Strachey’s distinction between ad hoc and parametric polymorphism throughout the library.
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Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi. A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bilotta_et_al:LIPIcs.CSL.2026.18,
  author =	{Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{18:1--18:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.18},
  URN =		{urn:nbn:de:0030-drops-254427},
  doi =		{10.4230/LIPIcs.CSL.2026.18},
  annote =	{Keywords: Modal logic, HOL Light, Labelled sequent calculi, Logical verification, Interactive theorem proving, Automated proof-search}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.26
A Formal Proof of Modal Completeness for Provability Logic

Authors: Marco Maggesi and Cosimo Perini Brogi

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
This work presents a formalized proof of modal completeness for Gödel-Löb provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation. In particular, we show how we adapted the proof in the Boolos' monograph according to the formal language and tools at hand. The strategy we develop here overcomes the technical difficulty due to the non-compactness of GL, and simplify the implementation. Moreover, it can be applied to other normal modal systems with minimal changes.
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Marco Maggesi and Cosimo Perini Brogi. A Formal Proof of Modal Completeness for Provability Logic. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{maggesi_et_al:LIPIcs.ITP.2021.26,
  author =	{Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Formal Proof of Modal Completeness for Provability Logic}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.26},
  URN =		{urn:nbn:de:0030-drops-139215},
  doi =		{10.4230/LIPIcs.ITP.2021.26},
  annote =	{Keywords: Provability Logic, Higher-Order Logic, Mechanized Mathematics, HOL Light Theorem Prover}
}
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