8 Search Results for "Ciabattoni, Agata"

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.
Cite as

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.CSL.2026.14
Satisfiability in Łukasiewicz Logic and Its Unbounded Relative

Authors: Zuzana Haniková and Filip Jankovec

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

Abstract
Unbounded Łukasiewicz logic is a substructural logic that combines features of infinite-valued Łukasiewicz logic with those of abelian logic. The logic is finitely strongly complete w.r.t. the additive 𝓁-group on the reals expanded with a distinguished element -1. We show that the existential theory of this structure is NP-complete. This provides a complexity upper bound for the set of theorems and the finite consequence relation of unbounded Łukasiewicz logic. The result is obtained by reducing the problem to the existential theory of the MV-algebra on the reals, the standard semantics of Łukasiewicz logic. This provides a new connection between both logics. The result entails a translation of the existential theory of the standard MV-algebra into itself.
Cite as

Zuzana Haniková and Filip Jankovec. Satisfiability in Łukasiewicz Logic and Its Unbounded Relative. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hanikova_et_al:LIPIcs.CSL.2026.14,
  author =	{Hanikov\'{a}, Zuzana and Jankovec, Filip},
  title =	{{Satisfiability in {\L}ukasiewicz Logic and Its Unbounded Relative}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{14:1--14:18},
  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.2026.14},
  URN =		{urn:nbn:de:0030-drops-254380},
  doi =		{10.4230/LIPIcs.CSL.2026.14},
  annote =	{Keywords: unbounded {\L}ukasiewicz Logic, {\L}ukasiewicz Logic, Abelian Logic, existential theory, computational complexity, NP-completeness}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.17
A Uniform Cut-Elimination Theorem for Linear Logics with Fixed Points and Super Exponentials

Authors: Alexis Saurin and Esaïe Bauer

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

Abstract
In the realm of light logics deriving from linear logic, a number of variants of exponential rules have been investigated. The profusion of such proof systems induces the need for cut-elimination theorems for each logic, the proofs of which may be redundant. A number of approaches in proof theory have been adopted to cope with this need. In the present paper, we consider this issue from the point of view of enhancing linear logic with least and greatest fixed-points and considering such a variety of exponential connectives. Our main contribution is to provide a uniform cut-elimination theorem for a parametrized system with fixed-points by combining two approaches: cut-elimination proofs by reduction (or translation) to another system and the identification of sufficient conditions for cut-elimination. More precisely, we examine a broad range of systems, taking inspiration from Nigam and Miller’s subexponentials and from the first author and Laurent’s super exponentials. Our work is motivated, on the one hand, by Baillot’s work on light logics with recursive types and on the other hand by our recent work on the proof theory of the modal μ-calculus.
Cite as

Alexis Saurin and Esaïe Bauer. A Uniform Cut-Elimination Theorem for Linear Logics with Fixed Points and Super Exponentials. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 17:1-17:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{saurin_et_al:LIPIcs.CSL.2026.17,
  author =	{Saurin, Alexis and Bauer, Esa\"{i}e},
  title =	{{A Uniform Cut-Elimination Theorem for Linear Logics with Fixed Points and Super Exponentials}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{17:1--17:23},
  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.2026.17},
  URN =		{urn:nbn:de:0030-drops-254418},
  doi =		{10.4230/LIPIcs.CSL.2026.17},
  annote =	{Keywords: cut elimination, exponential modalities, fixed-points, linear logic, light logics, mu-calculus, non-wellfounded proofs, proof theory, sequent calculus, subexponentials, super exponentials}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.22
Branch Sequentialization in Quantum Polytime

Authors: Emmanuel Hainry, Romain Péchoux, and Mário Silva

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Quantum algorithms leverage the use of quantumly-controlled data in order to achieve computational advantage. This implies that the programs use constructs depending on quantum data and not just classical data such as measurement outcomes. Current compilation strategies for quantum control flow involve compiling the branches of a quantum conditional, either in-depth or in-width, which in general leads to circuits of exponential size. This problem is coined as the branch sequentialization problem. We introduce and study a compilation technique for avoiding branch sequentialization on a language that is sound and complete for quantum polynomial time, thus, improving on existing polynomial-size-preserving compilation techniques.
Cite as

Emmanuel Hainry, Romain Péchoux, and Mário Silva. Branch Sequentialization in Quantum Polytime. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hainry_et_al:LIPIcs.FSCD.2025.22,
  author =	{Hainry, Emmanuel and P\'{e}choux, Romain and Silva, M\'{a}rio},
  title =	{{Branch Sequentialization in Quantum Polytime}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.22},
  URN =		{urn:nbn:de:0030-drops-236373},
  doi =		{10.4230/LIPIcs.FSCD.2025.22},
  annote =	{Keywords: Quantum Programs, Implicit Computational Complexity, Quantum Circuits}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.42
Unifying Sequent Systems for Gödel-Löb Provability Logic via Syntactic Transformations

Authors: Tim S. Lyon

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We demonstrate the inter-translatability of proofs between the most prominent sequent-based formalisms for Gödel-Löb provability logic. In particular, we consider Sambin and Valentini’s sequent system GL_{seq}, Shamkanov’s non-wellfounded and cyclic sequent systems GL_∞ and GL_{circ}, Poggiolesi’s tree-hypersequent system CSGL, and Negri’s labeled sequent system G3GL. Shamkanov provided proof-theoretic correspondences between GL_{seq}, GL_∞, and GL_{circ}, and Goré and Ramanayake showed how to transform proofs between CSGL and G3GL, however, the exact nature of proof transformations between the former three systems and the latter two systems has remained an open problem. We solve this open problem by showing how to restructure tree-hypersequent proofs into an end-active form and introduce a novel linearization technique that transforms such proofs into linear nested sequent proofs. As a result, we obtain a new proof-theoretic tool for extracting linear nested sequent systems from tree-hypersequent systems, which yields the first cut-free linear nested sequent calculus LNGL for Gödel-Löb provability logic. We show how to transform proofs in LNGL into a certain normal form, where proofs repeat in stages of modal and local rule applications, and which are translatable into GL_{seq} and G3GL proofs. These new syntactic transformations, together with those mentioned above, establish full proof-theoretic correspondences between GL_{seq}, GL_∞, GL_{circ}, CSGL, G3GL, and LNGL while also giving (to the best of the author’s knowledge) the first constructive proof mappings between structural (viz. labeled, tree-hypersequent, and linear nested sequent) systems and a cyclic sequent system.
Cite as

Tim S. Lyon. Unifying Sequent Systems for Gödel-Löb Provability Logic via Syntactic Transformations. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lyon:LIPIcs.CSL.2025.42,
  author =	{Lyon, Tim S.},
  title =	{{Unifying Sequent Systems for G\"{o}del-L\"{o}b Provability Logic via Syntactic Transformations}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{42:1--42:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.42},
  URN =		{urn:nbn:de:0030-drops-227992},
  doi =		{10.4230/LIPIcs.CSL.2025.42},
  annote =	{Keywords: Cyclic proof, G\"{o}del-L\"{o}b logic, Labeled sequent, Linear nested sequent, Modal logic, Non-wellfounded proof, Proof theory, Proof transformation, Tree-hypersequent}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.41
Taking Bi-Intuitionistic Logic First-Order: A Proof-Theoretic Investigation via Polytree Sequents

Authors: Tim S. Lyon, Ian Shillito, and Alwen Tiu

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting problem to find a sound and complete proof system for first-order bi-intuitionistic logic with non-constant domains that is also conservative over first-order intuitionistic logic. We solve this problem by presenting the first sound and complete proof system for first-order bi-intuitionistic logic with increasing domains. We formalize our proof system as a polytree sequent calculus (a notational variant of nested sequents), and prove that it enjoys cut-elimination and is conservative over first-order intuitionistic logic. A key feature of our calculus is an explicit eigenvariable context, which allows us to control precisely the scope of free variables in a polytree structure. Semantically this context can be seen as encoding a notion of Scott’s existence predicate for intuitionistic logic. This turns out to be crucial to avoid the collapse of domains and to prove the completeness of our proof system. The explicit consideration of the variable context in a formula sheds light on a previously overlooked dependency between the residuation principle and the existence predicate in the first-order setting, which may help to explain the difficulty in designing a sound and complete proof system for first-order bi-intuitionistic logic.
Cite as

Tim S. Lyon, Ian Shillito, and Alwen Tiu. Taking Bi-Intuitionistic Logic First-Order: A Proof-Theoretic Investigation via Polytree Sequents. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 41:1-41:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lyon_et_al:LIPIcs.CSL.2025.41,
  author =	{Lyon, Tim S. and Shillito, Ian and Tiu, Alwen},
  title =	{{Taking Bi-Intuitionistic Logic First-Order: A Proof-Theoretic Investigation via Polytree Sequents}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{41:1--41:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.41},
  URN =		{urn:nbn:de:0030-drops-227987},
  doi =		{10.4230/LIPIcs.CSL.2025.41},
  annote =	{Keywords: Bi-intuitionistic, Cut-elimination, Conservativity, Domain, First-order, Polytree, Proof theory, Reachability, Sequent}
}
Document
DOI: 10.4230/DagRep.13.4.1
Normative Reasoning for AI (Dagstuhl Seminar 23151)

Authors: Agata Ciabattoni, John F. Horty, Marija Slavkovik, Leendert van der Torre, and Aleks Knoks

Published in: Dagstuhl Reports, Volume 13, Issue 4 (2023)

Abstract
Normative reasoning is reasoning about normative matters - such as obligations, permissions, and the rights of individuals or groups. It is prevalent in both legal and ethical discourse, and it can - and arguably should - play a crucial role in the construction of autonomous agents. We often find it important to know whether specific norms apply in a given situation, and to understand why and when they apply, and why some other norms do not apply. In most cases, our reasons for wanting to know are purely practical - we want to make the correct decision - but they can also be more theoretical - as they are when we engage in theoretical ethics. Either way, the same questions are crucial for designing autonomous agents sensitive to legal, ethical, and social norms. This Dagstuhl Seminar brought together experts in computer science, logic (including deontic logic and argumentation), philosophy, ethics, and law with the aim of finding effective ways of formalizing norms and embedding normative reasoning in AI systems. We discussed new ways of using deontic logic and argumentation to provide explanations answering normative why questions, including such questions as "Why should I do A (rather than B)?", "Why should you do A (rather than I)?", "Why do you have the right to do A despite a certain fact or a certain norm?", and "Why does one normative system forbid me to do A, while another one allows it?". We also explored the use of formal methods in combination with sub-symbolic AI (or Machine Learning) with a view towards designing autonomous agents that can follow (legal, ethical, and social) norms.
Cite as

Agata Ciabattoni, John F. Horty, Marija Slavkovik, Leendert van der Torre, and Aleks Knoks. Normative Reasoning for AI (Dagstuhl Seminar 23151). In Dagstuhl Reports, Volume 13, Issue 4, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{ciabattoni_et_al:DagRep.13.4.1,
  author =	{Ciabattoni, Agata and Horty, John F. and Slavkovik, Marija and van der Torre, Leendert and Knoks, Aleks},
  title =	{{Normative Reasoning for AI (Dagstuhl Seminar 23151)}},
  pages =	{1--23},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{4},
  editor =	{Ciabattoni, Agata and Horty, John F. and Slavkovik, Marija and van der Torre, Leendert and Knoks, Aleks},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.4.1},
  URN =		{urn:nbn:de:0030-drops-192367},
  doi =		{10.4230/DagRep.13.4.1},
  annote =	{Keywords: deontic logic, autonomous agents, AI ethics, deontic explanations}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CSL.2016.4
Analytic Calculi for Non-Classical Logics: Theory and Applications (Invited Talk)

Authors: Agata Ciabattoni

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)

Abstract
The possession of a suitable proof-calculus is the starting point for many investigations into a logic, including decidability and complexity, computational interpretations and automated theorem proving. By suitable proof-calculus we mean a calculus whose proofs exhibit some notion of subformula property ("analyticity"). In this talk we describe a method for the algorithmic introduction of analytic sequent-style calculi for a wide range of non-classical logics starting from Hilbert systems. To demonstrate the widespread applicability of this method, we discuss how to use the introduced calculi for proving various results ranging from Curry-Howard isomorphism to new interpretative tools for Indology.
Cite as

Agata Ciabattoni. Analytic Calculi for Non-Classical Logics: Theory and Applications (Invited Talk). In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{ciabattoni:LIPIcs.CSL.2016.4,
  author =	{Ciabattoni, Agata},
  title =	{{Analytic Calculi for Non-Classical Logics: Theory and Applications}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.4},
  URN =		{urn:nbn:de:0030-drops-65440},
  doi =		{10.4230/LIPIcs.CSL.2016.4},
  annote =	{Keywords: Proof theory, Fuzzy logic}
}
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