3 Search Results for "Pereira, Luiz Carlos"

Document
DOI: 10.4230/LIPIcs.FSCD.2025.34
Monad Translations for Higher-Order Logic

Authors: Thomas Traversié

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

Abstract
Classical logic can be embedded into intuitionistic logic by inserting double negations in formulas. Several translations generalize this idea by using monad operators instead of double negations. They eliminate particular axioms, for instance the principle of excluded middle or the principle of explosion, and therefore can be used to embed classical logic into intuitionistic logic or intuitionistic logic into minimal logic. Such translations have been defined for first-order logic. In this paper, we define a translation, parameterized by monad operators, for higher-order logic. In particular, the property that any formula and its translation are equivalent in the presence of the eliminated axiom holds under functional extensionality and propositional extensionality. We apply this translation to embed higher-order classical (respectively intuitionistic) logic into higher-order intuitionistic (respectively minimal) logic. By adapting Friedman’s trick, we show that coherent formulas correspond to a constructive fragment of higher-order classical logic, meaning that we can transform classical proofs into intuitionistic proofs without modifying the proven statements.
Cite as

Thomas Traversié. Monad Translations for Higher-Order Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 34:1-34:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{traversie:LIPIcs.FSCD.2025.34,
  author =	{Traversi\'{e}, Thomas},
  title =	{{Monad Translations for Higher-Order Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{34:1--34:14},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-236495},
  doi =		{10.4230/LIPIcs.FSCD.2025.34},
  annote =	{Keywords: Higher-order logic, Intuitionistic logic, Kuroda’s translation, Monad}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.160
Using Games and Universal Trees to Characterise the Nondeterministic Index of Tree Languages

Authors: Olivier Idir and Karoliina Lehtinen

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
The parity index problem of tree automata asks, given a regular tree language L and a set of priorities J, is L J-feasible, that is, recognised by a nondeterministic parity automaton with priorities J? This is a long-standing open problem, of which only a few sub-cases and variations are known to be decidable. In a significant but technically difficult step, Colcombet and Löding reduced the problem to the uniform universality of distance-parity automata. In this article, we revisit the index problem using tools from the parity game literature. We add some counters to Lehtinen’s register game, originally used to solve parity games in quasipolynomial time, and use this novel game to characterise J-feasibility. This provides a alternative proof to Colcombet and Löding’s reduction. We then provide a second characterisation, based on the notion of attractor decompositions and the complexity of their structure, as measured by a parameterised version of their Strahler number, which we call n-Strahler number. Finally, we rephrase this result using the notion of universal tree extended to automata: a guidable automaton recognises a [1,2j]-feasible language if and only if it admits a universal tree with n-Strahler number j, for some n. In particular, a language recognised by a guidable automaton {A} is Büchi-feasible if and only if there is a uniform bound n ∈ ℕ such that all trees in the language admit an accepting run with an attractor decomposition of width bounded by n. Equivalently, the language is Büchi-feasible if and only if {A} admits a finite universal tree. While we do not solve the decidability of the index problem, our work makes the state-of-the-art more accessible and brings to light the deep relationships between the J-feasibility of a language and attractor decompositions, universal trees and Lehtinen’s register game.
Cite as

Olivier Idir and Karoliina Lehtinen. Using Games and Universal Trees to Characterise the Nondeterministic Index of Tree Languages. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 160:1-160:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{idir_et_al:LIPIcs.ICALP.2025.160,
  author =	{Idir, Olivier and Lehtinen, Karoliina},
  title =	{{Using Games and Universal Trees to Characterise the Nondeterministic Index of Tree Languages}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{160:1--160:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.160},
  URN =		{urn:nbn:de:0030-drops-235377},
  doi =		{10.4230/LIPIcs.ICALP.2025.160},
  annote =	{Keywords: Tree automata, parity automata, Mostowski index, Strahler number, attractor decomposition, universal trees}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.CALCO.2023.3
A Tour on Ecumenical Systems (Invited Talk)

Authors: Elaine Pimentel and Luiz Carlos Pereira

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)

Abstract
Ecumenism can be understood as a pursuit of unity, where diverse thoughts, ideas, or points of view coexist harmoniously. In logic, ecumenical systems refer, in a broad sense, to proof systems for combining logics. One captivating area of research over the past few decades has been the exploration of seamlessly merging classical and intuitionistic connectives, allowing them to coexist peacefully. In this paper, we will embark on a journey through ecumenical systems, drawing inspiration from Prawitz' seminal work [Dag Prawitz, 2015]. We will begin by elucidating Prawitz' concept of "ecumenism" and present a pure sequent calculus version of his system. Building upon this foundation, we will expand our discussion to incorporate alethic modalities, leveraging Simpson’s meta-logical characterization. This will enable us to propose several proof systems for ecumenical modal logics. We will conclude our tour with some discussion towards a term calculus proposal for the implicational propositional fragment of the ecumenical logic, the quest of automation using a framework based in rewriting logic, and an ecumenical view of proof-theoretic semantics.
Cite as

Elaine Pimentel and Luiz Carlos Pereira. A Tour on Ecumenical Systems (Invited Talk). In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{pimentel_et_al:LIPIcs.CALCO.2023.3,
  author =	{Pimentel, Elaine and Pereira, Luiz Carlos},
  title =	{{A Tour on Ecumenical Systems}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.3},
  URN =		{urn:nbn:de:0030-drops-188003},
  doi =		{10.4230/LIPIcs.CALCO.2023.3},
  annote =	{Keywords: Intuitionistic logic, classical logic, modal logic, ecumenical systems, proof theory}
}
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