2 Search Results for "Haselwarter, Philipp G."

Document
DOI: 10.4230/LIPIcs.CSL.2025.24
Propositional Logics of Overwhelming Truth

Authors: Thibaut Antoine and David Baelde

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

Abstract
Cryptographers consider that asymptotic security holds when, for any possible attacker running in polynomial time, the probability that the attack succeeds is negligible, i.e. that it tends fast enough to zero with the size of secrets. In order to reason formally about cryptographic truth, one may thus consider logics where a formula is satisfied when it is true with overwhelming probability, i.e. a probability that tends fast enough to one with the size of secrets. In such logics it is not always the case that either ϕ or ⌝ϕ is satisfied by a given model. However, security analyses will inevitably involve specific formulas, which we call determined, satisfying this property - typically because they are not probabilistic. The Squirrel proof assistant, which implements a logic of overwhelming truth, features ad-hoc proof rules for this purpose. In this paper, we study several propositional logics whose semantics rely on overwhelming truth. We first consider a modal logic of overwhelming truth, and show that it coincides with S5. In addition to providing an axiomatization, this brings a well-behaved proof system for our logic in the form of Poggiolesi’s hypersequent calculus. Further, we show that this system can be adapted to elegantly incorporate reasoning on determined atoms. We then consider a logic that is closer to Squirrel’s language, where the overwhelming truth modality cannot be nested. In that case, we show that a simple proof system, based on regular sequents, is sound and complete. This result justifies the core of Squirrel’s proof system.
Cite as

Thibaut Antoine and David Baelde. Propositional Logics of Overwhelming Truth. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antoine_et_al:LIPIcs.CSL.2025.24,
  author =	{Antoine, Thibaut and Baelde, David},
  title =	{{Propositional Logics of Overwhelming Truth}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{24:1--24:19},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-227818},
  doi =		{10.4230/LIPIcs.CSL.2025.24},
  annote =	{Keywords: Cryptography, Modal Logic, Sequent Calculus}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2016.5
Design and Implementation of the Andromeda Proof Assistant

Authors: Andrej Bauer, Gaëtan Gilbert, Philipp G. Haselwarter, Matija Pretnar, and Christopher A. Stone

Published in: LIPIcs, Volume 97, 22nd International Conference on Types for Proofs and Programs (TYPES 2016)

Abstract
Andromeda is an LCF-style proof assistant where the user builds derivable judgments by writing code in a meta-level programming language AML. The only trusted component of Andromeda is a minimalist nucleus (an implementation of the inference rules of an object-level type theory), which controls construction and decomposition of type-theoretic judgments. Since the nucleus does not perform complex tasks like equality checking beyond syntactic equality, this responsibility is delegated to the user, who implements one or more equality checking procedures in the meta-language. The AML interpreter requests witnesses of equality from user code using the mechanism of algebraic operations and handlers. Dynamic checks in the nucleus guarantee that no invalid object-level derivations can be constructed. To demonstrate the flexibility of this system structure, we implemented a nucleus consisting of dependent type theory with equality reflection. Equality reflection provides a very high level of expressiveness, as it allows the user to add new judgmental equalities, but it also destroys desirable meta-theoretic properties of type theory (such as decidability and strong normalization). The power of effects and handlers in AML is demonstrated by a standard library that provides default algorithms for equality checking, computation of normal forms, and implicit argument filling. Users can extend these new algorithms by providing local "hints" or by completely replacing these algorithms for particular developments. We demonstrate the resulting system by showing how to axiomatize and compute with natural numbers, by axiomatizing the untyped lambda-calculus, and by implementing a simple automated system for managing a universe of types.
Cite as

Andrej Bauer, Gaëtan Gilbert, Philipp G. Haselwarter, Matija Pretnar, and Christopher A. Stone. Design and Implementation of the Andromeda Proof Assistant. In 22nd International Conference on Types for Proofs and Programs (TYPES 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 97, pp. 5:1-5:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bauer_et_al:LIPIcs.TYPES.2016.5,
  author =	{Bauer, Andrej and Gilbert, Ga\"{e}tan and Haselwarter, Philipp G. and Pretnar, Matija and Stone, Christopher A.},
  title =	{{Design and Implementation of the Andromeda Proof Assistant}},
  booktitle =	{22nd International Conference on Types for Proofs and Programs (TYPES 2016)},
  pages =	{5:1--5:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-065-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{97},
  editor =	{Ghilezan, Silvia and Geuvers, Herman and Ivetic, Jelena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2016.5},
  URN =		{urn:nbn:de:0030-drops-98574},
  doi =		{10.4230/LIPIcs.TYPES.2016.5},
  annote =	{Keywords: type theory, proof assistant, equality reflection, computational effects}
}
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