47 Search Results for "Ghica, Dan R."

Volume

LIPIcs, Volume 119

27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

CSL 2018, September 4-7, 2018, Birmingham, GB

Editors: Dan R. Ghica and Achim Jung

Document
DOI: 10.4230/LIPIcs.FSCD.2023.14
Rewriting Modulo Traced Comonoid Structure

Authors: Dan R. Ghica and George Kaye

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
In this paper we adapt previous work on rewriting string diagrams using hypergraphs to the case where the underlying category has a traced comonoid structure, in which wires can be forked and the outputs of a morphism can be connected to its input. Such a structure is particularly interesting because any traced Cartesian (dataflow) category has an underlying traced comonoid structure. We show that certain subclasses of hypergraphs are fully complete for traced comonoid categories: that is to say, every term in such a category has a unique corresponding hypergraph up to isomorphism, and from every hypergraph with the desired properties, a unique term in the category can be retrieved up to the axioms of traced comonoid categories. We also show how the framework of double pushout rewriting (DPO) can be adapted for traced comonoid categories by characterising the valid pushout complements for rewriting in our setting. We conclude by presenting a case study in the form of recent work on an equational theory for sequential circuits: circuits built from primitive logic gates with delay and feedback. The graph rewriting framework allows for the definition of an operational semantics for sequential circuits.
Cite as

Dan R. Ghica and George Kaye. Rewriting Modulo Traced Comonoid Structure. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 14:1-14:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ghica_et_al:LIPIcs.FSCD.2023.14,
  author =	{Ghica, Dan R. and Kaye, George},
  title =	{{Rewriting Modulo Traced Comonoid Structure}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{14:1--14:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.14},
  URN =		{urn:nbn:de:0030-drops-179983},
  doi =		{10.4230/LIPIcs.FSCD.2023.14},
  annote =	{Keywords: symmetric traced monoidal categories, string diagrams, graph rewriting, comonoid structure, double pushout rewriting}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.6
Functorial String Diagrams for Reverse-Mode Automatic Differentiation

Authors: Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
We formulate a reverse-mode automatic differentiation (RAD) algorithm for (applied) simply typed lambda calculus in the style of Pearlmutter and Siskind [Barak A. Pearlmutter and Jeffrey Mark Siskind, 2008], using the graphical formalism of string diagrams. Thanks to string diagram rewriting, we are able to formally prove for the first time the soundness of such an algorithm. Our approach requires developing a calculus of string diagrams with hierarchical features in the spirit of functorial boxes, in order to model closed monoidal (and cartesian closed) structure. To give an efficient yet principled implementation of the RAD algorithm, we use foliations of our hierarchical string diagrams.
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Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi. Functorial String Diagrams for Reverse-Mode Automatic Differentiation. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{alvarezpicallo_et_al:LIPIcs.CSL.2023.6,
  author =	{Alvarez-Picallo, Mario and Ghica, Dan and Sprunger, David and Zanasi, Fabio},
  title =	{{Functorial String Diagrams for Reverse-Mode Automatic Differentiation}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.6},
  URN =		{urn:nbn:de:0030-drops-174674},
  doi =		{10.4230/LIPIcs.CSL.2023.6},
  annote =	{Keywords: string diagrams, automatic differentiation, hierarchical hypergraphs}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.37
String Diagrams for Non-Strict Monoidal Categories

Authors: Paul Wilson, Dan Ghica, and Fabio Zanasi

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied. In this paper, we provide a presentation by generators and relations of string diagrams for non-strict monoidal categories, and show how this construction can handle applications in domains such as digital circuits and programming languages. We prove the correctness of our construction, which yields a novel proof of Mac Lane’s strictness theorem. This in turn leads to an elementary graphical proof of Mac Lane’s coherence theorem, and in particular allows for the inductive construction of the canonical isomorphisms in a monoidal category.
Cite as

Paul Wilson, Dan Ghica, and Fabio Zanasi. String Diagrams for Non-Strict Monoidal Categories. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wilson_et_al:LIPIcs.CSL.2023.37,
  author =	{Wilson, Paul and Ghica, Dan and Zanasi, Fabio},
  title =	{{String Diagrams for Non-Strict Monoidal Categories}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{37:1--37:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.37},
  URN =		{urn:nbn:de:0030-drops-174981},
  doi =		{10.4230/LIPIcs.CSL.2023.37},
  annote =	{Keywords: String Diagrams, Strictness, Coherence}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.29
Rewriting for Monoidal Closed Categories

Authors: Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
This paper develops a formal string diagram language for monoidal closed categories. Previous work has shown that string diagrams for freely generated symmetric monoidal categories can be viewed as hypergraphs with interfaces, and the axioms of these categories can be realized by rewriting systems. This work proposes hierarchical hypergraphs as a suitable formalization of string diagrams for monoidal closed categories. We then show double pushout rewriting captures the axioms of these closed categories.
Cite as

Mario Alvarez-Picallo, Dan Ghica, David Sprunger, and Fabio Zanasi. Rewriting for Monoidal Closed Categories. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{alvarezpicallo_et_al:LIPIcs.FSCD.2022.29,
  author =	{Alvarez-Picallo, Mario and Ghica, Dan and Sprunger, David and Zanasi, Fabio},
  title =	{{Rewriting for Monoidal Closed Categories}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.29},
  URN =		{urn:nbn:de:0030-drops-163108},
  doi =		{10.4230/LIPIcs.FSCD.2022.29},
  annote =	{Keywords: string diagrams, rewriting, hierarchical hypergraph, monoidal closed category}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.CSL.2018
LIPIcs, Volume 119, CSL'18, Complete Volume

Authors: Dan Ghica and Achim Jung

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
LIPIcs, Volume 119, CSL'18, Complete Volume
Cite as

27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Proceedings{ghica_et_al:LIPIcs.CSL.2018,
  title =	{{LIPIcs, Volume 119, CSL'18, Complete Volume}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018},
  URN =		{urn:nbn:de:0030-drops-97444},
  doi =		{10.4230/LIPIcs.CSL.2018},
  annote =	{Keywords: Theory of computation, Software and its engineering, Formal language definitions, Formal software verification}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.CSL.2018.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Dan R. Ghica and Achim Jung

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 0:i-0:xiv, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ghica_et_al:LIPIcs.CSL.2018.0,
  author =	{Ghica, Dan R. and Jung, Achim},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{0:i--0:xiv},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.0},
  URN =		{urn:nbn:de:0030-drops-96679},
  doi =		{10.4230/LIPIcs.CSL.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.1
The Ackermann Award 2018

Authors: Dexter Kozen and Thomas Schwentick

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic in Computer Science. It is presented during the annual conference of the EACSL (CSL'xx). This contribution reports on the 2018 edition of the award.
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Dexter Kozen and Thomas Schwentick. The Ackermann Award 2018. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 1:1-1:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{kozen_et_al:LIPIcs.CSL.2018.1,
  author =	{Kozen, Dexter and Schwentick, Thomas},
  title =	{{The Ackermann Award 2018}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{1:1--1:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.1},
  URN =		{urn:nbn:de:0030-drops-96686},
  doi =		{10.4230/LIPIcs.CSL.2018.1},
  annote =	{Keywords: Ackermann Award}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.2
Relating Structure and Power: Comonadic Semantics for Computational Resources

Authors: Samson Abramsky and Nihil Shah

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraïssé games, pebble games, and bisimulation games play a central role. We show how each of these types of games can be described in terms of an indexed family of comonads on the category of relational structures and homomorphisms. The index k is a resource parameter which bounds the degree of access to the underlying structure. The coKleisli categories for these comonads can be used to give syntax-free characterizations of a wide range of important logical equivalences. Moreover, the coalgebras for these indexed comonads can be used to characterize key combinatorial parameters: tree-depth for the Ehrenfeucht-Fraïssé comonad, tree-width for the pebbling comonad, and synchronization-tree depth for the modal unfolding comonad. These results pave the way for systematic connections between two major branches of the field of logic in computer science which hitherto have been almost disjoint: categorical semantics, and finite and algorithmic model theory.
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Samson Abramsky and Nihil Shah. Relating Structure and Power: Comonadic Semantics for Computational Resources. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abramsky_et_al:LIPIcs.CSL.2018.2,
  author =	{Abramsky, Samson and Shah, Nihil},
  title =	{{Relating Structure and Power: Comonadic Semantics for Computational Resources}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.2},
  URN =		{urn:nbn:de:0030-drops-96698},
  doi =		{10.4230/LIPIcs.CSL.2018.2},
  annote =	{Keywords: Finite model theory, combinatorial games, Ehrenfeucht-Fra\"{i}ss\'{e} games, pebble games, bisimulation, comonads, coKleisli category, coalgebras of a comonad}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.3
Climbing up the Elementary Complexity Classes with Theories of Automatic Structures

Authors: Faried Abu Zaid, Dietrich Kuske, and Peter Lindner

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Automatic structures are structures that admit a finite presentation via automata. Their most prominent feature is that their theories are decidable. In the literature, one finds automatic structures with non-elementary theory (e.g., the complete binary tree with equal-level predicate) and automatic structures whose theories are at most 3-fold exponential (e.g., Presburger arithmetic or infinite automatic graphs of bounded degree). This observation led Durand-Gasselin to the question whether there are automatic structures of arbitrary high elementary complexity. We give a positive answer to this question. Namely, we show that for every h >=0 the forest of (infinitely many copies of) all finite trees of height at most h+2 is automatic and it's theory is complete for STA(*, exp_h(n, poly(n)), poly(n)), an alternating complexity class between h-fold exponential time and space. This exact determination of the complexity of the theory of these forests might be of independent interest.
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Faried Abu Zaid, Dietrich Kuske, and Peter Lindner. Climbing up the Elementary Complexity Classes with Theories of Automatic Structures. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{abuzaid_et_al:LIPIcs.CSL.2018.3,
  author =	{Abu Zaid, Faried and Kuske, Dietrich and Lindner, Peter},
  title =	{{Climbing up the Elementary Complexity Classes with Theories of Automatic Structures}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.3},
  URN =		{urn:nbn:de:0030-drops-96701},
  doi =		{10.4230/LIPIcs.CSL.2018.3},
  annote =	{Keywords: Automatic Structures, Complexity Theory, Model Theory}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.4
High-Level Signatures and Initial Semantics

Authors: Benedikt Ahrens, André Hirschowitz, Ambroise Lafont, and Marco Maggesi

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
We present a device for specifying and reasoning about syntax for datatypes, programming languages, and logic calculi. More precisely, we consider a general notion of "signature" for specifying syntactic constructions. Our signatures subsume classical algebraic signatures (i.e., signatures for languages with variable binding, such as the pure lambda calculus) and extend to much more general examples. In the spirit of Initial Semantics, we define the "syntax generated by a signature" to be the initial object - if it exists - in a suitable category of models. Our notions of signature and syntax are suited for compositionality and provide, beyond the desired algebra of terms, a well-behaved substitution and the associated inductive/recursive principles. Our signatures are "general" in the sense that the existence of an associated syntax is not automatically guaranteed. In this work, we identify a large and simple class of signatures which do generate a syntax. This paper builds upon ideas from a previous attempt by Hirschowitz-Maggesi, which, in turn, was directly inspired by some earlier work of Ghani-Uustalu-Hamana and Matthes-Uustalu. The main results presented in the paper are computer-checked within the UniMath system.
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Benedikt Ahrens, André Hirschowitz, Ambroise Lafont, and Marco Maggesi. High-Level Signatures and Initial Semantics. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ahrens_et_al:LIPIcs.CSL.2018.4,
  author =	{Ahrens, Benedikt and Hirschowitz, Andr\'{e} and Lafont, Ambroise and Maggesi, Marco},
  title =	{{High-Level Signatures and Initial Semantics}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.4},
  URN =		{urn:nbn:de:0030-drops-96713},
  doi =		{10.4230/LIPIcs.CSL.2018.4},
  annote =	{Keywords: initial semantics, signatures, syntax, monadic substitution, computer-checked proofs}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.5
The True Concurrency of Herbrand's Theorem

Authors: Aurore Alcolei, Pierre Clairambault, Martin Hyland, and Glynn Winskel

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Herbrand's theorem, widely regarded as a cornerstone of proof theory, exposes some of the constructive content of classical logic. In its simplest form, it reduces the validity of a first-order purely existential formula to that of a finite disjunction. In the general case, it reduces first-order validity to propositional validity, by understanding the structure of the assignment of first-order terms to existential quantifiers, and the causal dependency between quantifiers. In this paper, we show that Herbrand's theorem in its general form can be elegantly stated and proved as a theorem in the framework of concurrent games, a denotational semantics designed to faithfully represent causality and independence in concurrent systems, thereby exposing the concurrency underlying the computational content of classical proofs. The causal structure of concurrent strategies, paired with annotations by first-order terms, is used to specify the dependency between quantifiers implicit in proofs. Furthermore concurrent strategies can be composed, yielding a compositional proof of Herbrand's theorem, simply by interpreting classical sequent proofs in a well-chosen denotational model.
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Aurore Alcolei, Pierre Clairambault, Martin Hyland, and Glynn Winskel. The True Concurrency of Herbrand's Theorem. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{alcolei_et_al:LIPIcs.CSL.2018.5,
  author =	{Alcolei, Aurore and Clairambault, Pierre and Hyland, Martin and Winskel, Glynn},
  title =	{{The True Concurrency of Herbrand's Theorem}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.5},
  URN =		{urn:nbn:de:0030-drops-96723},
  doi =		{10.4230/LIPIcs.CSL.2018.5},
  annote =	{Keywords: Herbrand's theorem, Game semantics, True concurrency}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.6
Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities

Authors: Carlo Angiuli, Kuen-Bang Hou (Favonia), and Robert Harper

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
We present a dependent type theory organized around a Cartesian notion of cubes (with faces, degeneracies, and diagonals), supporting both fibrant and non-fibrant types. The fibrant fragment validates Voevodsky's univalence axiom and includes a circle type, while the non-fibrant fragment includes exact (strict) equality types satisfying equality reflection. Our type theory is defined by a semantics in cubical partial equivalence relations, and is the first two-level type theory to satisfy the canonicity property: all closed terms of boolean type evaluate to either true or false.
Cite as

Carlo Angiuli, Kuen-Bang Hou (Favonia), and Robert Harper. Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{angiuli_et_al:LIPIcs.CSL.2018.6,
  author =	{Angiuli, Carlo and Hou (Favonia), Kuen-Bang and Harper, Robert},
  title =	{{Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.6},
  URN =		{urn:nbn:de:0030-drops-96734},
  doi =		{10.4230/LIPIcs.CSL.2018.6},
  annote =	{Keywords: Homotopy Type Theory, Two-Level Type Theory, Computational Type Theory, Cubical Sets}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.7
Definable Inapproximability: New Challenges for Duplicator

Authors: Albert Atserias and Anuj Dawar

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution guaranteed to be within a fixed constant factor of the optimum. We show, in several such instances and without any complexity theoretic assumption, that no algorithm that is expressible in fixed-point logic with counting (FPC) can compute an approximate solution. Since important algorithmic techniques for approximation algorithms (such as linear or semidefinite programming) are expressible in FPC, this yields lower bounds on what can be achieved by such methods. The results are established by showing lower bounds on the number of variables required in first-order logic with counting to separate instances with a high optimum from those with a low optimum for fixed-size instances.
Cite as

Albert Atserias and Anuj Dawar. Definable Inapproximability: New Challenges for Duplicator. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{atserias_et_al:LIPIcs.CSL.2018.7,
  author =	{Atserias, Albert and Dawar, Anuj},
  title =	{{Definable Inapproximability: New Challenges for Duplicator}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.7},
  URN =		{urn:nbn:de:0030-drops-96742},
  doi =		{10.4230/LIPIcs.CSL.2018.7},
  annote =	{Keywords: Descriptive Compleixty, Hardness of Approximation, MAX SAT, Vertex Cover, Fixed-point logic with counting}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.8
Safety, Absoluteness, and Computability

Authors: Arnon Avron, Shahar Lev, and Nissan Levi

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
The semantic notion of dependent safety is a common generalization of the notion of absoluteness used in set theory and the notion of domain independence used in database theory for characterizing safe queries. This notion has been used in previous works to provide a unified theory of constructions and operations as they are used in different branches of mathematics and computer science, including set theory, computability theory, and database theory. In this paper we provide a complete syntactic characterization of general first-order dependent safety. We also show that this syntactic safety relation can be used for characterizing the set of strictly decidable relations on the natural numbers, as well as for characterizing rudimentary set theory and absoluteness of formulas within it.
Cite as

Arnon Avron, Shahar Lev, and Nissan Levi. Safety, Absoluteness, and Computability. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{avron_et_al:LIPIcs.CSL.2018.8,
  author =	{Avron, Arnon and Lev, Shahar and Levi, Nissan},
  title =	{{Safety, Absoluteness, and Computability}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.8},
  URN =		{urn:nbn:de:0030-drops-96754},
  doi =		{10.4230/LIPIcs.CSL.2018.8},
  annote =	{Keywords: Dependent Safety, Computability, Absoluteness, Decidability, Domain Independence}
}
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