13 Search Results for "Kurz, Alexander"

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.25
A Unifying Categorical View of Nondeterministic Iteration and Tests

Authors: Sergey Goncharov and Tarmo Uustalu

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study Kleene iteration in the categorical context. A celebrated completeness result by Kozen introduced Kleene algebra (with tests) as a ubiquitous tool for lightweight reasoning about program equivalence, and yet, numerous variants of it came along afterwards to answer the demand for more refined flavors of semantics, such as stateful, concurrent, exceptional, hybrid, branching time, etc. We detach Kleene iteration from Kleene algebra and analyze it from the categorical perspective. The notion, we arrive at is that of Kleene-iteration category (with coproducts and tests), which we show to be general and robust in the sense of compatibility with programming language features, such as exceptions, store, concurrent behaviour, etc. We attest the proposed notion w.r.t. various yardsticks, most importantly, by characterizing the free model as a certain category of (nondeterministic) rational trees.
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Sergey Goncharov and Tarmo Uustalu. A Unifying Categorical View of Nondeterministic Iteration and Tests. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goncharov_et_al:LIPIcs.CONCUR.2024.25,
  author =	{Goncharov, Sergey and Uustalu, Tarmo},
  title =	{{A Unifying Categorical View of Nondeterministic Iteration and Tests}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{25:1--25:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.25},
  URN =		{urn:nbn:de:0030-drops-207979},
  doi =		{10.4230/LIPIcs.CONCUR.2024.25},
  annote =	{Keywords: Kleene iteration, Elgot iteration, Kleene algebra, coalgebraic resumptions}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.17
A Categorical Approach to DIBI Models

Authors: Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
The logic of Dependence and Independence Bunched Implications (DIBI) is a logic to reason about conditional independence (CI); for instance, DIBI formulas can characterise CI in discrete probability distributions and in relational databases, using a probabilistic DIBI model and a similarly-constructed relational model. Despite the similarity of the two models, there lacks a uniform account. As a result, the laborious case-by-case verification of the frame conditions required for constructing new models hinders them from generalising the results to CI in other useful models such that continuous distribution. In this paper, we develop an abstract framework for systematically constructing DIBI models, using category theory as the unifying mathematical language. We show that DIBI models arise from arbitrary symmetric monoidal categories with copy-discard structure. In particular, we use string diagrams - a graphical presentation of monoidal categories - to give a uniform definition of the parallel composition and subkernel relation in DIBI models. Our approach not only generalises known models, but also yields new models of interest and reduces properties of DIBI models to structures in the underlying categories. Furthermore, our categorical framework enables a comparison between string diagrammatic approaches to CI in the literature and a logical notion of CI, defined in terms of the satisfaction of specific DIBI formulas. We show that the logical notion is an extension of string diagrammatic CI under reasonable conditions.
Cite as

Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi. A Categorical Approach to DIBI Models. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gu_et_al:LIPIcs.FSCD.2024.17,
  author =	{Gu, Tao and Bao, Jialu and Hsu, Justin and Silva, Alexandra and Zanasi, Fabio},
  title =	{{A Categorical Approach to DIBI Models}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.17},
  URN =		{urn:nbn:de:0030-drops-203469},
  doi =		{10.4230/LIPIcs.FSCD.2024.17},
  annote =	{Keywords: Conditional Independence, Dependence Independence Bunched Implications, String Diagrams, Markov Categories}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.25
Substitution for Non-Wellfounded Syntax with Binders Through Monoidal Categories

Authors: Ralph Matthes, Kobe Wullaert, and Benedikt Ahrens

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal categories and strong functors between them. A language is specified by a multi-sorted binding signature, say Σ. First, we provide sufficient criteria for Σ to generate a language of possibly infinite terms, through ω-continuity. Second, we construct a monadic substitution operation for the language generated by Σ. A cornerstone in this construction is a mild generalization of the notion of heterogeneous substitution systems developed by Matthes and Uustalu; such a system encapsulates the necessary corecursion scheme for implementing substitution. The results are formalized in the Coq proof assistant, through the UniMath library of univalent mathematics.
Cite as

Ralph Matthes, Kobe Wullaert, and Benedikt Ahrens. Substitution for Non-Wellfounded Syntax with Binders Through Monoidal Categories. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{matthes_et_al:LIPIcs.FSCD.2024.25,
  author =	{Matthes, Ralph and Wullaert, Kobe and Ahrens, Benedikt},
  title =	{{Substitution for Non-Wellfounded Syntax with Binders Through Monoidal Categories}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{25:1--25:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.25},
  URN =		{urn:nbn:de:0030-drops-203540},
  doi =		{10.4230/LIPIcs.FSCD.2024.25},
  annote =	{Keywords: Non-wellfounded syntax, Substitution, Monoidal categories, Actegories, Tensorial strength, Proof assistant Coq, UniMath library}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2023.17
Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties

Authors: Alexander Kurz and Wolfgang Poiger

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

Abstract
We study many-valued coalgebraic logics with primal algebras of truth-degrees. We describe a way to lift algebraic semantics of classical coalgebraic logics, given by an endofunctor on the variety of Boolean algebras, to this many-valued setting, and we show that many important properties of the original logic are inherited by its lifting. Then, we deal with the problem of obtaining a concrete axiomatic presentation of the variety of algebras for this lifted logic, given that we know one for the original one. We solve this problem for a class of presentations which behaves well with respect to a lattice structure on the algebra of truth-degrees.
Cite as

Alexander Kurz and Wolfgang Poiger. Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{kurz_et_al:LIPIcs.CALCO.2023.17,
  author =	{Kurz, Alexander and Poiger, Wolfgang},
  title =	{{Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{17:1--17:17},
  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.2023.17},
  URN =		{urn:nbn:de:0030-drops-188147},
  doi =		{10.4230/LIPIcs.CALCO.2023.17},
  annote =	{Keywords: coalgebraic modal logic, many-valued logic, primal algebras, algebraic semantics, presenting functors}
}
Document
(Co)algebraic pearls
DOI: 10.4230/LIPIcs.CALCO.2021.13
How to Write a Coequation ((Co)algebraic pearls)

Authors: Fredrik Dahlqvist and Todd Schmid

Published in: LIPIcs, Volume 211, 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)

Abstract
There is a large amount of literature on the topic of covarieties, coequations and coequational specifications, dating back to the early seventies. Nevertheless, coequations have not (yet) emerged as an everyday practical specification formalism for computer scientists. In this review paper, we argue that this is partly due to the multitude of syntaxes for writing down coequations, which seems to have led to some confusion about what coequations are and what they are for. By surveying the literature, we identify four types of syntaxes: coequations-as-corelations, coequations-as-predicates, coequations-as-equations, and coequations-as-modal-formulas. We present each of these in a tutorial fashion, relate them to each other, and discuss their respective uses.
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Fredrik Dahlqvist and Todd Schmid. How to Write a Coequation ((Co)algebraic pearls). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 13:1-13:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dahlqvist_et_al:LIPIcs.CALCO.2021.13,
  author =	{Dahlqvist, Fredrik and Schmid, Todd},
  title =	{{How to Write a Coequation}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{13:1--13:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-212-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{211},
  editor =	{Gadducci, Fabio and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2021.13},
  URN =		{urn:nbn:de:0030-drops-153686},
  doi =		{10.4230/LIPIcs.CALCO.2021.13},
  annote =	{Keywords: Coalgebra, coequation, covariety}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2019.18
Nominal String Diagrams

Authors: Samuel Balco and Alexander Kurz

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

Abstract
We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we develop the beginnings of a theory of monoidal categories internal in a symmetric monoidal category. As an instance, we obtain a notion of a nominal PROP as a PROP internal in nominal sets. A 2-dimensional calculus of simultaneous substitutions is an application.
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Samuel Balco and Alexander Kurz. Nominal String Diagrams. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{balco_et_al:LIPIcs.CALCO.2019.18,
  author =	{Balco, Samuel and Kurz, Alexander},
  title =	{{Nominal String Diagrams}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.18},
  URN =		{urn:nbn:de:0030-drops-114466},
  doi =		{10.4230/LIPIcs.CALCO.2019.18},
  annote =	{Keywords: string diagrams, nominal sets, separated product, simultaneous substitutions, internal category, monoidal category, internal monoidal categories, PROP}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2017.9
The Positivication of Coalgebraic Logics

Authors: Fredrik Dahlqvist and Alexander Kurz

Published in: LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)

Abstract
We present positive coalgebraic logic in full generality, and show how to obtain a positive coalgebraic logic from a boolean one. On the model side this involves canonically computing a endofunctor T': Pos->Pos from an endofunctor T: Set->Set, in a procedure previously defined by the second author et alii called posetification. On the syntax side, it involves canonically computing a syntax-building functor L': DL->DL from a syntax-building functor L: BA->BA, in a dual procedure which we call positivication. These operations are interesting in their own right and we explicitly compute posetifications and positivications in the case of several modal logics. We show how the semantics of a boolean coalgebraic logic can be canonically lifted to define a semantics for its positive fragment, and that weak completeness transfers from the boolean case to the positive case.
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Fredrik Dahlqvist and Alexander Kurz. The Positivication of Coalgebraic Logics. In 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 72, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dahlqvist_et_al:LIPIcs.CALCO.2017.9,
  author =	{Dahlqvist, Fredrik and Kurz, Alexander},
  title =	{{The Positivication of Coalgebraic Logics}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Bonchi, Filippo 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.CALCO.2017.9},
  URN =		{urn:nbn:de:0030-drops-80425},
  doi =		{10.4230/LIPIcs.CALCO.2017.9},
  annote =	{Keywords: Coalgebraic logic, coalgebras, enriched category theory, boolean algebra, distributive lattice, positive modal logic, monotone modal logic}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.17
Extensions of Functors From Set to V-cat

Authors: Adriana Balan, Alexander Kurz, and Jiri Velebil

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
We show that for a commutative quantale V every functor from Set to V-cat has an enriched left-Kan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V-cat. Moreover, one can build functors on V-cat by equipping Set-functors with a metric.
Cite as

Adriana Balan, Alexander Kurz, and Jiri Velebil. Extensions of Functors From Set to V-cat. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 17-34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{balan_et_al:LIPIcs.CALCO.2015.17,
  author =	{Balan, Adriana and Kurz, Alexander and Velebil, Jiri},
  title =	{{Extensions of Functors From Set to V-cat}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{17--34},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.17},
  URN =		{urn:nbn:de:0030-drops-55244},
  doi =		{10.4230/LIPIcs.CALCO.2015.17},
  annote =	{Keywords: enriched category, quantale, final coalgebra}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2015.205
Approximation of Nested Fixpoints – A Coalgebraic View of Parametric Dataypes

Authors: Alexander Kurz, Alberto Pardo, Daniela Petrisan, Paula Severi, and Fer-Jan de Vries

Published in: LIPIcs, Volume 35, 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)

Abstract
The question addressed in this paper is how to correctly approximate infinite data given by systems of simultaneous corecursive definitions. We devise a categorical framework for reasoning about regular datatypes, that is, datatypes closed under products, coproducts and fixpoints. We argue that the right methodology is on one hand coalgebraic (to deal with possible nontermination and infinite data) and on the other hand 2-categorical (to deal with parameters in a disciplined manner). We prove a coalgebraic version of Bekic lemma that allows us to reduce simultaneous fixpoints to a single fix point. Thus a possibly infinite object of interest is regarded as a final coalgebra of a many-sorted polynomial functor and can be seen as a limit of finite approximants. As an application, we prove correctness of a generic function that calculates the approximants on a large class of data types.
Cite as

Alexander Kurz, Alberto Pardo, Daniela Petrisan, Paula Severi, and Fer-Jan de Vries. Approximation of Nested Fixpoints – A Coalgebraic View of Parametric Dataypes. In 6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 35, pp. 205-220, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kurz_et_al:LIPIcs.CALCO.2015.205,
  author =	{Kurz, Alexander and Pardo, Alberto and Petrisan, Daniela and Severi, Paula and de Vries, Fer-Jan},
  title =	{{Approximation of Nested Fixpoints – A Coalgebraic View of Parametric Dataypes}},
  booktitle =	{6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
  pages =	{205--220},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-84-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{35},
  editor =	{Moss, Lawrence S. and Sobocinski, Pawel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2015.205},
  URN =		{urn:nbn:de:0030-drops-55351},
  doi =		{10.4230/LIPIcs.CALCO.2015.205},
  annote =	{Keywords: coalgebra, Bekic lemma, infinite data, functional programming, type theory}
}
Document
DOI: 10.4230/DagRep.5.1.197
Coalgebraic Semantics of Reflexive Economics (Dagstuhl Seminar 15042)

Authors: Samson Abramsky, Alexander Kurz, Pierre Lescanne, and Viktor Winschel

Published in: Dagstuhl Reports, Volume 5, Issue 1 (2015)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 15042 "Coalgebraic Semantics of Reflexive Economics".
Cite as

Samson Abramsky, Alexander Kurz, Pierre Lescanne, and Viktor Winschel. Coalgebraic Semantics of Reflexive Economics (Dagstuhl Seminar 15042). In Dagstuhl Reports, Volume 5, Issue 1, pp. 197-206, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@Article{abramsky_et_al:DagRep.5.1.197,
  author =	{Abramsky, Samson and Kurz, Alexander and Lescanne, Pierre and Winschel, Viktor},
  title =	{{Coalgebraic Semantics of Reflexive Economics (Dagstuhl Seminar 15042)}},
  pages =	{197--206},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2015},
  volume =	{5},
  number =	{1},
  editor =	{Abramsky, Samson and Kurz, Alexander and Lescanne, Pierre and Winschel, Viktor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.5.1.197},
  URN =		{urn:nbn:de:0030-drops-50398},
  doi =		{10.4230/DagRep.5.1.197},
  annote =	{Keywords: Programming language semantics, Coalgebra, Category theory, Economics, Epistemic game theory}
}
Document
DOI: 10.4230/DagRep.3.10.58
Nominal Computation Theory (Dagstuhl Seminar 13422)

Authors: Mikolaj Bojanczyk, Bartek Klin, Alexander Kurz, and Andrew M. Pitts

Published in: Dagstuhl Reports, Volume 3, Issue 10 (2014)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 13422 "Nominal Computation Theory". The underlying theme of the seminar was nominal sets (also known as sets with atoms or Fraenkel-Mostowski sets) and they role and applications in three distinct research areas: automata over infinite alphabets, program semantics using nominal sets and nominal calculi of concurrent processes.
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Mikolaj Bojanczyk, Bartek Klin, Alexander Kurz, and Andrew M. Pitts. Nominal Computation Theory (Dagstuhl Seminar 13422). In Dagstuhl Reports, Volume 3, Issue 10, pp. 58-71, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Article{bojanczyk_et_al:DagRep.3.10.58,
  author =	{Bojanczyk, Mikolaj and Klin, Bartek and Kurz, Alexander and Pitts, Andrew M.},
  title =	{{Nominal Computation Theory (Dagstuhl Seminar 13422)}},
  pages =	{58--71},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2014},
  volume =	{3},
  number =	{10},
  editor =	{Bojanczyk, Mikolaj and Klin, Bartek and Kurz, Alexander and Pitts, Andrew M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.3.10.58},
  URN =		{urn:nbn:de:0030-drops-44285},
  doi =		{10.4230/DagRep.3.10.58},
  annote =	{Keywords: nominal sets, Fraenkel-Mostowski sets}
}
Document
DOI: 10.4230/DagRep.2.10.38
Coalgebraic Logics (Dagstuhl Seminar 12411)

Authors: Ernst-Erich Doberkat and Alexander Kurz

Published in: Dagstuhl Reports, Volume 2, Issue 10 (2013)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 12411 "Coalgebraic Logics". The seminar deals with recent developments in the area of coalgebraic logic, a branch of logics which combines modal logics with coalgebraic semantics. Modal logic finds its uses when reasoning about behavioural and temporal properties of computation and communication, coalgebras have evolved into a general theory of systems. Consequently, it is natural to combine both areas for a mathematical description of system specification. Coalgebraic logics are closely related to the broader categories semantics/formal methods and verification/logic.
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Ernst-Erich Doberkat and Alexander Kurz. Coalgebraic Logics (Dagstuhl Seminar 12411). In Dagstuhl Reports, Volume 2, Issue 10, pp. 38-59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@Article{doberkat_et_al:DagRep.2.10.38,
  author =	{Doberkat, Ernst-Erich and Kurz, Alexander},
  title =	{{Coalgebraic Logics (Dagstuhl Seminar 12411)}},
  pages =	{38--59},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{2},
  number =	{10},
  editor =	{Doberkat, Ernst-Erich and Kurz, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.2.10.38},
  URN =		{urn:nbn:de:0030-drops-38938},
  doi =		{10.4230/DagRep.2.10.38},
  annote =	{Keywords: Modal Logic, Coalgebra, Category Theory, Stochastic Logic, Categorical Semantics}
}
Document
DOI: 10.4230/DagSemProc.09502.1
09502 Abstracts Collection – Coalgebraic Logics

Authors: Ernst-Erich Doberkat and Alexander Kurz

Published in: Dagstuhl Seminar Proceedings, Volume 9502, Coalgebraic Logics (2010)

Abstract
The seminar dealt with recent developments in the emerging area of coalgebraic logic and was the first Dagstuhl seminar on that topic. Coalgebraic logic is a branch of logic which studies coalgebras as models of systems and their logics. It can be seen as generalising and extending the classical theory of modal logic to more general models of systems than labelled transition systems. Traditionally, modal logics find their use when reasoning about behavioural and temporal properties of computation and communication, whereas coalgebras give a uniform account for a large class of different systems. The seminar discussed foundational topics in a particular branch of logic, so problems which command a direct application in an industrial context were outside the seminar's scope. We expect, however, that specification methods related to coalgebraic logics will enter fields like model checking and other areas of industrial interest, once the mathematical foundations in this area are firmer and better understood.
Cite as

Ernst-Erich Doberkat and Alexander Kurz. 09502 Abstracts Collection – Coalgebraic Logics. In Coalgebraic Logics. Dagstuhl Seminar Proceedings, Volume 9502, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{doberkat_et_al:DagSemProc.09502.1,
  author =	{Doberkat, Ernst-Erich and Kurz, Alexander},
  title =	{{09502 Abstracts Collection – Coalgebraic Logics}},
  booktitle =	{Coalgebraic Logics},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9502},
  editor =	{Ernst-Erich Doberkat and Alexander Kurz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09502.1},
  URN =		{urn:nbn:de:0030-drops-24203},
  doi =		{10.4230/DagSemProc.09502.1},
  annote =	{Keywords: Modal logics, coalgebras, bisimulation and behavioral equivalence, relations, Markov transition systems}
}
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