2 Search Results for "Miculan, Marino"


Document
Fuzzy Algebraic Theories

Authors: Davide Castelnovo and Marino Miculan

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)


Abstract
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics for this calculus and show that there is a notion of free model for any theory in this system, allowing us (with some restrictions) to recover models as Eilenberg-Moore algebras for some monad. We will also prove a completeness result: a formula is derivable from a given theory if and only if it is satisfied by all models of the theory. Finally, leveraging results by Milius and Urbat, we give HSP-like characterizations of subcategories of algebras which are categories of models of particular kinds of theories.

Cite as

Davide Castelnovo and Marino Miculan. Fuzzy Algebraic Theories. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{castelnovo_et_al:LIPIcs.CSL.2022.13,
  author =	{Castelnovo, Davide and Miculan, Marino},
  title =	{{Fuzzy Algebraic Theories}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.13},
  URN =		{urn:nbn:de:0030-drops-157332},
  doi =		{10.4230/LIPIcs.CSL.2022.13},
  annote =	{Keywords: categorical logic, fuzzy sets, algebraic reasoning, equational axiomatisations, monads, Eilenberg-Moore algebras}
}
Document
Closure Hyperdoctrines

Authors: Davide Castelnovo and Marino Miculan

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


Abstract
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we present an abstract theoretical framework for the systematic investigation of the logical aspects of closure spaces. To this end, we introduce the notion of closure (hyper)doctrines, i.e. doctrines endowed with inflationary operators (and subject to suitable conditions). The generality and effectiveness of this concept is witnessed by many examples arising naturally from topological spaces, fuzzy sets, algebraic structures, coalgebras, and covering at once also known cases such as Kripke frames and probabilistic frames (i.e., Markov chains). By leveraging general categorical constructions, we provide axiomatisations and sound and complete semantics for various fragments of logics for closure operators. Hence, closure hyperdoctrines are useful both for refining and improving the theory of existing spatial logics, and for the definition of new spatial logics for new applications.

Cite as

Davide Castelnovo and Marino Miculan. Closure Hyperdoctrines. In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 12:1-12:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{castelnovo_et_al:LIPIcs.CALCO.2021.12,
  author =	{Castelnovo, Davide and Miculan, Marino},
  title =	{{Closure Hyperdoctrines}},
  booktitle =	{9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021)},
  pages =	{12:1--12:21},
  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.2021.12},
  URN =		{urn:nbn:de:0030-drops-153678},
  doi =		{10.4230/LIPIcs.CALCO.2021.12},
  annote =	{Keywords: categorical logic, topological semantics, closure operators, spatial logic}
}
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