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Documents authored by Jaakkola, Reijo


Document
Relating Description Complexity to Entropy

Authors: Reijo Jaakkola, Antti Kuusisto, and Miikka Vilander

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
We demonstrate some novel links between entropy and description complexity, a notion referring to the minimal formula length for specifying given properties. Let MLU be the logic obtained by extending propositional logic with the universal modality, and let GMLU be the corresponding extension with the ability to count. In the finite, MLU is expressively complete for specifying sets of variable assignments, while GMLU is expressively complete for multisets. We show that for MLU, the model classes with maximal Boltzmann entropy are the ones with maximal description complexity. Concerning GMLU, we show that expected Boltzmann entropy is asymptotically equivalent to expected description complexity multiplied by the number of proposition symbols considered. To contrast these results, we prove that this link breaks when we move to considering first-order logic FO over vocabularies with higher-arity relations. To establish the aforementioned result, we show that almost all finite models require relatively large FO-formulas to define them. Our results relate to links between Kolmogorov complexity and entropy, demonstrating a way to conceive such results in the logic-based scenario where relational structures are classified by formulas of different sizes.

Cite as

Reijo Jaakkola, Antti Kuusisto, and Miikka Vilander. Relating Description Complexity to Entropy. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 38:1-38:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{jaakkola_et_al:LIPIcs.STACS.2023.38,
  author =	{Jaakkola, Reijo and Kuusisto, Antti and Vilander, Miikka},
  title =	{{Relating Description Complexity to Entropy}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{38:1--38:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.38},
  URN =		{urn:nbn:de:0030-drops-176903},
  doi =		{10.4230/LIPIcs.STACS.2023.38},
  annote =	{Keywords: finite model theory, entropy, formula size, randomness, formula size game}
}
Document
Complexity of Polyadic Boolean Modal Logics: Model Checking and Satisfiability

Authors: Reijo Jaakkola

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


Abstract
We study the computational complexity of model checking and satisfiability problems of polyadic modal logics extended with permutations and Boolean operators on accessibility relations. First, we show that the combined complexity of the model checking problem for the resulting logic is PTime-complete. Secondly, we show that the satisfiability problem of polyadic modal logic extended with negation on accessibility relations is ExpTime-complete. Finally, we show that the satisfiability problem of polyadic modal logic with permutations and Boolean operators on accessibility relations is ExpTime-complete, under the assumption that both the number of accessibility relations that can be used and their arities are bounded by a constant. If NExpTime is not contained in ExpTime, then this assumption is necessary, since already the satisfiability problem of modal logic extended with Boolean operators on accessibility relations is NExpTime-hard.

Cite as

Reijo Jaakkola. Complexity of Polyadic Boolean Modal Logics: Model Checking and Satisfiability. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 26:1-26:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{jaakkola:LIPIcs.CSL.2023.26,
  author =	{Jaakkola, Reijo},
  title =	{{Complexity of Polyadic Boolean Modal Logics: Model Checking and Satisfiability}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{26:1--26:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.26},
  URN =		{urn:nbn:de:0030-drops-174875},
  doi =		{10.4230/LIPIcs.CSL.2023.26},
  annote =	{Keywords: Polyadic modal logics, Boolean modal logics, Model checking, Satisfiability}
}
Document
Complexity Classifications via Algebraic Logic

Authors: Reijo Jaakkola and Antti Kuusisto

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


Abstract
Complexity and decidability of logics is an active research area involving a wide range of different logical systems. We introduce an algebraic approach to complexity classifications of computational logics. Our base system GRA, or general relation algebra, is equiexpressive with first-order logic FO. It resembles cylindric algebra but employs a finite signature with only seven different operators, thus also giving a very succinct characterization of the expressive capacities of first-order logic. We provide a comprehensive classification of the decidability and complexity of the systems obtained by limiting the allowed sets of operators of GRA. We also discuss variants and extensions of GRA, and we provide algebraic characterizations of a range of well-known decidable logics.

Cite as

Reijo Jaakkola and Antti Kuusisto. Complexity Classifications via Algebraic Logic. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 27:1-27:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{jaakkola_et_al:LIPIcs.CSL.2023.27,
  author =	{Jaakkola, Reijo and Kuusisto, Antti},
  title =	{{Complexity Classifications via Algebraic Logic}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{27:1--27:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.27},
  URN =		{urn:nbn:de:0030-drops-174880},
  doi =		{10.4230/LIPIcs.CSL.2023.27},
  annote =	{Keywords: Decidability, complexity, algebraic logic, fragments of first-order logic}
}
Document
Towards a Model Theory of Ordered Logics: Expressivity and Interpolation

Authors: Bartosz Bednarczyk and Reijo Jaakkola

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. While the complexities of their satisfiability problems are now well-established, their model theory, however, is poorly understood. Our paper aims to provide some insight into it. We start by providing suitable notions of bisimulation for ordered logics. We next employ bisimulations to compare the relative expressive power of ordered logics, and to characterise our logics as bisimulation-invariant fragments of FO à la van Benthem. Afterwards, we study the Craig Interpolation Property (CIP). We refute yet another claim from the infamous work by Purdy, by showing that the fluted and forward fragments do not enjoy CIP. We complement this result by showing that the ordered fragment and the guarded ordered logics enjoy CIP. These positive results rely on novel and quite intricate model constructions, which take full advantage of the "forwardness" of our logics.

Cite as

Bartosz Bednarczyk and Reijo Jaakkola. Towards a Model Theory of Ordered Logics: Expressivity and Interpolation. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 15:1-15:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bednarczyk_et_al:LIPIcs.MFCS.2022.15,
  author =	{Bednarczyk, Bartosz and Jaakkola, Reijo},
  title =	{{Towards a Model Theory of Ordered Logics: Expressivity and Interpolation}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{15:1--15:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert 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.MFCS.2022.15},
  URN =		{urn:nbn:de:0030-drops-168132},
  doi =		{10.4230/LIPIcs.MFCS.2022.15},
  annote =	{Keywords: ordered fragments, fluted fragment, guarded fragment, model theory, Craig Interpolation Property, expressive power, model checking}
}
Document
Ordered Fragments of First-Order Logic

Authors: Reijo Jaakkola

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
Using a recently introduced algebraic framework for classifying fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the ordered logic and the fluted logic by modifying some of their syntactical restrictions.

Cite as

Reijo Jaakkola. Ordered Fragments of First-Order Logic. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 62:1-62:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{jaakkola:LIPIcs.MFCS.2021.62,
  author =	{Jaakkola, Reijo},
  title =	{{Ordered Fragments of First-Order Logic}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{62:1--62:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.62},
  URN =		{urn:nbn:de:0030-drops-145025},
  doi =		{10.4230/LIPIcs.MFCS.2021.62},
  annote =	{Keywords: ordered logic, fluted logic, complexity, decidability}
}
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