Search Results

Documents authored by Wolter, Frank

Document
DOI: 10.4230/LIPIcs.LICS.2026.26
The Size of Interpolants in Modal Logics

Authors: Balder ten Cate, Louwe B. Kuijer, and Frank Wolter

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
We start a systematic investigation of the size of Craig interpolants, uniform interpolants, and strongest implicates for (quasi-)normal modal logics. Our main upper bound states that for tabular modal logics, the computation of strongest implicates can be reduced in polynomial time to uniform interpolant computation in classical propositional logic. Hence they are of polynomial dag-size iff NP is included in P/poly. The reduction also holds for Craig interpolants if the tabular modal logic has the Craig interpolation property. Our main lower bound shows an unconditional exponential lower bound on the size of Craig interpolants and strongest implicates covering almost all non-tabular standard normal modal logics. For normal modal logics contained in or containing S4 or GL we obtain the following dichotomy: tabular logics have "propositionally sized" interpolants while for non-tabular logics an unconditional exponential lower bound holds.
Cite as

Balder ten Cate, Louwe B. Kuijer, and Frank Wolter. The Size of Interpolants in Modal Logics. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 26:1-26:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{tencate_et_al:LIPIcs.LICS.2026.26,
  author =	{ten Cate, Balder and Kuijer, Louwe B. and Wolter, Frank},
  title =	{{The Size of Interpolants in Modal Logics}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{26:1--26:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.26},
  URN =		{urn:nbn:de:0030-drops-268132},
  doi =		{10.4230/LIPIcs.LICS.2026.26},
  annote =	{Keywords: Modal logic, strongest implicates, uniform interpolants, Craig interpolants}
}
Document
DOI: 10.4230/LIPIcs.LICS.2026.60
Computation and Size of Interpolants for Hybrid Modal Logics

Authors: Jean Christoph Jung, Jędrzej Kołodziejski, and Frank Wolter

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
Recent research has established complexity results for the problem of deciding the existence of interpolants in logics lacking the Craig interpolation property (CIP). The proof techniques developed so far are non-constructive, and no meaningful bounds on the size of interpolants are known. Hybrid modal logics (or modal logics with nominals) are a particularly interesting class of logics without CIP: in their case, CIP cannot be restored without sacrificing decidability and, in applications, interpolants in these logics can serve as definite descriptions and separators between positive and negative data examples in description logic knowledge bases. In this contribution we show, using a new hypermosaic elimination technique, that in many standard hybrid modal logics Craig interpolants can be computed in fourfold exponential time, if they exist. On the other hand, we show that the existence of uniform interpolants is undecidable, which is in stark contrast to modal or intuitionistic logic where uniform interpolants always exist.
Cite as

Jean Christoph Jung, Jędrzej Kołodziejski, and Frank Wolter. Computation and Size of Interpolants for Hybrid Modal Logics. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 60:1-60:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{jung_et_al:LIPIcs.LICS.2026.60,
  author =	{Jung, Jean Christoph and Ko{\l}odziejski, J\k{e}drzej and Wolter, Frank},
  title =	{{Computation and Size of Interpolants for Hybrid Modal Logics}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{60:1--60:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.60},
  URN =		{urn:nbn:de:0030-drops-268475},
  doi =		{10.4230/LIPIcs.LICS.2026.60},
  annote =	{Keywords: Interpolation, Modal Logic, Hybrid Logic, Separator Computation}
}
Document
DOI: 10.4230/DagMan.10.1.1
Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract
Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.
Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}
Document
DOI: 10.4230/DagRep.12.7.62
Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Seminar 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, Milene Santos Teixeira, and Frank Wolter

Published in: Dagstuhl Reports, Volume 12, Issue 7 (2023)

Abstract
The area of Knowledge Representation and Reasoning (KR) is a central area in Artificial Intelligence that deals with the explicit, declarative representation of knowledge along with inference procedures for deriving further, implicit information from this knowledge. The goal of this Perspectives Seminar was to assess the area of KR, including its history, current state, and future prospects, and from this assessment to provide suggestions and recommendations for advancing the field, increasing participation in the area, and furthering links with related areas. Over the course of 5 days, 25 participants from a cross-section of subareas in KR and areas adjacent to KR met to discuss these topics. The workshop was composed of a number of invited talks and panels for reviewing the history and state of the art of KR, along with several working groups and general open discussions. In common with other Perspectives Workshops, a Manifesto will be produced; as well, recommendations contained in the manifesto will be also forwarded to the steering committee of the Principles of Knowledge Representation and Reasoning conference series for their consideration.
Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, Milene Santos Teixeira, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Seminar 22282). In Dagstuhl Reports, Volume 12, Issue 7, pp. 62-79, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@Article{delgrande_et_al:DagRep.12.7.62,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Teixeira, Milene Santos and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Seminar 22282)}},
  pages =	{62--79},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{12},
  number =	{7},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Teixeira, Milene Santos and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.7.62},
  URN =		{urn:nbn:de:0030-drops-176126},
  doi =		{10.4230/DagRep.12.7.62},
  annote =	{Keywords: applications of logics, declarative representations, formal logic, knowledge representation and reasoning}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.TIME.2017.1
Ontology-Mediated Query Answering over Temporal Data: A Survey (Invited Talk)

Authors: Alessandro Artale, Roman Kontchakov, Alisa Kovtunova, Vladislav Ryzhikov, Frank Wolter, and Michael Zakharyaschev

Published in: LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

Abstract
We discuss the use of various temporal knowledge representation formalisms for ontology-mediated query answering over temporal data. In particular, we analyse ontology and query languages based on the linear temporal logic LTL, the multi-dimensional Halpern-Shoham interval temporal logic HS_n, as well as the metric temporal logic MTL. Our main focus is on the data complexity of answering temporal ontology-mediated queries and their rewritability into standard first-order and datalog queries.
Cite as

Alessandro Artale, Roman Kontchakov, Alisa Kovtunova, Vladislav Ryzhikov, Frank Wolter, and Michael Zakharyaschev. Ontology-Mediated Query Answering over Temporal Data: A Survey (Invited Talk). In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 1:1-1:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{artale_et_al:LIPIcs.TIME.2017.1,
  author =	{Artale, Alessandro and Kontchakov, Roman and Kovtunova, Alisa and Ryzhikov, Vladislav and Wolter, Frank and Zakharyaschev, Michael},
  title =	{{Ontology-Mediated Query Answering over Temporal Data: A Survey}},
  booktitle =	{24th International Symposium on Temporal Representation and Reasoning (TIME 2017)},
  pages =	{1:1--1:37},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-052-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{90},
  editor =	{Schewe, Sven and Schneider, Thomas and Wijsen, Jef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017.1},
  URN =		{urn:nbn:de:0030-drops-79338},
  doi =		{10.4230/LIPIcs.TIME.2017.1},
  annote =	{Keywords: Description Logic, Temporal Logic, Ontology Mediated Query Answering, Data Complexity}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.108
Conservative Extensions in Guarded and Two-Variable Fragments

Authors: Jean Christoph Jung, Carsten Lutz, Mauricio Martel, Thomas Schneider, and Frank Wolter

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO2 and the guarded fragment GF. We prove that conservative extensions are undecidable in any FO fragment that contains FO2 or GF (even the three-variable fragment thereof), and that they are decidable and 2ExpTime-complete in the intersection GF2 of FO2 and GF.
Cite as

Jean Christoph Jung, Carsten Lutz, Mauricio Martel, Thomas Schneider, and Frank Wolter. Conservative Extensions in Guarded and Two-Variable Fragments. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 108:1-108:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{jung_et_al:LIPIcs.ICALP.2017.108,
  author =	{Jung, Jean Christoph and Lutz, Carsten and Martel, Mauricio and Schneider, Thomas and Wolter, Frank},
  title =	{{Conservative Extensions in Guarded and Two-Variable Fragments}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{108:1--108:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.108},
  URN =		{urn:nbn:de:0030-drops-74647},
  doi =		{10.4230/LIPIcs.ICALP.2017.108},
  annote =	{Keywords: Conservative Extensions, Decidable Fragments of First-Order Logic, Computational Complexity\}}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2015.363
On the Relationship between Consistent Query Answering and Constraint Satisfaction Problems

Authors: Carsten Lutz and Frank Wolter

Published in: LIPIcs, Volume 31, 18th International Conference on Database Theory (ICDT 2015)

Abstract
Recently, Fontaine has pointed out a connection between consistent query answering (CQA) and constraint satisfaction problems (CSP) [Fontaine, LICS 2013]. We investigate this connection more closely, identifying classes of CQA problems based on denial constraints and GAV constraints that correspond exactly to CSPs in the sense that a complexity classification of the CQA problems in each class is equivalent (up to FO-reductions) to classifying the complexity of all CSPs. We obtain these classes by admitting only monadic relations and only a single variable in denial constraints/GAVs and restricting queries to hypertree UCQs. We also observe that dropping the requirement of UCQs to be hypertrees corresponds to transitioning from CSP to its logical generalization MMSNP and identify a further relaxation that corresponds to transitioning from MMSNP to GMSNP (also know as MMSNP_2). Moreover, we use the CSP connection to carry over decidability of FO-rewritability and Datalog-rewritability to some of the identified classes of CQA problems.
Cite as

Carsten Lutz and Frank Wolter. On the Relationship between Consistent Query Answering and Constraint Satisfaction Problems. In 18th International Conference on Database Theory (ICDT 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 31, pp. 363-379, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{lutz_et_al:LIPIcs.ICDT.2015.363,
  author =	{Lutz, Carsten and Wolter, Frank},
  title =	{{On the Relationship between Consistent Query Answering and Constraint Satisfaction Problems}},
  booktitle =	{18th International Conference on Database Theory (ICDT 2015)},
  pages =	{363--379},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-79-8},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{31},
  editor =	{Arenas, Marcelo and Ugarte, Mart{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2015.363},
  URN =		{urn:nbn:de:0030-drops-49958},
  doi =		{10.4230/LIPIcs.ICDT.2015.363},
  annote =	{Keywords: Consistent Query Answering, Constraint Satisfaction, Data Complexity, Dichotomies, Rewritability}
}
Document
DOI: 10.4230/LIPIcs.CSL.2011.4
Ontology-Based Data Access and Constraint Satisfaction

Authors: Frank Wolter

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

Abstract
We present first results on the relationship between ontology-based data access using description logics and constraint satisfaction problems.
Cite as

Frank Wolter. Ontology-Based Data Access and Constraint Satisfaction. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, p. 4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

Copy BibTex To Clipboard

@InProceedings{wolter:LIPIcs.CSL.2011.4,
  author =	{Wolter, Frank},
  title =	{{Ontology-Based Data Access and Constraint Satisfaction}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{4--4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.4},
  URN =		{urn:nbn:de:0030-drops-32186},
  doi =		{10.4230/LIPIcs.CSL.2011.4},
  annote =	{Keywords: description logic, constraint satisfaction, conjunctive query}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact