Mundici's representation of MV-algebras as intervals in Abelian lattice-ordered groups was a landmark result in a number of ways. Besides its key role in the theory of MV-algebras, it sparked the search for further representations of ordered algebras arising in non-classical logic by means of partially ordered groups (po-groups), with the aim of leveraging the extensively studied theory of po-groups to understand these wider (and wilder) classes of algebras. Two notable results in this direction are the representation due to Galatos & Tsinakis of GMV-algebras as so-called nuclear images of certain submonoids of lattice-ordered groups, and the representation due to Dvurečenskij & Vetterlein of so-called pseudo-effect algebras as intervals in po-groups. In this talk, we show that in the project of representing ordered monoidal structures in terms of pogroups, the class of so-called integrally closed po-monoids plays a central role. On the one hand, they are precisely the algebras representable as nuclear images of submonoids of po-groups. This vastly extends the previous representation results in this direction, showing in particular that every integral po-monoid arises from a po-group. On the other hand, they also form the basic building blocks of a different construction, which decomposes a (sufficiently well-behaved) po-monoid into a family of subalgebras associated with its positive idempotent elements.
Welcome to the webpages of the Logic Group of the Institute of Computer Science of the Czech Academy of Sciences (ICS CAS). You'll find us here.
Latest News & Updates
Members
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Marta Bílková
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Petr Cintula
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Wesley Fussner
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Zuzana Haniková
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Filip Jankovec
PhD Student
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Roman Kuznets
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Chun-Yu Lin
PhD Student
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Ondrej Majer
Project Researcher
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Wolfgang Poiger
Postdoctoral Researcher
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Igor Sedlár
Past members: Paolo Baldi (→ University of Milan), Stefano Bonzio (→ Polytechnic University of the Marche in Ancona), Libor Běhounek (→ University of Ostrava), Thomas Macaulay Ferguson (→ Rensselaer Polytechnic Institute), Nicholas Ferenz (→ University of Lisbon); David Fernández-Duque (→ University of Barcelona), Karel Chvalovský (→ Czech Technical University), Petr Hájek (✞), Dagmar Harmancová, Rostislav Horčík (→ Czech Technical University), Tommaso Moraschini (→ University of Barcelona), Milan Petrík (→ Czech University of Life Sciences), Adam Přenosil (→ University of Barcelona), Luca Reggio (→ University of Oxford), Andrew Tedder (→ Ruhr University Bochum), Amanda Vidal (→ IIIA-CSIC Barcelona), Jamie Wannenburg (→ University of Pretoria), Kentarô Yamamoto (→ Polish Academy of Sciences, Institute of Mathematics).
Our Research Focus
Research topics: non-classical logic, modal logic, substructural logics, dynamic logic, abstract algebraic logic, universal algebra, philosophy of mathematics, epistemic logic, relevant logic, algebras for program verification, probabilistic logics, and much more...
Current Projects:
- INTERACT: Interpolation, Amalgamation, and Computation (PI: Wesley Fussner)
2025-2029 (Czech Science Foundation Junior Star) - Modern Czech Logic in the Philosophy of Mathematics (PI: Zuzana Haniková)
2025-2027 (Czech Science Foundation) - KATRA: Knowledge, Action and Time - A Relevant Approach (PI: Igor Sedlár)
2025-2027 (Czech Science Foundation) - CELIA: Coalition and Epistemic Logic - An Intensional Approach to Groups (PI: Olivier Roy & Marta Bílková, coPI: Ondrej Majer)
2022-2025 (Czech Science Foundation and German Science Foundation, Lead Agency) - We're a partner in the MOSAIC project
2020-2025 (EU MSCA-RISE)
Recent Projects:
- GRADLACT: Graded Logics of Action (PI: Igor Sedlár)
2022-2024 (Czech Science Foundation) - MetaSuMo: Metamathematics of Substructural Modal Logics (PI: Petr Cintula)
2022-2024 (Czech Science Foundation) - NOCLID: Nonclassical Logical Models of Information Dynamics (PI Igor Sedlár), 2018-2021, Czech Science Foundation (Junior Project)
Upcoming Seminars & Events
Our regular research seminar runs on Wednesdays 4pm and talks are often streamed via Zoom. More information can be found at the seminar webpage. To join the seminar mailing list, contact the organisers, Zuzana Haniková and Igor Sedlár.
Upcoming talks:
- 21 May Adam Přenosil (University of Barcelona): Which po-monoids arise from po-groups?
- 28 May Wolfgang Poiger (Institute of Computer Science, Czech Academy of Sciences): tba
This list will be updated.
Join Us
The ICS and the Czech Academy of Sciences regularly open calls for postdoctoral researchers, and tenure-track positions are opened on a yearly basis at the ICS. Let us know if you are interested in applying.
Current calls:
- Postdoctoral researcher within the TRUST project (work package Logical aspects of rationality and knowledge). Deadline: 31 March 2025.
- Postdoctoral researcher within the TRUST project (work package Logical analysis of language and communication). Deadline: 31 March 2025.
- Postdoctoral researcher within the DEZINFO project (work package Non-classical logics of disinformation). Deadline: 31 March 2025.
- Tenure track in computer science. Deadline: 31 March 2025.
The ICS welcomes applications within international schemes such as the MSCA Postdoctoral Fellowships. Applications are particularly encouraged since the government of the Czech Republic supports no-money MSCA-PF projects. Another funding option are the Individual Postdoctoral Fellowships of the Czech Science Foundation. Do get in touch if you're interested in applying.
Teaching and Supervision
Members of the group offer supervision of Master and PhD theses focusing on their research topics. We can serve as supervisors and co-supervisors for students based at universities in and outside the Czech Republic. Get in touch if you're interested in writing your thesis with us.
Current PhD students:
- Giorgio Cignarale (co-supervised by Roman Kuznets at TU Wien)
- Filip Jankovec (co-supervised by Petr Cintula)
- Chun-Yu Lin (supervised by Marta Bílková)
- Rojo Randrianomentsoa (co-supervised by Roman Kuznets at TU Wien)
- Thomas Schlögl (co-supervised by Roman Kuznets at TU Wien)
- Pietro Vigiani (co-supervised by Igor Sedlár at the Scuola Normale Superiore di Pisa)
Past PhD students:
- Adam Přenosil (supervised by Marta Bílková at the Charles University in Prague, thesis Reasoning With Inconsistent Information defended in 2018)
- Karel Chvalovský (supervised by Marta Bílková at the Charles University in Prague, thesis Undecidability of Some Substructural Logics defended in 2015)
Recently taught courses:
- Dynamic Logic. Charles University, Fall 2023.
- Dynamic Logic. Charles University, Fall 2021.
- Mathematical Logic 2021/22. Czech Technical University.