- reasoning with graded notions

- non-classical modal and predicate logics
- (abstract) algebraic logic

- mathematical fuzzy logic

- substructural logics
- non-classical mathematics

Basic scientometric data:

- 46 papers in peer-reviewed journals; 17 papers in conference proceedings; and 4 book chapters
- Citations: 800+ indexed by Web of Science, 2500+ by Google Scholar, and 300+ by MathSciNet
- H-index: 17 by Web of Science, 27 by Google Scholar, and 11 by MathSciNet

Notable invited lectures:

- Towards a general theory of
lattice-valued models, model
theory session at XVIII
Latin
American Symposium on Mathematical Logic, Chile, 2019

- Lattice-valued predicate logics, XIV
Congreso Dr. Antonio Monteiro, Argentina, 2017

- Substructural logics: A logical glimpse at residuated lattices, The 91st Workshop on General Algebra, Czech Republic, 2016
- Logics of graded predicates, ManyVal 2015, Switzerland, 2015
- First-order non-classical logics: an order-based approach, Compositional Meaning in Logic, Austria, 2014
- From (deductive) fuzzy logic to (logic-based) fuzzy mathematics, 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Italy, 2009
- Fuzzy Class Theory: A State of the Art, 30th Linz Seminar on Fuzzy Set Theory, Austria, 2009

Edited books:

- P. Cintula, C. Fermüller, C. Noguera. Handbook of Mathematical Fuzzy Logic - Volume 3. Volume 58 of Studies in Logic, Mathematical Logic and Foundations. College Publications, London, 2015. 384 pages.
- P. Cintula, P. Hájek, C. Noguera. Handbook of Mathematical Fuzzy Logic - Volume 2. Volume 38 of Studies in Logic, Mathematical Logic and Foundations. College Publications, London, 2011. 480 pages.
- P. Cintula, P. Hájek, C. Noguera. Handbook of Mathematical Fuzzy Logic - Volume 1. Volume 37 of Studies in Logic, Mathematical Logic and Foundations. College Publications, London, 2011. 492 pages.
- P. Cintula, C. Fermüller, L. Godo, P. Hájek. Understanding Vagueness. Logical, Philosophical and Linguistic Perspectives. Volume 36 of Studies in Logic. College Publications, London, 2011. 421 pages.
- P. Cintula, Z. Haniková, V. Švejdar. Witnessed Years: Essays in Honour of Petr Hájek. Volume 37 of Tributes. College Publications, London, 2009. 416 pages.

Other major activities:

- Deputy
director for Research of the
Institute of Computer Science

- Editor of Archive for Mathematical Logic and Journal of Applied Logic
- Chair of Programme Committee at NCMPL
2017 (Canton), NCMPL
2011 (Canton), and Linz
Seminar 2010 (Linz)

- Chair of Organizing Committee for
TACL
2017,
ManyVal
2013,
LATD
2010, NCM
2009, and LoMoReVI
2009

- Coordinator of the workgroup of Mathematical Fuzzy Logic (2007–2016)
- Head of the Department of Theoretical Computer Science of the Institute of Computer Science (2017–2020)
- Chairman of the board of the Institute of Computer Science (2012–2017)