- reasoning with graded notions

- mathematical fuzzy logic
- (abstract) algebraic logic
- substructural logics

- 37 papers in peer-reviewed journals; 5 edited books; 16 papers in conference proceedings; and 4 book chapters
- Citations: 450+ indexed by Web of Science, 550+ by Scopus, 1750+ by Google Scholar, and 190+ by MathSciNet
- H-index: 15 by Web of Science, 15 by Scopus, 23 by Google Scholar, and 9 by MathSciNet

- Young researchers award for outstanding achievements by ASCR (2007)
- Josef Hlávka award for young employees of ASCR (2006)
- Junior Scientist Award of the Learned Society of CR (2006)
- 1st class award of the rector of the Czech Technical University for an outstanding PhD thesis (2005)
- Otto Wichterle award by ASCR (2005)

- Substructural logics: A logical glimpse at residuated lattices, The 91st Workshop on General Algebra, Brno, Czech Republic, 2016
- Logics of graded predicates, ManyVal 2015,Les Diablerets, Switzerland, 2015
- First-order non-classical logics: an order-based approach, Compositional Meaning in Logic, Vienna, Austria, 2014
- Mathematical Fuzzy Logic: First-order and beyond, International Workshop Information, Uncertainty, and Imprecision, two lectures tutorial, Olomouc, Czech Republic, 2013
- From (deductive) fuzzy logic to (logic-based) fuzzy mathematics, 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Verona, Italy, 2009
- Fuzzy Class Theory: A State of the Art, 30th Linz Seminar on Fuzzy Set Theory, Linz, Austria, 2009
- First-order fuzzy logics: Recent development (with P. Hájek), Universal Logic 2007, Xi'an, China, 2007
- The apparatus of Fuzzy Class Theory (with L. Běhounek), Fuzzy Set Theory and its Applications, Liptovský Ján, Slovakia, 2006

- 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.

- Editor of Archive
for Mathematical Logic, Fuzzy
Sets and Systems, and Journal
of Applied Logic

- Chairman of the board of the Institute of
Computer Science (2012–present),
member since 2007

- Chair of Programme Committee at Linz Seminar 2010 (Linz) and NCMPL 2011 (Canton)
- Chair of Organizing Committee for
NCM
2009, LoMoReVI
2009, LATD
2010, ManyVal
2013, and TACL 2017

- Coordinator of the workgroup of Mathematical Fuzzy Logic (100+ members from 20+ countries)