# Hájek Petr, prof., RNDr., DrSc.

Born February 6, 1940 in Prague

## Study and professional preparation

Graduated from Faculty of Mathematics and Physics of Charles University (CU) in 1962, thesis on algebra, post-graduate student at the Institute of Mathematics of the Czechoslovak Academy of Sciences (CSAS), later Academy of sciences of the Czech Republic (AS CR; (mathematical logic, PhD. thesis on set theory); CSc. in 1965; DrSc. 1990; Assist. prof. (CU) 1993; Honorarprofessor of the Technical University in Vienna from 1994. Professor (CU) 1997.

## Employment

Institute of Mathematics CSAS/AS CR to 1992 (last as head scientific worker), from March 1992 to the end of February 2000, Director of the Institute of Computer Science AS CR; now senior scientific worker there.

## Domain of expertise

Mathematical logic and logical foundations of computer science. Present topic of main activity; mathematical (deductive) fuzzy logic as a many-valued logic with a comparative notion of truth. Over 200 scientific papers (see selection below).

## Membership and positions in international organizations and societies

- Member of the Asssociation for Symbolic Logic (twice member of its council)
- 1995-1999 First Vice-President of the International Union for History and Philosophy of Science, Division Logic, Methodology and Philosophy of Science.
- 1999-2003 President of the Kurt Godel Society.
- He is or was a member of the editorial boards of the journals Czechoslovak Mathematical Journal, Studia Logica, Archive for Mathematical Logic, Soft Computing, Fundamenta Informaticae

## Honors

- Medal of the Minister of Education of the Czech republic 2002. Medal "De scientiae et humanitate optime meritis" (from the Academy of Sciences of the Czech Republic) 2006.
- Medal from the President of the Czech Republic 2006.

## Selection of publications

### A. Books

- Vopůnka P., Hájek P.: The theory of semisets. North-Holland Publ. Comp. 1972, 332 pp.
- Hájek P., Havránek T., Chytil M.: Metoda GUHA - automatická tvorba hypotéz. Academia Prague 1983, 316 pp.
- Hájek P., Havránek T.: Mechanizing hypothesis formation (mathematical foundations for a general theory), Springer-Verlag Berlin-Heidelberg-New York, 1978, 396 pp.
- Hájek P., Pudlák P.: Metamathematics of first-order arithmetic, Springer-Verlag 1993, 460 pp.
- Hájek P., Havránek T., Jiroušek R.: Processing uncertain information in expert systems, CRC.Press (USA) 1992, 285 pp.
- Hájek P.: Metamathematics of Fuzzy Logic. Kluwer 1998, 297 pp.

### B. Some selected papers

- What is Mathematical Fuzzy Logic. Fuzzy Sets and Systems, Vol. 157, 2006, pp. 597-603
- On Arithmetic in the Cantor-Lukasiewicz Fuzzy Set Theory. Archive for Mathematical Logic, Vol. 44, 2005, pp. 763-782
- Arithmetical Complexity of Fuzzy Predicate Logics - A Survey. Soft Computing, Vol. 9, 2005, pp. 935-941
- (with Holeňa M.)Formal Logics of Discovery and Hypothesis Formation by Machine. Theoretical Computer Science, Vol. 292, 2003, pp. 345-357
- A New Small Emendation of Gődels Ontological Proof. - Studia Logica, Vol. 71, 2002, pp. 149-164
- (with Shepherdson J.) A Note on the Notion of Truth in Fuzzy Logic. Annals of Pure and Applied Logic, Vol. 109, 2001, pp. 65-69
- (with Paris J., Shepherdson J.) The Liar Paradox and Fuzzy Logics. Journal of Symbolic Logic, Vol. 65, 2000, No. 1, pp. 339-346
- Interpretability and Fragments of Arithmetic.In: Arithmetic, Proof Theory and Computational Complexity. (Ed.: Clote P., Krajíček J.) - Oxford, Clarendon Press 1993, pp. 185-196
- (with Clote P.,Paris J.)On Some Formalized Conservation Results in Arithmetic. Archive for Mathematical Logic, Vol. 31, 1991, pp. 201-218
- (with Montagna F.) The Logic of Pi-1 Conservativity. Archive for Mathematical Logic, Vol. 30, 1990, pp. 113-123
- (with Kučera A.) On Recursion Theory in IE1. The Journal Symbolic of Logic, Vol. 54, 1989, pp. 576-589
- Arithmetical Interpretations of Dynamic Logic. Journal of Symbolic Logic, Vol. 48, 1983, pp. 704-71
- (with Hájková M.) On Interpretability in Theories Containing Arithmetic. Fundamenta Mathematicae, Vol. 76, 1972, pp. 131-137
- (with Havel I., Chytil M.) The GUHA-Method of Automatic Hypotheses Determination. Computing, Vol. 1, 1966, pp. 293-308
- The Consistency of Church's Alternatives. Bull. Acad. Polon. Sci., Vol. 14, 1966, pp. 31-47

## Freely available on internet

- The book Hájek-Havránek: Mechanizing hypothesis formation
- A letter by R.M. Solovay to Hájek from August 1976 on interpretability on set theories. (.pdf)
- A letter by R.M. Solovay to Hájek from May 1976 on interpretability in Peano Arithmetic (.pdf)

## Učební texty

## Address

Institute of computer science Academy of sciences of the Czech Republic Pod vodárenskou věží 2 182 07 Prague Czech Republic e-mail: hajek[-at-]cs.cas.cz phone: (+420) 266053760