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

1. What is Mathematical Fuzzy Logic. Fuzzy Sets and Systems, Vol. 157, 2006, pp. 597-603
2. On Arithmetic in the Cantor-Lukasiewicz Fuzzy Set Theory. Archive for Mathematical Logic, Vol. 44, 2005, pp. 763-782
3. Arithmetical Complexity of Fuzzy Predicate Logics - A Survey. Soft Computing, Vol. 9, 2005, pp. 935-941
4. (with Holeňa M.)Formal Logics of Discovery and Hypothesis Formation by Machine. Theoretical Computer Science, Vol. 292, 2003, pp. 345-357
5. A New Small Emendation of Gődels Ontological Proof. - Studia Logica, Vol. 71, 2002, pp. 149-164
6. (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
7. (with Paris J., Shepherdson J.) The Liar Paradox and Fuzzy Logics. Journal of Symbolic Logic, Vol. 65, 2000, No. 1, pp. 339-346
8. Interpretability and Fragments of Arithmetic.In: Arithmetic, Proof Theory and Computational Complexity. (Ed.: Clote P., Krajíček J.) - Oxford, Clarendon Press 1993, pp. 185-196
9. (with Clote P.,Paris J.)On Some Formalized Conservation Results in Arithmetic. Archive for Mathematical Logic, Vol. 31, 1991, pp. 201-218
10. (with Montagna F.) The Logic of Pi-1 Conservativity. Archive for Mathematical Logic, Vol. 30, 1990, pp. 113-123
11. (with Kučera A.) On Recursion Theory in IE1. The Journal Symbolic of Logic, Vol. 54, 1989, pp. 576-589
12. Arithmetical Interpretations of Dynamic Logic. Journal of Symbolic Logic, Vol. 48, 1983, pp. 704-71
13. (with Hájková M.) On Interpretability in Theories Containing Arithmetic. Fundamenta Mathematicae, Vol. 76, 1972, pp. 131-137
14. (with Havel I., Chytil M.) The GUHA-Method of Automatic Hypotheses Determination. Computing, Vol. 1, 1966, pp. 293-308
15. The Consistency of Church's Alternatives. Bull. Acad. Polon. Sci., Vol. 14, 1966, pp. 31-47

Full list of publications

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

• Hájek Petr: Logika pro pedagogy (.ps)
• Hájek Petr: Fuzzy logika (.ps)

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