Skip to main content
Log in

Willem Blok's Contribution to Abstract Algebraic Logic

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

Willem Blok was one of the founders of the field Abstract Algebraic Logic. The paper describes his research in this field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. BLOK, W. J., and E. HOOGLAND, ‘The Beth Property in Algebraic Logic’, Studia Logica 49–90 of this issue.

  2. BLOK, W. J., and B. JONSSON, Algebraic structures for logic. A course given at the 23rd Holiday Mathematics Symposium, New Mexico State University, January 1999. Available at http://math.nmsu.edu/ holysymp/

  3. BLOK, W.J., and B. JONSSON, ‘Equivalence of Consequence Operations’, Studia Logica 91–110 of this issue.

  4. BLOK, W. J., and P. KOHLER, ‘Algebraic Semantics for Quasi-Classical Modal Logics’, The Journal of Symbolic Logic 48 (1984), 941–964.

    Article  Google Scholar 

  5. BLOK, W. J., P. KOHLER, and D. PIGOZZI, ‘On the structure of varieties with equationally definable principal congruences II’, Algebra Universalis 18 (1984), 334–379.

    Article  Google Scholar 

  6. BLOK, W. J., and D. PlGOZZI, ‘On the structure of varieties with equationally definable principal congruences I’, Algebra Universalis 15 (1982), 195–227.

    Google Scholar 

  7. BLOK, W. J., and D. PIGOZZI, ‘Protoalgebraic logics’, Studia Logica 45 (1986), 337–369.

    Article  Google Scholar 

  8. BLOK, W. J., and D. PlGOZZI, Algebraizable logics, vol. 396 of Mem. Amer. Math. Soc. A.M.S., Providence, January 1989.

  9. BLOK, W. J., and D. PIGOZZI, ‘Local deduction theorems in algebraic logic’, in H. Andreka, J. D. Monk, and I. Nemeti, (eds.), Algebraic Logic, vol. 54 of Colloq. Math. Soc. Jdnos Bolyai. North-Holland, Amsterdam, 1991, pp. 75–109.

    Google Scholar 

  10. BLOK, W. J., and D. PIGOZZI, ‘Algebraic semantics for universal Horn logic without equality’, in A. Romanowska and J. D. H. Smith, (eds.), Universal Algebra and Quasigroup Theory, A. Romanowska and J. D. H. Smith, (eds.), Heldermann, Berlin, 1992, pp. 1–56.

    Google Scholar 

  11. BLOK, W. J., and D. PlGOZZI, ‘On the structure of varieties with equationally definable principal congruences IIP, Algebra Universalis 32 (1994), 545–608.

    Article  Google Scholar 

  12. BLOK, W. J., and D. PlGOZZI, ‘On the structure of varieties with equationally definable principal congruences IV, Algebra Universalis 31 (1994), 1–35.

    Article  Google Scholar 

  13. BLOK, W. J., and D. PlGOZZI, ‘Abstract algebraic logic and the deduction theorem’. Manuscript 1997. Available at http://orion.math.iastate.edu/dpigozzi

  14. BLOK, W. J., and J. G. RAFTERY, ‘Ideals in quasivarieties of algebras’, in X. Caicedo and C. H. Montenegro, (eds.), Models, algebras and proofs, X. Caicedo and C. H. Montenegro, (eds.), vol. 203 of Lecture Notes in Pure and Applied Mathematics. Marcel Dekker, New York, 1999, pp. 167–186.

    Google Scholar 

  15. BLOK, W.J., and J. G. RAFTERY, ‘Assertionally equivalent quasivarieties’. Manuscript, 2003, 88 pp.

  16. BLOK, W. J., and J. REBAGLIATO, ‘Algebraic Semantics for Deductive systems’, Studia Logica 74, Special Issue on Abstract Algebraic Logic-Part II, J.M. Font, R. Jansana and D. Pigozzi (eds.), (2003), 153–180.

  17. CZELAKOWSKI, J., ‘R.educed products of logical matrices’, Studia Logica 39 (1980), 19–43.

    Article  Google Scholar 

  18. CZELAKOWSKI, J., Protoalgebraic Logics, vol. 10 of Trends in Logic. Studia Logica Library. Kluwer Academic Publishers, Dordrecht, 2001.

    Google Scholar 

  19. KOHLER, P., and D. PIGOZZI, ‘Varieties with equationally definable principal congruences’, Algebra Universalis 11 (1980), 213–219.

    Google Scholar 

  20. FONT, J.M., R. JANSANA, D. PIGOZZI, ‘A Survey of Abstract Algebraic Logic’, Studia Logica. Special Issue on Algebraic Logic II, 74 (2003), 13–97.

    Google Scholar 

  21. GYURIS, V., Variations of algebraizability. PhD thesis, University of Illinois at Chicago, 1999.

  22. PIGOZZI, D., ‘Abstract Algebraic Logic: Past, present and future’, in J.M. Font, J. Jansana, D. Piggozi, (eds.), Workshop on Abstract Algebraic Logic, Quaderns, 10 CRM, Bellaterra 1998.

  23. RAUTENBERG, W., F. WOLTER, M. ZAKHARYASCHEV, ‘WillemBlok and modal logic’, Studia Logica 15–30 of this issue.

  24. TARSKI, A., Logic. Semantics. Metamathematics. Papers from 1923 to 1938. Hackett Pub. Co., Indianapolis, Indiana, second edition, 1983. Edited by J. Corcoran.

    Google Scholar 

  25. WOJCICKI, R., ‘Matrix approach in the methodology of sentential calculi’, Studia Logical (1973), 7–37.

  26. WOJCICKI, R., Theory of logical calculi. Basic theory of consequence operations, vol. 199 of Synthese Library. Reidel, Dordrecht, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ramon Jansana.

Additional information

Dedicated to the memory of Willem Johannes Blok

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jansana, R. Willem Blok's Contribution to Abstract Algebraic Logic. Stud Logica 83, 31–48 (2006). https://doi.org/10.1007/s11225-006-8297-1

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-006-8297-1

Keywords

Navigation