Michal Walicki

Address: University of Bergen 
         Department of Informatics
         HiB, 5020 Bergen, NORWAY
Ph.       : +47 55 58-41-78
Fx.       : +47 55 58-41-99
E-mail : michal(at)ii(dot)uib(dot)no

Interests: Logical methods in software development and modeling, 
more specifically (in order of current importance):
- Logic: 
    Consistency as the existence of digraph kernels
    Variants of compactness in infinitary propositional logic 
                      (as properties of corresponding digraphs)
    Paradoxes of self-reference

The current conjecture: If a dag has no kernel then it has a ray with infinitely many vertices dominating it.

(PAST): - Universal algebra and category theory: Categories of multialgebras Relational and power structures Algebraic treatment of nondeterminism

Lecture Notes:

  1. INF-227 - Introduction to mathematical logic
  2. INF-220 - Algebraic Specification:
  3. INF-121 (h-2005)

Some papers:

Files which are mentioned as available for ftp, can also be obtained directly by anonymous ftp from the directory /pub/michal on the server ftp.ii.uib.no.


    Truth, graphs and paradox

  1. Self-reference and paradoxes (infinitary theories and kernels of digraphs; later works on this list are with Sjur Dyrkolbotn)

  2. Argumenatation, paradox and kernels in directed graphs - a Ph.D. thesis by Sjur Dyrkolbotn, written (and defended) under my supervision in 2012.

  3. Kernels of digraphs and satisfiability - some reverse mathematical results, at APAL, vol. 162, no. 3, March 2012

    Modal / Epistemic / Sequence logic / Bounded (finite) agents

  4. Sequence Logic

  5. "Modalities as Interactions between the Classical and the Intuitionistic Logics", Tech.Rep. no.330, June 2006, (in the classical algebraic semantics, modalities can be viewed as combinations of classical and intuitionisitc negations)

  6. Bounded agents

  7. Complete axiomatisations of properties of finite sets, Logic Journal of the IGPL, vol.16, no.3, June 2008.

    Logic of multifunctions

    see "Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions" below

  8. "A Complete Calculus for the Multialgebraic and Functional Semantics of Nondeterminism"
    [ACM TOPLAS, Vol. 17, No. 2, March 1995]

  9. Quantifier-free logic for multialgebraic theories, WOLLIC, 2003 [revised version in Theoretical Computer Science, 2006]

  10. A digression:"On Specialization of Derivations in Axiomatic Equality Theories" [in Proc. of LFCS'94,LNCS vol. 813, 1994]

    Rewriting in multialgebras

  11. "Reasoning and Rewriting with Set-Relations I: Ground Completeness"
    [Proc. of CSL'94, L.Pacholski, J.Tiuryn (eds.), LNCS vol. 933, 1995]

  12. "Reasoning and Rewriting with Set-Relations II: Completeness for the Non-Ground Case"
    [Recent Trends in Data Type Specification, LNCS. vol.1130, (eds. M.Haveraaen, O.Owe, O.-J.Dahl), Oslo, 1995]

  13. "Nondeterministic Algebraic Specifications in Relational Syntax"
    [Proc. of Nordic Workshop on Programming Theory, B.Bjerner, M.Larsson, B.Norstroem (eds.), Rep. 86, The Programming Methodology Group, Goeteborg University, pp.185-203, 1996]

    Algebra, semantics

    Relations, multi-functions, universal multi-algebra

  14. "Relations, Multialgebras and Homomorphism"

  15. "The institution of Multialgebras - a general framework for algebraic software development"
    (a Ph.D. thesis written under my supervision by Yngve Lamo, 2003)

  16. A digression: "computation Algebras"
    [Tech. Rep. no. 117, Dept. of Informatics, University of Bergen, 1996]

    Multialgebraic semantics of nondeterminism

  17. "Algebraic Approaches to Nondeterminism - an Overview"
    [ACM Computing Surveys,29, 1, March, 1997]

  18. "Generated Models and the Omega-rule: the Nondterministic Case"
    [Proc. of TAPSOFT'95, LNCS, vol. 915, 1995]

  19. "Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions"
    [ADT'94, in Recent Trends in Data Type Specification,LNCS, vol. 906, 1995]

  20. "Initiality + Nondeterminism => Junk" [in Proc. of NIK'94,Tapir, 1994]

  21. "Singular and Plural Nondeterministic Parameters"
    [SIAM Journal on Computing, 26-3, 1997 (1995)]

  22. "Nondeterminism vs. Underspecification", SCI 2001

  23. "The Institution of Multialgebras"
    Tech.Rep. no.209, Department of Informatics, University of Bergen, 2000

    Applications and extensions of nondeterministic specifications

  24. "Structured Specifications and Implementation of Nondeterminisitc Data Types"
    [Nordic Journal of Computing, no. 2, 1995]
    [Tech. Rep. TUM-I9442, Inst. fur Informatik, Technische Universitat Munchen, 1994]

  25. "Modeling partiality by nondeterminism"
    [Tech. Rep. 178, Department of Informatics, University of Bergen, 1999

  26. "Combining specification formalisms in the `general logic' of multialgebras", FLIRTS 2002 (2003)

  27. "Composition and refinement of specifications of parameterized data types", REFINE 2002

  28. Specification of Parameterized Programs - persistency revisited, Nordic Journal of Computing, 2001

    Other things:

    1. philosophy, skiing.


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