Michal Walicki
Address: University of Bergen
Department of Informatics
HiB, 5020 Bergen, NORWAY
Ph. : +47 55 584178
Fx. : +47 55 584199
Email : myforenameatiidotuibdotno
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 selfreference
The current conjecture:
If a digraph has no kernel then it has an odd cycle or
a ray with infinitely many vertices dominating it.
Proven for:
 graphs with finite number of ends
 graphs where each vertex belongs to finitely many ends (follows from the above)
 graphs with countably many ends, where no end is contained in another
(PAST):
 Universal algebra and category theory:
Categories of multialgebras
Relational and power structures
Algebraic treatment of nondeterminism
Lecture Notes:

INF227  Introduction to mathematical logic

INF220  Algebraic Specification:
 INF121 (h2005)
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.
Logic
Kernels of digraphs and paradox
 Kernels of digraphs (and satisfiability)
 Kernels of digraphs with finitely many ends, a proof of the main conjecture (top of this page) for graphs with finitely many ends, [preprint; Discrete Mathematics, 342, 473486, 2019]
 some reverse mathematical results, at APAL, vol. 162, no. 3, March 2012
 "Finding kernels or solving SAT": analysing
the relations between the algorithms for kernels and SAT, [Journal of Discrete Algorithms, vol.10, 146164, 2012]
 Selfreference and paradoxes (infinitary theories and kernels of digraphs; later works on this list are with Sjur Dyrkolbotn)
 "Resolving infinitary paradoxes", complete reasoning with classical resolution about and in the presence of inconsistency [preprint, final version in
JSL,82,(2),2017,709723]
 Paraconsistent semantics, refining the above: maximal, predecessorclosed local kernels provide general semantics for the resolution logic; when the theory is consistent, they coincide with the classical semantics, while otherwise provide a classical semantics for the maximal consistent subdiscourse (kernel for maximal ``consistent'' induced subgraph); [preprint; submitted]
 "Reference, paradoxes and truth",
graphbased (or boolean equations based) approach to paradoxes of
selfreference. Many cases problematic for earlier approaches are solved in a
simple way. [preprint; the final version in Synthese, available at www.springerlink.com or at JStore.]
 "Propositional Discourse Logic": graph structure of paradoxes, diagnosis of semantic paradoxes [preprint; appeared in Synthese]
 Argumentation, paradox and kernels in directed graphs  a Ph.D. thesis by Sjur Dyrkolbotn, written (and defended) under my supervision in 2012.
Modal / Epistemic / Sequence logic / Bounded (finite) agents
 Sequence Logic
 "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)
 Bounded agents
 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
 "A Complete Calculus for the
Multialgebraic and Functional Semantics of Nondeterminism"
[ACM TOPLAS, Vol. 17, No. 2, March 1995],
(view the .ps file)
 Quantifierfree logic for multialgebraic
theories, WOLLIC, 2003 [revised version in Theoretical Computer Science, 2006]
 A digression:"On Specialization of Derivations in Axiomatic Equality Theories"
[in Proc. of LFCS'94,LNCS vol. 813, 1994]
Rewriting in multialgebras
 "Reasoning and Rewriting with SetRelations I: Ground Completeness"
[Proc. of CSL'94, L.Pacholski, J.Tiuryn (eds.), LNCS vol. 933, 1995]
 "Reasoning and Rewriting with SetRelations II: Completeness for the
NonGround Case"
[Recent Trends in Data Type Specification, LNCS. vol.1130,
(eds. M.Haveraaen, O.Owe, O.J.Dahl), Oslo, 1995]
 "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.185203, 1996]
Algebra, semantics
Relations, multifunctions, universal multialgebra
 "Relations, Multialgebras and Homomorphism"
 "The institution of Multialgebras  a general
framework for algebraic software development"
(a Ph.D. thesis written under my supervision by Yngve Lamo, 2003)
 A digression: "computation Algebras"
[Tech. Rep. no. 117, Dept. of Informatics, University of Bergen, 1996]
Multialgebraic semantics of nondeterminism
 "Algebraic Approaches to Nondeterminism  an Overview"
[ACM Computing Surveys,29, 1, March, 1997]
 "Generated Models and the Omegarule: the Nondterministic Case"
[Proc. of TAPSOFT'95, LNCS, vol. 915, 1995]
 "Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions"
[ADT'94, in Recent Trends in Data Type Specification,LNCS, vol. 906, 1995]
 "Initiality + Nondeterminism => Junk"
[in Proc. of NIK'94,Tapir, 1994]
 "Singular and Plural Nondeterministic Parameters"
[SIAM Journal on Computing, 263, 1997 (1995)]
 "Nondeterminism vs. Underspecification", SCI 2001
 "The Institution of Multialgebras"
Tech.Rep. no.209, Department of Informatics, University of Bergen, 2000
Applications and extensions of nondeterministic specifications
 "Structured Specifications and Implementation of Nondeterminisitc Data Types"
[Nordic Journal of Computing, no. 2, 1995]
[Tech. Rep. TUMI9442, Inst. fur Informatik,
Technische Universitat Munchen, 1994]
 "Modeling partiality by nondeterminism"
[Tech. Rep. 178, Department of Informatics, University of Bergen, 1999
 "Combining specification formalisms in the
`general logic' of multialgebras", FLIRTS 2002 (2003)
 "Composition and refinement of
specifications of parameterized data types", REFINE 2002
 Specification
of Parameterized Programs  persistency revisited, Nordic Journal of
Computing, 2001
Other things:
 philosophy, skiing.
Miscellanous:
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