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 : myforename-at-ii-dot-uib-dot-no
Interests: Logical methods in software development and modeling,
more specifically (in order of current importance):
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 digraph has no kernel then it has an odd cycle or
a ray with infinitely many vertices dominating it.
- Universal algebra and category theory:
Categories of multialgebras
Relational and power structures
Algebraic treatment of nondeterminism
- 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
INF-227 - Introduction to mathematical logic
INF-220 - Algebraic Specification:
- INF-121 (h-2005)
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.
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, 473-486, 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, 146-164, 2012]
- Self-reference 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
- Paraconsistent semantics, refining the above: maximal, predecessor-closed 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",
graph-based (or boolean equations based) approach to paradoxes of
self-reference. 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
- "A Complete Calculus for the
Multialgebraic and Functional Semantics of Nondeterminism"
[ACM TOPLAS, Vol. 17, No. 2, March 1995],
(view the .ps file)
- Quantifier-free 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 Set-Relations I: Ground Completeness"
[Proc. of CSL'94, L.Pacholski, J.Tiuryn (eds.), LNCS vol. 933, 1995]
- "Reasoning and Rewriting with Set-Relations II: Completeness for the
[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.185-203, 1996]
Relations, multi-functions, universal multi-algebra
- "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 Omega-rule: 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, 26-3, 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. TUM-I9442, 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
of Parameterized Programs - persistency revisited, Nordic Journal of
- philosophy, skiing.
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