Michal Walicki
Address: University of Bergen
Department of Informatics
HiB, 5020 Bergen, NORWAY
Ph. : +47 55 584178
Fx. : +47 55 584199
Email : myforenameatiidotuibdotno
Interests: selfreference and semantic closure, digraph kernels, paraconsistency, logical methods.
more specifically:
(CURRENT) Graph representation of logical theories:
Standard/paraconsistent semantics represented by digraph kernels/semikernels
Graph Normal Form and its applications
Logical circularity as graph cycles
Semantic paradoxes, selfreference
Transparent sentential truth predicate
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
Some papers:
1. Logic
Selfreference, paradoxes, infinitary theories and kernels of digraphs
(earlier works, further down on this list, are with Sjur Dyrkolbotn)
 Logic of sentential predicates. LSP
extends LK with 2 rules for sentential quantifiers, providing a
complete reasoning for language extending any FOL language with
predicates over sentences and quantification over
sentences. Single axiom captures convention (T), which extends
conservatively any theory with a fresh truth predicate. Paradoxes of intensional type and
of indirect discourse can be analyzed in the same way as direct
ones, while modal operators are special cases of sentential
predicates. [in preparation 2021]
 "Extensions in Graph Normal Form"
 graph normal form for firstorder logic, with applications to (conservative) extensions [to appear in Logic Journal of the IGPL, 2020]
 "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 2016]
 "Propositional Discourse Logic": graph structure of paradoxes, diagnosis of semantic paradoxes [preprint; appeared in Synthese, 2013]
 Argumentation, paradox and kernels in directed graphs  a Ph.D. thesis by Sjur Dyrkolbotn, written (and defended) under my supervision in 2012.
 "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, 2009.]
Kernels of digraphs, pradoxes 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]
 Graph Normal Form for propositional logic and 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]
Modal / Epistemic / Sequence logic / Bounded (finite) agents
Sequence Logic
 "A strongly complete logic of dense
time intervals", ESSLI06, (logic relating sequential descriptions (in an arbitrary
parameter logic) of systems passing through changing states)
 "Developing Bounded Reasoning" (a preliminary
version, 2008. The original publication is available at www.springerlink.com)
 "Completeness and decidability in Sequence Logic" , LPAR'07
 "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 and finite sets
 Strongly Complete Axiomatizations of
``Knowing At Most'' in Standard Syntactic Assignments, CLIMA'05.
 Complete Axiomatization of Finite Syntactic
Epistemic States, in Declarative Agent Languages and Technologies, workshop
at AAMAS'2005.
 "The Logic of Finite Syntactic States"
(a Ph.D. thesis written under my supervision by Thomas AAgotnes, 2004
(epistemic logic of finite agents with bounded resources) with a small errata)
 "Developing Bounded Reasoning" (a preliminary
version, 2008. The original publication is available at www.springerlink.com)
 Complete axiomatisations of properties of finite sets, Logic
Journal of the IGPL, vol.16, no.3, June 2008.
Logic of multifunctions
 Quantifierfree logic for multialgebraic
theories, WOLLIC, 2003 [revised version in Theoretical Computer Science, 2006]
 "A Complete Calculus for the
Multialgebraic and Functional Semantics of Nondeterminism"
[ACM TOPLAS, Vol. 17, No. 2, March 1995],
 A digression:"On Specialization of Derivations in Axiomatic Equality Theories"
[in Proc. of LFCS'94,LNCS vol. 813, 1994]
 "Multialgebras, Power Algebras and Complete Calculi of Identities and
Inclusions" [ADT'94, in Recent Trends in Data Type Specification,LNCS, vol. 906, 1995]
Rewriting in multialgebras
 "Reasoning and Rewriting with SetRelations I: Ground Completeness"
[Proc. of CSL'94, L.Pacholski, J.Tiuryn (eds.), LNCS vol. 933, 1995]
 ps file or
a longer version with more proofs
 "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]
2. Algebra, semantics
Relations, multifunctions, homomorphisms, universal multialgebra
 "Universal Multialgebra", summarises all
earlier results, presenting an interesting notion of multialgebraic
homomorphism and congruence. A revised version appears as a chapter in "New Topics in Theoretical Computer Science", Nova Science Publishers, 2008.
 "Bireachability and final
multialgebras" [Proceedings of CALCO'05, LNCS 3629]
 "A
category for studying the standarization of reporting languages" [TR, also in Proceedings of the 9th Asian
Conference on Logic]
 "Compositional Homomorphisms of Relational
Structures", FTC 2001
 "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], appeared in Mathematical
Structures in Computer Science, 2001
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
Applications and extensions of nondeterministic specifications
 "Structured Specifications and Implementation of Nondeterminisitc Data Types" [Tech. Rep. TUMI9442, Inst. fur Informatik,
Technische Universitat Munchen, 1994], appeared also in
Nordic Journal of Computing, no. 2, 1995.
 "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.
3. Lecture Notes:

INF227  Introduction to mathematical logic

INF220  Algebraic Specification:
 INF121 (h2005)
4. Other things:
 philosophy, skiing.
 trafny opis
 HOLDUP, a film in French about current affairs
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