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 : myforename-at-ii-dot-uib-dot-no

Interests: self-reference 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, self-reference
    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:

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


Some papers:

1. Logic

    Self-reference, paradoxes, infinitary theories and kernels of digraphs

    (earlier works, further down on this list, are with Sjur Dyrkolbotn)
    1. 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]
    2. "Extensions in Graph Normal Form" - graph normal form for first-order logic, with applications to (conservative) extensions [to appear in Logic Journal of the IGPL, 2020]
    3. "Resolving infinitary paradoxes", complete reasoning with classical resolution about and in the presence of inconsistency [preprint, final version in JSL,82,(2),2017,709-723]
    4. 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 2016]
    5. "Propositional Discourse Logic": graph structure of paradoxes, diagnosis of semantic paradoxes [preprint; appeared in Synthese, 2013]
    6. Argumentation, paradox and kernels in directed graphs - a Ph.D. thesis by Sjur Dyrkolbotn, written (and defended) under my supervision in 2012.
    7. "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, 2009.]

    Kernels of digraphs, pradoxes and satisfiability

    1. 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]
    2. Graph Normal Form for propositional logic and some reverse mathematical results, at APAL, vol. 162, no. 3, March 2012
    3. "Finding kernels or solving SAT": analysing the relations between the algorithms for kernels and SAT, [Journal of Discrete Algorithms, vol.10, 146-164, 2012]

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

    Sequence Logic

    1. "A strongly complete logic of dense time intervals", ESSLI-06, (logic relating sequential descriptions (in an arbitrary parameter logic) of systems passing through changing states)
    2. "Developing Bounded Reasoning" (a preliminary version, 2008. The original publication is available at www.springerlink.com)
    3. "Completeness and decidability in Sequence Logic" , LPAR'07
    4. "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

    1. Strongly Complete Axiomatizations of ``Knowing At Most'' in Standard Syntactic Assignments, CLIMA'05.
    2. Complete Axiomatization of Finite Syntactic Epistemic States, in Declarative Agent Languages and Technologies, workshop at AAMAS'2005.
    3. "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)
    4. "Developing Bounded Reasoning" (a preliminary version, 2008. The original publication is available at www.springerlink.com)
    5. Complete axiomatisations of properties of finite sets, Logic Journal of the IGPL, vol.16, no.3, June 2008.

    Logic of multifunctions

    1. Quantifier-free logic for multialgebraic theories, WOLLIC, 2003 [revised version in Theoretical Computer Science, 2006]
    2. "A Complete Calculus for the Multialgebraic and Functional Semantics of Nondeterminism" [ACM TOPLAS, Vol. 17, No. 2, March 1995],
    3. A digression:"On Specialization of Derivations in Axiomatic Equality Theories" [in Proc. of LFCS'94,LNCS vol. 813, 1994]
    4. "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

    1. "Reasoning and Rewriting with Set-Relations 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
    2. "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]
    3. "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]

    2. Algebra, semantics

    Relations, multi-functions, homomorphisms, universal multi-algebra

    1. "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.
    2. "Bireachability and final multialgebras" [Proceedings of CALCO'05, LNCS 3629]
    3. "A category for studying the standarization of reporting languages" [TR, also in Proceedings of the 9th Asian Conference on Logic]
    4. "Compositional Homomorphisms of Relational Structures", FTC 2001
    5. "The institution of Multialgebras - a general framework for algebraic software development"
      (a Ph.D. thesis written under my supervision by Yngve Lamo, 2003)
    6. 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

    1. "Algebraic Approaches to Nondeterminism - an Overview" [ACM Computing Surveys,29, 1, March, 1997]
    2. "Generated Models and the Omega-rule: the Nondterministic Case" [Proc. of TAPSOFT'95, LNCS, vol. 915, 1995]
    3. "Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions" [ADT'94, in Recent Trends in Data Type Specification,LNCS, vol. 906, 1995]
    4. "Initiality + Nondeterminism => Junk" [in Proc. of NIK'94,Tapir, 1994]
    5. "Singular and Plural Nondeterministic Parameters" [SIAM Journal on Computing, 26-3, 1997 (1995)]
    6. "Nondeterminism vs. Underspecification", SCI 2001

    Applications and extensions of nondeterministic specifications

    1. "Structured Specifications and Implementation of Nondeterminisitc Data Types" [Tech. Rep. TUM-I9442, Inst. fur Informatik, Technische Universitat Munchen, 1994], appeared also in Nordic Journal of Computing, no. 2, 1995.
    2. "Modeling partiality by nondeterminism" [Tech. Rep. 178, Department of Informatics, University of Bergen, 1999.
    3. "Combining specification formalisms in the `general logic' of multialgebras", FLIRTS 2002 (2003).
    4. "Composition and refinement of specifications of parameterized data types", REFINE 2002.
    5. Specification of Parameterized Programs - persistency revisited, Nordic Journal of Computing, 2001.

    3. Lecture Notes:

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

    4. Other things:

    1. philosophy, skiing.
    2. trafny opis
    3. HOLD-UP, a film in French about current affairs

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