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Janusz Czelakowski [101]J. Czelakowski [7]
  1.  33
    Protoalgebraic Logics.Janusz Czelakowski - 2001 - Kluwer Academic Publishers.
    This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...
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  2.  20
    Equivalential logics.Janusz Czelakowski - 1981 - Studia Logica 40 (3):227-236.
    The class of equivalential logics comprises all implicative logics in the sense of Rasiowa [9], Suszko's logic SCI and many others. Roughly speaking, a logic is equivalential iff the greatest strict congruences in its matrices are determined by polynomials. The present paper is the first part of the survey in which systematic investigations into this class of logics are undertaken. Using results given in [3] and general theorems from the theory of quasi-varieties of models [5] we give a characterization of (...)
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  3.  66
    Equivalential logics (I).Janusz Czelakowski - 1981 - Studia Logica 40 (3):227 - 236.
    The class of equivalential logics comprises all implicative logics in the sense of Rasiowa [9], Suszko's logicSCI and many Others. Roughly speaking, a logic is equivalential iff the greatest strict congruences in its matrices (models) are determined by polynomials. The present paper is the first part of the survey in which systematic investigations into this class of logics are undertaken. Using results given in [3] and general theorems from the theory of quasi-varieties of models [5] we give a characterization of (...)
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  4. Protoalgebraic Logics.Janusz Czelakowski - 2003 - Studia Logica 74 (1):313-342.
     
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  5.  59
    Algebraic aspects of deduction theorems.Janusz Czelakowski - 1985 - Studia Logica 44 (4):369 - 387.
    The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary (...)
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  6.  39
    Equivalential logics (II).Janusz Czelakowski - 1981 - Studia Logica 40 (4):355 - 372.
    In the first section logics with an algebraic semantics are investigated. Section 2 is devoted to subdirect products of matrices. There, among others we give the matrix counterpart of a theorem of Jónsson from universal algebra. Some positive results concerning logics with, finite degrees of maximality are presented in Section 3.
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  7.  52
    Reduced products of logical matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.
    The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...)
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  8.  25
    Fregean logics.J. Czelakowski & D. Pigozzi - 2004 - Annals of Pure and Applied Logic 127 (1-3):17-76.
    According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense.A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A deductive system is a second-order matrix over the formula algebra of some fixed but arbitrary language. A second-order matrix A is (...)
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  9.  32
    Local deductions theorems.Janusz Czelakowski - 1986 - Studia Logica 45 (4):377 - 391.
    The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued ukasiewicz logic C ) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).
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  10. Weakly algebraizable logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.
    In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.
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  11.  35
    Logical matrices and the amalgamation property.Janusz Czelakowski - 1982 - Studia Logica 41 (4):329 - 341.
    The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.
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  12.  52
    A deduction theorem schema for deductive systems of propositional logics.Janusz Czelakowski & Wies?aw Dziobiak - 1991 - Studia Logica 50 (3-4):385 - 390.
    We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.
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  13.  16
    The Suszko Operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1-2):181-231.
    The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.
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  14.  42
    The Suszko operator. Part I.Janusz Czelakowski - 2003 - Studia Logica 74 (1-2):181 - 231.
    The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.
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  15. Weakly Algebraizable Logics.Janusz Czelakowski & Ramon Jansana - 2000 - Journal of Symbolic Logic 65 (2):641-668.
    In the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.
     
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  16.  64
    Filter distributive logics.Janusz Czelakowski - 1984 - Studia Logica 43 (4):353 - 377.
    The present paper is thought as a formal study of distributive closure systems which arise in the domain of sentential logics. Special stress is laid on the notion of a C-filter, playing the role analogous to that of a congruence in universal algebra. A sentential logic C is called filter distributive if the lattice of C-filters in every algebra similar to the language of C is distributive. Theorem IV.2 in Section IV gives a method of axiomatization of those filter distributive (...)
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  17.  29
    Leśniewski's systems.Jan T. J. Srzednicki, V. F. Rickey & J. Czelakowski (eds.) - 1984 - Hingham, MA, USA: Distributors for the United States and Canada, Kluwer Boston.
  18.  54
    Fregean logics with the multiterm deduction theorem and their algebraization.J. Czelakowski & D. Pigozzi - 2004 - Studia Logica 78 (1-2):171 - 212.
    A deductive system (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas.
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  19.  43
    Matrices, primitive satisfaction and finitely based logics.Janusz Czelakowski - 1983 - Studia Logica 42 (1):89 - 104.
    We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.
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  20.  42
    Sentential logics and Maehara interpolation property.Janusz Czelakowski - 1985 - Studia Logica 44 (3):265 - 283.
    With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The main theorem of (...)
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  21.  41
    Deontology of Compound Actions.Janusz Czelakowski - 2020 - Studia Logica 108 (1):5-47.
    This paper, being a companion to the book [2] elaborates the deontology of sequential and compound actions based on relational models and formal constructs borrowed from formal linguistics. The semantic constructions presented in this paper emulate to some extent the content of [3] but are more involved. Although the present work should be regarded as a sequel of [3] it is self-contained and may be read independently. The issue of permission and obligation of actions is presented in the form of (...)
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  22. Algebraic aspects of deduction theorems.Janusz Czelakowski - 1983 - Bulletin of the Section of Logic 12 (3):111-114.
    By a sentential logic we understand a pair, where S is a sentential language, i.e. an absolutely free algebra freely generated by an infinite set p, q, r,... of sentential variables and endowed with countably many finitary connectives §1, §2,... and C is a consequence operation on S, the underlying set of S, satisfying the condition of structurality: eC ⊆ C, for every endomorphism e of S and for every X ⊆ S. If no confusion is likely we shall identify (...)
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  23.  12
    Fregean logics with the multiterm deduction theorem and their algebraization.J. Czelakowski & D. Pigozzi - 2004 - Studia Logica 78 (1-2):171-212.
    A deductive system \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{S}$$ \end{document} (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\{ \left\langle {\alpha,\beta } \right\rangle :T,\alpha \vdash s \beta and T,\beta \vdash s \alpha \},$$ \end{document}is a congruence relation on the formula algebra. The multiterm deduction-detachment theorem is a natural generalization of the (...)
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  24.  41
    Logics based on partial Boolean σ-algebras (1).Janusz Czelakowski - 1974 - Studia Logica 33 (4):371 - 396.
  25.  17
    Logics based on partial Boolean σ-algebras.Janusz Czelakowski - 1974 - Studia Logica 33 (4):371-396.
  26.  40
    Some theorems on structural entailment relations.Janusz Czelakowski - 1983 - Studia Logica 42 (4):417 - 429.
    The classesMatr( ) of all matrices (models) for structural finitistic entailments are investigated. The purpose of the paper is to prove three theorems: Theorem I.7, being the counterpart of the main theorem from Czelakowski [3], and Theorems II.2 and III.2 being the entailment counterparts of Bloom's results [1]. Theorem I.7 states that if a classK of matrices is adequate for , thenMatr( ) is the least class of matrices containingK and closed under the formation of ultraproducts, submatrices, strict homomorphisms and (...)
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  27.  77
    Key notions of Tarski's methodology of deductive systems.Janusz Czelakowski & Grzegorz Malinowski - 1985 - Studia Logica 44 (4):321 - 351.
    The aim of the article is to outline the historical background and the present state of the methodology of deductive systems invented by Alfred Tarski in the thirties. Key notions of Tarski's methodology are presented and discussed through, the recent development of the original concepts and ideas.
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  28. Action and Deontology.Janusz Czelakowski - 2015 - In Freedom and Enforcement in Action: A Study in Formal Action Theory. Dordrecht, Netherland: Springer.
     
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  29.  19
    Freedom and Enforcement in Action: A Study in Formal Action Theory.Janusz Czelakowski - 2015 - Dordrecht, Netherland: Springer.
    Situational aspects of action are discussed. The presented approach emphasizes the role of situational contexts in which actions are performed. These contexts influence the course of an action; they are determined not only by the current state of the system but also shaped by other factors as time, the previously undertaken actions and their succession, the agents of actions and so on. The distinction between states and situations is explored from the perspective of action systems. The notion of a situational (...)
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  30. RETRACTED ARTICLE: The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I).Janusz Czelakowski - 2023 - Studia Logica 111 (2):357-358.
    The paper is concerned with the old conjecture that there are infinitely many twin primes. In the paper we show that this conjecture is true, that is, it is true in the standard model of arithmetic. The proof is based on Rasiowa–Sikorski Lemma. The key role are played by the derived notion of a Rasiowa–Sikorski set and the method of forcing adjusted to arbitrary first–order languages. This approach was developed in the papers Czelakowski [ 4, 5 ]. The central idea (...)
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  31. Equivalential logics.Janusz Czelakowski - 1980 - Bulletin of the Section of Logic 9 (2):8-91.
    In the present note we continue the investigations undertaken in [2]. A full version of the paper has been submitted to Studia Logica. x1 Our goal is to give a characterization of the so called factorial matrices for a logic. A matrix M = is factorial i the greatest congruence M of M coincides with the diagonal of A. Recall that is a congruence of a matrix M = i is a congruence of the algebra A and for any a; (...)
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  32. Model-Theoretic Methods in Methodology of Propositional Calculi.Janusz Czelakowski - 1981 - Studia Logica 40 (4):415-416.
     
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  33. Equivalential logics.Janusz Czelakowski - 1980 - Bulletin of the Section of Logic 9 (3):108-113.
    By an algebraic semantics we shall mean a class K of matrices M = for a propositional language L such that D is a singleton, D = fdg. A logic has an algebraic semantics i C =6 ; and there exists an algebraic semantics K strongly adequate for C, i.e., C = CnK. Proposition. If a logic has an algebraic semantics, then every factorial matrix M 2 M atr has the following properties: M is of the form, where 1A 2 (...)
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  34.  49
    Another proof that ISP r is the least quasivariety containing K.Janusz Czelakowski & Wies?aw Dziobiak - 1982 - Studia Logica 41 (4):343 - 345.
    Let q(K) denote the least quasivariety containing a given class K of algebraic structures. Mal'cev [3] has proved that q(K) = ISP r(K)(1). Another description of q(K) is given in Grätzer and Lakser [2], that is, q(K) = ISPP u(K)2. We give here other proofs of these results. The method which enables us to do that is borrowed from prepositional logics (cf. [1]).
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  35.  62
    Logics based on partial Boolean sigma-algebras.Janusz Czelakowski - 1975 - Studia Logica 34:69.
  36. Logics based on partial Boolean σ-algebras.Janusz Czelakowski - 1974 - Bulletin of the Section of Logic 3 (2):31-37.
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  37. Relatively point-regular quasivarieties.J. Czelakowski & D. Pigozzi - 1989 - Bulletin of the Section of Logic 18 (4):183-195.
     
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  38.  26
    RETRACTED ARTICLE: There are Infinitely Many Mersenne Prime Numbers. Applications of Rasiowa–Sikorski Lemma in Arithmetic (II).Janusz Czelakowski - 2023 - Studia Logica 111 (2):359-359.
    The paper is concerned with the old conjecture that there are infinitely many Mersenne primes. It is shown in the work that this conjecture is true in the standard model of arithmetic. The proof refers to the general approach to first–order logic based on Rasiowa-Sikorski Lemma and the derived notion of a Rasiowa–Sikorski set. This approach was developed in the papers [ 2 – 4 ]. This work is a companion piece to [ 4 ].
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  39.  40
    John F. horthy, agency and deontic logic.Janusz Czelakowski - 2003 - Erkenntnis 58 (1):116-126.
  40.  3
    Biogram.Janusz Czelakowski - 2024 - In Jacek Malinowski & Rafał Palczewski (eds.), Janusz Czelakowski on Logical Consequence. Springer Verlag. pp. 9-47.
    algebraic logic, universal algebra, action theory, infinitistic methods in the theory of definitions, algebraic methods in set theory, methods of mathematical logic in number theory.
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  41.  40
    24th European Summer School on Logic, Language and Information.Janusz Czelakowski, Urszula Wybraniec-Skardowska & Jacek Waldmajer - 2013 - Bulletin of Symbolic Logic 19 (4):519-522.
    The European Summer Schools in Logic, Language and Information (ESSLLI) have been organised every year since 1989 under the auspices of the Association for Logic, Language and Information (FoLLI) in different cities around Europe. The 24th European Summer School in Logic, Language and Information (ESSLLI 2012) took place at the University of Opole, Poland, during August 6-17, 2012. The organisation committee was chaired by Janusz Czelakowski and Urszula Wybraniec-Skardowska (Institute of Mathematics and Informatics, University of Opole) and the programme committee (...)
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  42. Another approach to partial Boolean algebras.Janusz Czelakowski - 1973 - Bulletin of the Section of Logic 2 (3):175-177.
     
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  43. A Characterization Of Matr.Janusz Czelakowski - 1979 - Bulletin of the Section of Logic 8 (2):83-85.
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  44. A Local Property Of Imbeddings For Partial Boolean Algebras.Janusz Czelakowski - 1973 - Bulletin of the Section of Logic 2 (3):182-184.
     
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  45. Additivity of the commutator and residuation.Janusz Czelakowski - 2008 - Reports on Mathematical Logic.
    The notion of a commutator lattice is investigated. It is shown that the class of commutator lattices is coextensive with the class of lattices with residuation.
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  46. A Purely Algebraic Proof Of The Omitting Types Theorem.Janusz Czelakowski - 1979 - Bulletin of the Section of Logic 8 (1):7-9.
    In the present note we make use of some information given in [2]. Also, the terminology and notation do not dier from those accepted in [2]; in particular this concerns the formalism for the predicate calculus. Let A be a model of a rst-order language L. We say that A realizes a set of formulas Fla i A j= [a] for some valuation a in A and all 2 . We say that A omits i A does not realize . (...)
     
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  47.  21
    A remark on free products.Janusz Czelakowski - 1980 - Bulletin of the Section of Logic 9 (3):125-128.
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  48.  19
    A remark on countable algebraic models.Janusz Czelakowski - 1979 - Bulletin of the Section of Logic 8 (1):2-4.
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  49. Correction to my note "Partial Boolean σ-algebras".Janusz Czelakowski - 1974 - Bulletin of the Section of Logic 3 (3-4):37-40.
     
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  50.  9
    Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science.Janusz Czelakowski (ed.) - 2018 - Cham, Switzerland: Springer Verlag.
    This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise (...)
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