71 found
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  1.  35
    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. Protoalgebraic Logics.Janusz Czelakowski - 2003 - Studia Logica 74 (1):313-342.
     
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  3.  60
    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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  4.  40
    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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  5. 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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  6.  42
    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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  7.  59
    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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  8.  46
    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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  9.  70
    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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  10.  46
    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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  11.  53
    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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  12.  50
    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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  13.  24
    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 (...)
  14. (1 other version)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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  15.  20
    (1 other version)Logics based on partial Boolean σ-algebras.Janusz Czelakowski - 1974 - Studia Logica 33 (4):371-396.
  16.  50
    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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  17.  82
    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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  18. 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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  19. Model-Theoretic Methods in Methodology of Propositional Calculi.Janusz Czelakowski - 1981 - Studia Logica 40 (4):415-416.
     
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  20. 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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  21. (3 other versions)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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  22.  56
    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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  23.  49
    Logics based on partial Boolean sigma-algebras.Janusz Czelakowski - 1975 - Studia Logica 34:69.
  24.  31
    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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  25.  42
    John F. horthy, agency and deontic logic.Janusz Czelakowski - 2003 - Erkenntnis 58 (1):116-126.
  26.  7
    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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  27.  25
    Logics of Order and Related Notions.Janusz Czelakowski & Adam Olszewski - 2022 - Studia Logica 110 (6):1417-1464.
    The aim of the paper is twofold. First, we want to recapture the genesis of the logics of order. The origin of this notion is traced back to the work of Jerzy Kotas, Roman Suszko, Richard Routley and Robert K. Meyer. A further development of the theory of logics of order is presented in the papers of Jacek K. Kabziński. Quite contemporarily, this notion gained in significance in the papers of Carles Noguera and Petr Cintula. Logics of order are named (...)
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  28.  45
    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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  29. Another approach to partial Boolean algebras.Janusz Czelakowski - 1973 - Bulletin of the Section of Logic 2 (3):175-177.
     
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  30. A Characterization Of Matr.Janusz Czelakowski - 1979 - Bulletin of the Section of Logic 8 (2):83-85.
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  31. 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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  32. 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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  33. 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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  34.  25
    A remark on free products.Janusz Czelakowski - 1980 - Bulletin of the Section of Logic 9 (3):125-128.
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  35.  22
    A remark on countable algebraic models.Janusz Czelakowski - 1979 - Bulletin of the Section of Logic 8 (1):2-4.
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  36. 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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  37.  12
    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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  38. Epistemic Aspects of Action Systems.Janusz Czelakowski - 2015 - In Freedom and Enforcement in Action: A Study in Formal Action Theory. Dordrecht, Netherland: Springer.
     
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  39. Elementary Action Systems.Janusz Czelakowski - 2015 - In Freedom and Enforcement in Action: A Study in Formal Action Theory. Dordrecht, Netherland: Springer.
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  40.  31
    Foreword.Janusz Czelakowski, Wiesław Dziobiak & Jacek Malinowski - 2011 - Studia Logica 99 (1-3):1-6.
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  41.  18
    Fixed-points for relations and the back and forth method.Janusz Czelakowski - 2006 - Bulletin of the Section of Logic 35 (2/3):63-71.
  42.  24
    Filtered subdirect products.Janusz Czelakowski - 1996 - Bulletin of the Section of Logic 24:92-96.
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  43.  19
    General Theory of the Commutator for Deductive Systems. Part I. Basic Facts.Janusz Czelakowski - 2006 - Studia Logica 83 (1-3):183-214.
    The purpose of this paper is to present in a uniform way the commutator theory for k-deductive system of arbitrary positive dimension k. We are interested in the logical perspective of the research — an emphasis is put on an analysis of the interconnections holding between the commutator and logic. This research thus qualifies as belonging to abstract algebraic logic, an area of universal algebra that explores to a large extent the methods provided by the general theory of deductive systems. (...)
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  44.  24
    Logics and operators.Janusz Czelakowski - 1995 - Logic and Logical Philosophy 3:87-100.
    Two connectives are of special interest in metalogical investigations — the connective of implication which is important due to its connections to the notion of inference, and the connective of equivalence. The latter connective expresses, in the material sense, the fact that two sentences have the same logical value while in the strict sense it expresses the fact that two sentences are interderivable on the basis of a given logic. The process of identification of equivalent sentences relative to theories of (...)
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  45.  22
    “Large” matrices which induce finite consequence operations.Janusz Czelakowski - 1979 - Bulletin of the Section of Logic 8 (2):79-81.
  46.  3
    My Final Comments to the Volume.Janusz Czelakowski - 2024 - In Jacek Malinowski & Rafał Palczewski (eds.), Janusz Czelakowski on Logical Consequence. Springer Verlag. pp. 447-462.
    I wish to thank all those who contributed to the publication of this volume. In the first place, I am indebted to Professor Jacek Malinowski, the idea-giver and animator of the whole enterprise, and to dr. hab. Rafał Palczewski, responsible for the editorial work on this volume. I also thank Professor Heinrich Wansing for valuable comments on the content of some parts of this book.
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  47. Ordered Action Systems.Janusz Czelakowski - 2015 - In Freedom and Enforcement in Action: A Study in Formal Action Theory. Dordrecht, Netherland: Springer.
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  48. On imbedding of partial Boolean algebras into Boolean algebras.Janusz Czelakowski - 1973 - Bulletin of the Section of Logic 2 (3):178-181.
     
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  49. On truth-schemes for intensional logics.Janusz Czelakowski & Wieslaw Dziobiak - 2006 - Reports on Mathematical Logic.
     
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  50.  54
    Partial Boolean algebras in a broader sense.Janusz Czelakowski - 1979 - Studia Logica 38 (1):1 - 16.
    The article deals with compatible families of Boolean algebras. We define the notion of a partial Boolean algebra in a broader sense (PBA(bs)) and then we show that there is a mutual correspondence between PBA(bs) and compatible families of Boolean algebras (Theorem (1.8)). We examine in detail the interdependence between PBA(bs) and the following classes: partial Boolean algebras in the sense of Kochen and Specker (§ 2), ortholattices (§ 3, § 5), and orthomodular posets (§ 4), respectively.
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