Janusz Czelakowski on Logical Consequence (Outstanding Contributions to Logic, 27)

✍ Scribed by Jacek Malinowski (editor), Rafał Palczewski (editor)

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 473
• Category: Library

✦ Synopsis

This book is dedicated to the life and work of logician Janusz Czelakowski on the topic of logical consequence. It consists of three parts – a biography, a survey and research sections. The volume begins with an autobiographic chapter by Janusz Czelakowski followed by a historical chapter written by Jacek Malinowski.

The survey section forms the backbone of the volume with each chapter covering one of Janusz Czelakowski’s results. They focus on his results in the area of logical consequence, demonstrate how his results influenced following research, and presents potential future results, problems and applications. This volume is of interest to logicians and mathematicians.

✦ Table of Contents

Preface
Contents
Editors and Contributors
1 Introduction
References
Part I Biography
2 Biogram
2.1 A Digressive Tale of My Life
2.1.1 My Early Youth and Student's Years
2.1.2 `Que Sera, Sera.' Everyday Life with a Tint of Politics
2.2 Beyond Logic There Is only Nonsense'' 2.2.1 My Adventures with Logic 2.2.2 After the Year 1981 2.3The Colors of Fall''. the Recent Years
2.3.1 Opole
2.4 Epilog
3 Section of Logic in Łódź 1982–1992
3.1 Introduction
3.2 How I Joined the Section of Logic
3.3 Algebraic Seminar
3.4 Changes in the Section of Logic 1986–1988
3.5 My Logical Research
3.6 Moving to 8 Marca Street
3.7 Autumn Schools of Logic
3.8 Conferences on History of Logic in Kraków
3.9 Jabłonna 1988
3.10 Moscow and Tbilisi 1989
3.11 Logic Colloquium in West Berlin 1989
3.12 International School of the Philosophy of Sciences, Trieste, 1989
3.13 Ph.D. Defence
3.14 After Ph.D. Defence
3.15 Seminar in Kraków
3.16 Przysiek, Donovaly and Varna 1990
3.17 Bulletin of the Section of Logic
3.18 Closedown
Part II Surveys
4 Janusz Czelakowski's Research on the Theory of Matrices and its Applications in the Seventies and Eighties of the 20th Century
4.1 Introduction
4.2 Basic Concepts and Notation
4.3 The Characterization Theorems of the Class of the Matrix Models of a Logic
4.4 Equivalential Logics
4.5 Logics with a Unital Semantics
4.6 Filter-Distributive Logics
4.7 Finitely Based Logics
4.8 Interpolation Properties
4.9 The Deduction Theorem and the Local Deduction Theorem
4.9.1 The Deduction Theorem
4.9.2 The Local Deduction Theorem
4.10 The Evolution and Influence of Czelakowski's Work
References
5 A Gentle Introduction to the Leibniz Hierarchy
5.1 Introduction
5.2 Logics and Matrices
5.2.1 Propositional Logics
5.2.2 Deductive Filters
5.2.3 The Leibniz Congruence
5.2.4 Reduced Models
5.3 Protoalgebraic Logics
5.3.1 Sets of Equivalence Formulas
5.3.2 A Syntactic Description
5.3.3 The Leibniz Operator
5.3.4 A Model Theoretic Description
5.3.5 The Correspondence Property
5.3.6 The Parametrized Local Deduction Theorem
5.4 Equivalential Logics
5.4.1 The Leibniz Operator
5.4.2 A Model Theoretic Description
5.5 Truth Equational Logics
5.5.1 Equational Completeness Theorems
5.5.2 The Leibniz Operator
5.5.3 Implicit Definability
5.6 Algebraizable Logics
5.6.1 Generalized Quasivarieties
5.6.2 Algebraization
5.6.3 The Isomorphism Theorem
5.7 Farewell
References
6 Czelakowski's Work on Quasivarieties
6.1 Introduction
6.2 Preliminaries
6.3 Relative Principal Congruences
6.3.1 C-Sets from Quasi-equational Bases
6.3.2 CEP and DPC
6.4 Relative Congruence Distributivity
6.4.1 RCD and C-Sets
6.4.2 Parameterized Equational Definability of Principal Meets
6.4.3 The Extension Principle and the Cap Property
6.4.4 More on D-Sets
6.5 Equationally Definable Principal Meets
6.5.1 Axiomatizing EDPM
6.5.2 EDPM and Subquasivarieties
6.6 Finite Basis Theorems
6.6.1 Finite Basis for Quasivarieties with EDPM
6.6.2 Finite Basis for Quasivarieties with DPC
References
7 On J. Czelakowski's Contributions to Quantum Logic and the Foundation of Quantum Mechanics
7.1 Introduction
7.2 Partial Boolean Algebras and the Hidden-Variables Problem
7.3 J. Czelakowski's Work on Partial Boolean Algebras
7.3.1 Characterization Theorems
7.3.2 A Coordinatization Theorem for Partial Boolean Algebras
7.4 Partial Boolean sigmaσ-Algebras
7.4.1 A Logical System for Partial Boolean sigmaσ-Algebras
7.5 Applications to Orthomodular Posets
7.5.1 Embedding Theorems for Orthomodular Posets
7.6 Partial Boolean Algebras in a Broader Sense
7.6.1 Embeddability Results for Partial Boolean Algebras in a Broader Sense
7.7 Partial Referential Matrices
7.8 Summary
References
8 Actions and Deontology: Janusz Czelakowski on Actions and their Assessment
8.1 Introduction
8.2 Background
8.2.1 Seven Approaches to Action Theory
8.2.2 Maria Nowakowska's Theory of Actions
8.2.3 Logic of Programs, PDL and Algebras of Actions
8.2.4 Models of Actions: Label Transition Systems and STIT Histories
8.3 Czelakowski's Account of Actions and Their Performability
8.3.1 Atomic and Compound Actions and Their Descriptions
8.3.2 Formal Definitions: Action Language and Relational Model
8.3.3 On Performability
8.3.4 Performability and Probability
8.4 Deontology of Compound Actions
8.5 Relation to Other Approaches
8.5.1 Relational Versus STIT-Like Models
8.5.2 Relation to PDL
8.6 Conclusions
References
Part III Research
9 Assertional Logics and the Frege Hierarchy
9.1 Introduction
9.2 Preliminaries
9.3 Relative Point-Regularity
9.4 Relative Congruence Orderability
9.4.1 Fully Fregean Assertional Logics
9.4.2 Fregean Assertional Logics
9.4.3 Selfextensional Assertional Logics
9.4.4 Relative Strong Congruence Orderability
9.5 The Variety Problem
References
10 Characterization of Strong Day Implication Systems
10.1 Introduction
10.2 Definitions and Notation
10.3 Axiomatic Closure Relations
10.4 Characterization of Strong Day Implication Systems
10.5 Conclusion
References
11 SCI–Sequent Calculi, Cut Elimination and Interpolation Property
11.1 Introduction
11.2 Preliminaries
11.3 Sequent Calculi for SCI
11.4 Analytic Sequent Calculus
11.5 Essential Cut Elimination Theorem for GSCI2
11.6 Interpolation
11.7 Modifications and Open Problems
References
12 Some More Theorems on Structural Entailment Relations and Non-deterministic Semantics
12.1 Introduction
12.2 Preliminaries
12.2.1 Non-deterministic Matrix Semantics
12.2.2 Illustrations: Logiken Ohne Eigenschaften
12.3 Constructions on Nmatrices
12.3.1 Strict Homomorphisms, Preimages and Quotients
12.3.2 Sound Homomorphisms and Quotients
12.3.3 Products and Ultraproducts
12.4 Characterizations
12.4.1 Characterizing Compact Logics
12.4.2 Characterizing Finitely Based Logics
12.4.3 Characterizing sans serif upper N m a t r left parenthesis contains as normal subgroup right parenthesisNmatr() When contains as normal subgroup is Compact
12.5 Conclusions and Futher Work
References
13 Boolean-Like Algebras of Finite Dimension: From Boolean Products to Semiring Products
13.1 Introduction
13.2 Preliminaries
13.2.1 Factor Congruences and Decomposition
13.2.2 Semimodules and Boolean Vector Spaces
13.2.3 Church Algebras of Finite Dimension
13.2.4 Boolean-like Algebras of Finite Dimension
13.3 Applications of nnBAs to Boolean Powers
13.4 Representation Theorems
13.4.1 The Inner Boolean Algebra of an nnBA
13.4.2 The Coordinates of an Element
13.4.3 The Main Theorems
References
14 Logic of Action from the Perspective of Knowledge Representation
14.1 Introduction
14.2 Actions and Their Descriptions
14.2.1 Background: Boolean Formulas
14.2.2 Describing Effects
14.2.3 Describing Abilities
14.2.4 Action Descriptions
14.3 Models of Attempts
14.3.1 Valuations
14.3.2 Successor of a Valuation
14.3.3 Agent Choices
14.4 The Logic LAAA
14.4.1 Language of LAAA
14.4.2 Truth Conditions and Validity
14.4.3 Relation with Individual Stit Logic
14.5 Axiomatisation
14.6 Extensions
14.6.1 Other Kinds of Performability Constraints
14.6.2 Compound Actions
14.7 Discussion and Conclusion
References
15 Implication in Sharply Paraorthomodular and Relatively Paraorthomodular Posets
15.1 Introduction
15.2 Basic Concepts
15.3 What Implication for Sharply Paraorthomodular Posets?
15.4 Amalgams of Kleene Lattices
15.5 Relatively Paraorthomodular Posets
15.6 Relatively Paraorthomodular Join-Semilattices
15.7 Adjointness
References
16 My Final Comments to the Volume
Appendix List of Publications of Janusz Czelakowski