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Algebraizable logics

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Author(s): W. J. Blok, Don Pigozzi
Series: Memoirs of the American Mathematical Society 396
Publisher: American Mathematical Society
Year: 1989

Language: English
Pages: 84

Title Page......Page 1
Abstract......Page 3
Contents......Page 4
Introduction......Page 7
1 Deductive Systems and Matrix Semantics......Page 11
1.1 The Lattice of Theories......Page 12
1.2 Matrix Semantics......Page 14
1.3 Deductive Systems as Elementary Theories......Page 15
1.4 The Elementary Leibniz Equivalence Relation......Page 16
1.4.1 Protoalgebraic Logics......Page 18
2 Equational Consequence and Algebraic Semantics......Page 19
2.1 Algebraic Semantics......Page 20
2.2 Equivalent Algebraic Semantics......Page 25
2.2.1 Uniqueness......Page 28
2.2.2 Axiomatization......Page 30
3 The Lattice of Theories......Page 33
4.1 The Leibniz Operator......Page 40
4.2 A Second Intrinsic Characterization......Page 45
5.1 Matrix Semantics and Algebraic Semantics......Page 48
5.2.1 Modal Logics......Page 52
5.2.2 Entailment and Relevance Logics......Page 54
5.2.3 Pure Implicational Logics......Page 55
5.2.4 Two Logics with the Same Algebraization......Page 60
5.2.5 Intuitionistic Propositional Logic without Implication......Page 62
5.2.6 Equivalential Logic......Page 63
A Elementary Definitional Equivalence......Page 66
B An Example......Page 69
C Predicate Logic......Page 73
Bibliography......Page 79
Index......Page 83