| Description |
1 online resource |
| Series |
Lecture notes in logic ; 7 |
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Lecture notes in logic ; 7.
|
| Contents |
Cover; Half-title ; Series information ; Title page ; Copyright information ; Table of contents ; INTRODUCTION; Some history; What is a logic?; Outline of the contents; Acknowledgements; Note to the second edition (2009); CHAPTER 1 GENERALITIES ON ABSTRACT LOGICS AND SENTENTIAL LOGICS; Algebras; Formulas, equations, interpretations; Matrices; Abstract logics; Logical congruences; Bilogical morphisms and logical quotients; Sentential logics; S-filters and S-matrices; The classes Alg* S and K[sub(S)] ; CHAPTER 2 ABSTRACT LOGICS AS MODELS OF SENTENTIAL LOGICS; 2.1. Models and full models |
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2.2. S-algebras2.3. The lattice of full models over an algebra; 2.4. Full models and metalogical properties; The congruence property; The Property of Conjunction; The Deduction-Detachment Theorem; The Property of Disjunction; The two forms of Reductio ad Absurdum; Some rules of introduction of modality; CHAPTER 3 APPLICATIONS TO PROTOALGEBRAIC AND ALGEBRAIZABLE LOGICS; CHAPTER 4 ABSTRACT LOGICS AS MODELS OF GENTZEN SYSTEMS; 4.1. Gentzen systems and their models; 4.2. Selfextensional logics with Conjunction; 4.3. Selfextensional logics having the Deduction Theorem |
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CHAPTER 5 APPLICATIONS TO PARTICULAR SENTENTIAL LOGICS5.1. Some non-protoalgebraic logics; 5.1.1. CPC[sub(wedge, vee)], the {wedge, vee}-fragment of Classical Logic ; 5.1.2. The logic of lattices; 5.1.3. Belnap's four-valued logic, and other related logics; 5.1.4. The implication-less fragment of IPC and its extensions; 5.2. Some Fregean algebraizable logics; 5.2.1. Alternative Gentzen systems adequate for IPC[sub(rightarrow)] not having the full Deduction Theorem; 5.3. Some modal logics; 5.3.1. A logic without a strongly adequate Gentzen system; 5.4. Other miscellaneous examples |
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5.4.1. Two relevance logics5.4.2. Sette's paraconsistent logic; 5.4.3. Tetravalent modal logic; 5.4.4. Logics related to cardinality restrictions in the Deduction Theorem; Bibliography ; Symbol Index ; General Index |
| Summary |
An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group |
| Notes |
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the seventh publication in the Lecture Notes in Logic series, Font and Jansana develop a very general approach to the algebraization of sentential logics and present its results on a number of particular logics. The authors compare their approach, which uses abstract logics, to the classical approach based on logical matrices and the equational consequence developed by Blok, Czelakowski, Pigozzi and others. This monograph presents a systematized account of some of the work on the algebraic study of sentential logics carried out by the logic group in Barcelona in the 1970s |
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Online resource; title from PDF title page (EBSCO, viewed April 18, 2017) |
| Subject |
Algebraic logic.
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MATHEMATICS -- General.
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Lógica algebraica
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Algebraic logic
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| Form |
Electronic book
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| Author |
Jansana, Ramon, author
|
| ISBN |
9781316754733 |
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1316754731 |
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9781316716915 |
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1316716910 |
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9781316748947 |
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1316748944 |
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1316752801 |
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9781316752807 |
|
