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A general algebraic semantics for sentential logics /
An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group.
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2017.
|
| Edición: | Second edition. |
| Colección: | Lecture notes in logic ;
7. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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
- 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
- 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