A General Algebraic Semantics for Sentential Logics
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-mat…
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- Full title :A General Algebraic Semantics for Sentential Logics
Summary
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-algebras -- 2.3. 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 LOGICS -- 5.1. 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 logics
5.4.2. 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
An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group
Edition Statements
- Publication Date:2017
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2017
The Physical Object
- Description:1 Online-Ressource (160 Seiten)
Edition Identifiers
- ISBN:9781316748947, 1316748944, 9781107167971, 1107167973
- oclc:on1020859626
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