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General Algebraic Semantics for Sentential Logics 2nd Revised edition [Hardback]

(Universitat de Barcelona), (Universitat de Barcelona)
  • Formāts: Hardback, 158 pages, height x width x depth: 235x157x17 mm, weight: 390 g
  • Sērija : Lecture Notes in Logic
  • Izdošanas datums: 02-Mar-2017
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1107167973
  • ISBN-13: 9781107167971
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General Algebraic Semantics for Sentential Logics 2nd Revised editionPalielināt
  • Formāts: Hardback, 158 pages, height x width x depth: 235x157x17 mm, weight: 390 g
  • Sērija : Lecture Notes in Logic
  • Izdošanas datums: 02-Mar-2017
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1107167973
  • ISBN-13: 9781107167971
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781107167971.html
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.

Papildus informācija

An exposition of the approach to the algebraization of sentential logics developed by the Barcelona logic group.
Introduction 1(14)
Chapter 1 Generalities on abstract logics and sentential logics
15(16)
Chapter 2 Abstract logics as models of sentential logics
31(28)
2.1 Models and full models
31(5)
2.2 S-algebras
36(4)
2.3 The lattice of full models over an algebra
40(5)
2.4 Full models and metalogical properties
45(14)
Chapter 3 Applications to protoalgebraic and algebraizable logics
59(16)
Chapter 4 Abstract logics as models of Gentzen systems
75(30)
4.1 Gentzen systems and their models
76(10)
4.2 Selfextensional logics with Conjunction
86(9)
4.3 Selfextensional logics having the Deduction Theorem
95(10)
Chapter 5 Applications to particular sentential logics
105(26)
5.1 Some non-protoalgebraic logics
107(7)
5.1.1 CPCΛΛ, the {Λ, Λ}-fragment of Classical Logic
107(3)
5.1.2 The logic of lattices
110(1)
5.1.3 Belnap's four-valued logic, and other related logics
111(2)
5.1.4 The implication-less fragment of IPC and its extensions
113(1)
5.2 Some Fregean algebraizable logics
114(3)
5.2.1 Alternative Gentzen systems adequate for IPC→ not having the full Deduction Theorem
116(1)
5.3 Some modal logics
117(4)
5.3.1 A logic without a strongly adequate Gentzen system
121(1)
5.4 Other miscellaneous examples
121(10)
5.4.1 Two relevance logics
122(1)
5.4.2 Sette's paraconsistent logic
123(2)
5.4.3 Tetravalent modal logic
125(1)
5.4.4 Cardinality restrictions in the Deduction Theorem
126(5)
Bibliography 131(12)
Symbol index 143(4)
General index 147
Josep Maria Font works in the Department of Probability, Logic and Statistics at the University of Barcelona. Ramon Jansana works in the Department of Logic, History and Philosophy of Science at the University of Barcelona.