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Systems of Formal Logic

The present work constitutes an effort to approach the subject of symbol­ ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela­ tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of...

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Bibliographic Details
Main Author: Hackstaff, L.H.
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1966, 1966
Edition:1st ed. 1966
Subjects:
Logic
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 4.2 The Bases of the System PND
  • 4.3 Proof and Derivation Techniques in PND
  • 4.4 Rules of Formation of PND
  • 4.5 The Structure of Proofs in PND
  • 4.6 Rules of Transformation of PND
  • 4.7 Proofs and Theorems of the System PND
  • 4.8 Theorems of the Full System PND
  • 4.9 A Decision Procedure for the System PND
  • 4.10 A Reduction of PND
  • 5 The Consistency and Completeness of Formal Systems
  • 5.1 Summary
  • 5.2 The Consistency of PLT’
  • 5.3 The Completeness of PLT’
  • 5.4 Metatheorems on P+
  • 6 Some Non-Standard Systems of Propositional Logic
  • 6.1 Summary
  • 6.2 What is a Non-Standard System?
  • 6.3 The Intuitionistic System and the Fitch Calculus (PI and PF)
  • 6.4 Rules of Formation of PI
  • 6.5 Rules of Transformation of PI
  • 6.6 Axioms of PI
  • 6.7 Definitions of PI
  • 6.8 Deductions in PI
  • 6.9 The Propositional Logic of F.B.Fitch
  • 6.10 The Johansson Minimum Calculus
  • 7 The Lower Functional Calculus
  • 7.1 Summary and Remarks
  • 1 Introduction: Some Concepts and Definitions
  • 1.0 Arguments and Argument Forms
  • 1.1 Symbolic Logic and its Precursors
  • 1.2 Symbolization
  • 1.3 Logical Functors and Their Definitions
  • 1.4 Tests of Validity Using Truth-tables
  • 1.5 Proof and Derivation
  • 1.6 The Axiomatic Method
  • 1.7 Interpreted and Uninterpreted Systems
  • 1.8 The Hierarchy of Logical Systems
  • 1.9 The Systems of the Present Book
  • 1.10 Abbreviations
  • 2 The System P+
  • 2.1 Summary
  • 2.2 Rules of Formation of P+
  • 2.3 Rules of Transformation of P+
  • 2.4 Axioms of P+
  • 2.5 Definitions of P+
  • 2.6 Deductions in P+
  • 3 Standard Systems with Negation (PLT, PLT’, PLTF, PPM)
  • 3.1 Summary
  • 3.2 Rules of Formation of PLT
  • 3.3 Rules of Transformation of PLT
  • 3.4 Axioms of PLT
  • 3.5 Definitions of PLT
  • 3.6 Deductions in PLT
  • 3.7 The Deduction Theorem
  • 3.8 The System PLT’
  • 3.9 Independence of Functors and Axioms
  • 4 The System PND. Systems of Natural Deduction
  • 4.1 Summary
  • 7.2 Rules of Formation of LFLT’
  • 7.3 Transformation of LFLT’
  • 7.4 Axioms of LFLT’
  • 7.5 Definitions of LFLT’
  • 7.6 Some Applications and Illustrations
  • 7.7 Rules of Transformation of LFLT’
  • 7.8 Axioms of LFLT’
  • 7.9 The Propositional Calculus and LFLT’
  • 7.10 Deductions in LFLT’
  • 8 An Extension of LFLT’ and Some Theorems of the Higher Functional System. The Calculus of Classes
  • 8.1 Summary and Modification of the Formation Rules of LFLT’
  • 8.2 The Lower Functional Calculus with Identity
  • 8.3 Quantification over Predicate Variables. The System 2FLT’=
  • 8.4 Abstraction and the Boolean Algebra
  • 8.5 The Boolean Algebra and Propositional Logic
  • 9 The Logical Paradoxes
  • 9.1 Self Membership
  • 9.2 The Russell Paradox
  • 9.3 Order Distinctions, Levels of Language, and the Semantic Paradoxes
  • 9.4 The Consistency of LFLT’
  • 9.5 The Decision Problem
  • 9.6 Consistency and Decision in Higher Functional Systems
  • 10 Non-Standard Functional Systems
  • 10.1 Summary
  • 10.2 Intuitionistic and Johansson Functional Logics
  • 10.3 The Fitch Functional Calculus of the First Order with Identity (LFFF=)

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