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219807757
Natural Deduction in Monadic Predicate Logic: Workbook 5 Extra Full Edition (Logic Self-Taught Workbooks)
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Elementas #:
219807757
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- Like personal trainers, the Workbooks offer a practical and empathic approach to introductory logic. They are designed for beginners and for anyone who wants to build confidence by doing more exercises. Workbook 5 presupposes your mastery of a Fitch-style natural deduction system with 11 propositional-connective inference rules (Workbook 3, Full or Extra Full Edition). Workbook 5 (Extra Full Edition) helps you learn how to:do proofs in monadic predicate logic by means of 4 quantifier inference rules (introduction and elimination rules for each quantifier)do proofs by means of quantifier replacement rulesdo proofs of theorems in monadic predicate logicdo proofs of invalidity using the finite-universe methoduse natural deduction as aid in more complex symbolizations.Each inference and replacement rule is introduced through numerous exercises. There are a variety of rule-application exercises, baby-proof exercises, and proof exercises. Their difficulty increases gradually. The point is to train your logic muscles until they become strong enough to carry heavy-weight content. Visual metaphors help to navigate even multiple subderivations. The study is aided by many examples worked out step by step, warnings of common errors, as well as complete solutions to all exercises.The Extra Full Edition includes more exercises than the Full Edition. Its two supplementary units aid in transitioning to the application of propositional connective (inference and replacement) rules in predicate logic.Workbook 5 focuses exclusively on monadic predicate logic. Workbook 6 considers the more general relational predicate logic. Whenever I use the term ‘predicate logic’ without a qualifier, I mean monadic predicate logic. I use the term ‘quantifier logic’ for the more general relational predicate logic.Various textbooks introduce restrictions on UG and EI in different ways. The rules presented here are modeled on those presented in the classic work by F.B. Fitch Symbolic Logic (1952). We follow Fitch in constructing subderivations (chambers) for both rules, which helps keep track of the restrictions. We must just make sure that (1) each chamber is assigned a unique arbitrary individual and (2) arbitrary individuals do not leave their chambers.Logic Self-Taught Workbooks are based on the insight that understanding logic is not sufficient for learning logic, just as understanding how to swim is not sufficient for learning to swim, and understanding the grammar of a foreign language is not sufficient for learning the language. You need to practice and take an active part in self-teaching. Through systematic work with the Workbooks, you will build self-confidence. You can learn logic, even its hardest parts.Contents:Unit 5.1 Inference Rules for Propositional Connectives in Monadic Predicate LogicUnit 5.2 Universal Instantiation and Existential GeneralizationInstances of GeneralizationsUniversal InstantiationExistential GeneralizationUnit 5.3 Universal GeneralizationOn Arbitrary Individuals and Their ChambersMore Proofs: Chambers in SubderivationsUnit 5.4 Existential InstantiationUnit 5.5 Logical Equivalence, Theorems, InvalidityUnit 5.6 Replacement RulesPropositional Connective Replacement RulesQuantifier Negation Replacement Rules (QN)Categorical Quantifier Negation Replacement Rules (CQN)Unit 5.7 More Complex SymbolizationsUnit 5.A Inference Rules for Propositional Connectives in Predicate LogicUnit 5.B Propositional Connective Replacement Rules in Predicate LogicSolutions to Exercises
| Publisher | Independently published |
| Publication date | 11 Mar. 2024 |
| Language | English |
| Print length | 424 pages |
| ISBN-13 | 979-8884328853 |
| Item weight | 1.2 kg |
| Dimensions | 21.59 x 2.44 x 27.94 cm |
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