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Logical Reasoning with Diagrams and Sentences

Using Hyperproof

New Edition

The Logical Reasoning with Diagrams and Sentences courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of textbook, desktop, and online materials. This package is sure to be an essential resource in a range of courses incorporating logical reasoning, including formal linguistics, philosophy, mathematics, and computer science.

Unlike traditional formal treatments of reasoning, this package uses both graphical and sentential representations to reflect common situations in everyday reasoning where information is expressed in many forms, such as finding your way to a location using a map and an address. It also teaches students how to construct and check the logical validity of a variety of proofs—of consequence and non-consequence, consistency and inconsistency, and independence—using an intuitive proof system which extends standard proof treatments with sentential, graphical, and heterogeneous inference rules, allowing students to focus on proof content rather than syntactic structure. Building upon the widely used Tarski’s World and Language, Proof and Logic courseware packages, Logical Reasoning with Diagrams and Sentences contains more than three hundred exercises, most of which can be assessed by the Grade Grinder online assessment service; is supported by an extensive website through which students and instructors can access online video lectures by the authors; and allows instructors to create their own exercises and assess their students’ work.

Logical Reasoning with Diagrams and Sentences is an expanded revision of the Hyperproof courseware package.

227 pages | 27 figures | 7 x 10 | © 2016

Lecture Notes

Language and Linguistics: General Language and Linguistics


“Traditional systems of formal logic would have us believe that good reasoning is being good at some sort of game of abstract symbol manipulation. Not so for Hyperproof. Hyperproof not only makes logic symbols come alive by relating them to actual concrete content, but also demonstrates the power and reality of multi-representational human reasoning.”

Bram Van Heuveln, Rensselaer Polytechnic Institute

Table of Contents

About Hyperproof
How to use this book
Acknowledgements (2nd edition)
What’s new in this edition?
Obtaining the software
Instructions about the exercises

I. Basic Concepts

1. Comparing Tarski’s World and Hyperproof
1.1 Worlds and situations
1.2 A new property and relation
1.3 Language differences
1.4 Kleene evaluation
1.5 Proofs

2. Proofs of Consequence and Nonconsequence
2.1 Observe
2.2 Assumptions and subproofs
2.3 Check Truth of the Assumptions (CTA)
2.4 Sentence goals 

3. Sentential Consequence Rules
3.1 Tautological consequence
3.2 First-order consequence
3.3 Analytical consequence

4. Proofs of Consistency and Inconsistency
4.1 Syntactic Close
4.2 Semantic Close
4.3 Consistency goals

II. Diagrammatic Reasoning

5. The Apply Rule
5.1 Apply
5.2 Some situation goals

6. Reasoning by Cases
6.1 Cases Exhaustive
6.2 Merge and Inspect
6.3 Recursive Close 
6.4 Name
6.5 Review exercises

7. Independence Proofs
7.1 Consequence, nonconsequence and independence
7.2 More independent goals
7.3 Constrained independence and consequence
7.4 Some final situation goals
7.5 Review exercises

III. Sentential Reasoning

8. Sentence Connective Rules
8.1 Reiteration
8.2 Conjunction rules
8.3 Disjunction rules
8.4 Negation rules
8.5 Conditional rules
8.6 Bioconditional rules
8.7 Matters of style

9. Quantifier and Identity Rules
9.1 Identity rules
9.2 Existential quantifier rules 
9.3 Universal quantifier rules
9.4 Multiple quantifiers
9.5 Numerical quantifier rules
9.6 Review exercises

10. Axioms and Analytical Consequence
10.1 The axiomatic method
10.2 Axiomatizing shape
10.3 Axiomatizing size
10.4 Location axioms

11. Logic and Observation

A. Summary of Goals

B. Using Hyperproof
B.1 Launching the program
B.2 Editing the situation
B.3 The body of the proof
B.4 Goals
B.5 Copying and pasting
B.6 Printing
B.7 Preferences
B.8 Setting up problems
B.9 Projecting Hyperproof in class

C. Using Submit
C.1 Getting Started
C.2 Choosing files to submit
C.3 How you know your files were received
C.4 Preferences and user data

Index of You Try It Files

Exercise Index

General Index

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