Tarski's World: Revised and Expanded

Dave Barker-Plummer, Jon Barwise and John Etchemendy in collaboration with Albert Liu

Tarski's World is an innovative and enjoyable way to introduce students to the language of first-order logic. Using this courseware package, students quickly master the meaning of the connectives and quantifiers and soon become fluent in the symbolic language at the core of modern logic.

The Tarski's World program allows the students to build three-dimensional worlds and to describe them in first-order logic. Students evaluate sentences within the constructed worlds and, if an evaluation is incorrect, the program provides them with a game that leads them to understand where they went wrong.

The Tarski's World program can be used in the various ways in which we learn a new language. In addition to translating back and forth from English, we can directly describe worlds, use the language to identify objects, construct worlds satisfying a description, and so forth.

The package contains over one-hundred exercises from very basic to highly sophisticated. For the first time, with this edition, students have access to an Internet-based grading service called the Grade Grinder. Solutions to many exercises may be submitted to the Grade Grinder for assessment and the results are returned to the student, and optionally the instructor, by email. This innovative service provides students with accurate and timely feedback on their work whenever they need it, day or night. A web-based interface allows instructors to manage assignments and grades for their classes.

This new edition of Tarski's World includes software for Windows, Macintosh and Linux operating systems.

Tarski's World is intended as a supplement to a standard logic text, or for use by anyone who wants to learn the language of first-order logic.

Praise for earlier editions of Tarski's World:

“Together the manual and program offer an excellent introduction to the syntax and semantics of logical notation.” – George Boolos, Journal of Symbolic Logic

“I heartily recommend Tarski's World and Turing's World…. Without a doubt logic instruction needs more programs like these.” – James Moore, Teaching Philosophy

“The authors are pioneers. [Tarski's World] is the only program that I know for teaching first-order semantics, and it sets a high standard. I warmly recommend it.” – Wilfrid Hodges, Queen Mary College

Dave Barker-Plummer is senior research scientist with the Openproof Project at CSLI. The late Jon Barwise was professor of philosophy, mathematics, and computer science at Indiana University and one of the founding members of CSLI. John Etchemendy is professor of philosophy and symbolic systems at Stanford University and a former director of CSLI. Albert Liu is a software developer at CSLI.

More information on this courseware can be found at https://www.gradegrinder.net/Products/tw-index.html.

How to Use This Book xi
To the student xii
To the instructor xiii
Acknowledgements xv
What's new in this edition? xv
More acknowledgements xvi
I Exercises
1 Instructions About the Exercises 3
2 Exercises on Propositional Logic 9
3 Exercises on First-order Logic 25
4 More Theoretical Exercises 53
II Using the Software
5 Using Tarski's World 67
- 5.1 Getting started 67
  - 5.1.1 Opening saved files 68
  - 5.1.2 Starting new files 68
  - 5.1.3 Saving a file 68
  - 5.1.4 Closing Tabs 69
  - 5.1.5 Reverting a File 69
  - 5.1.6 Printing 70
  - 5.1.7 Quitting (Exiting) Tarski's World 70
- 5.2 The World Panel 70
  - 5.2.1 Adding blocks 70
  - 5.2.2 Selecting blocks 70
  - 5.2.3 Moving blocks 70
  - 5.2.4 Sizing and shaping blocks 70
  - 5.2.5 Naming blocks 71
  - 5.2.6 Deleting blocks 71
  - 5.2.7 Cutting, copying, and pasting blocks 71
  - 5.2.8 Hiding labels 72
  - 5.2.9 2-D view 72
  - 5.2.10 Rotating Worlds 72
- 5.3 The Sentence Panel 72
  - 5.3.1 Writing formulas 72
  - 5.3.2 Commenting your sentences 73
  - 5.3.3 Creating a list of sentences 73
  - 5.3.4 Moving from sentence to sentence 73
  - 5.3.5 Deleting sentences 74
  - 5.3.6 Typing symbols from the keyboard 74
  - 5.3.7 Cutting, copying, and pasting 75
- 5.4 Verifying syntax and truth 75
- 5.5 Playing the game 76
  - 5.5.1 Picking blocks and sentences 76
  - 5.5.2 Backing up and giving up 76
  - 5.5.3 When to play the game 77
- 5.6 Preferences 78
6 Using Submit 81
- 6.1 Getting started 81
- 6.2 Choosing files to submit 83
- 6.3 How you know your files were received
Appendixes
A First-order Logic 89
- A.1 First-order languages 89
- A.2 Individual constants 90
- A.3 Predicate symbols 90
- A.4 Atomic sentences 91
- A.5 Connectives 92
- A.6 Variables 95
- A.7 Atomic wffs 96
- A.8 Quantifiers 96
- A.9 Wffs and sentences 97
- A.10 Satisfaction and truth 100
- A.11 Game rules 101
- A.12 Logical equivalences 103
- A.13 Validity and logical consequence 104
B Using Tarski's World 5.x 107
- B.1 Getting started 107
  - B.1.1 Launching Tarski's World 107
  - B.1.2 The main windows 107
  - B.1.3 Opening saved files 109
  - B.1.4 Starting new files 110
  - B.1.5 Saving a file 110
  - B.1.6 Quitting (Exiting) Tarski's World 110
- B.2 The world window 111
  - B.2.1 Adding blocks 111
  - B.2.2 Naming blocks 111
  - B.2.3 Moving blocks 111
  - B.2.4 Sizing and shaping blocks 112
  - B.2.5 Deleting blocks 112
  - B.2.6 Hiding labels 112
  - B.2.7 2-D view 112
  - B.2.8 Rotating Worlds 113
- B.3 The keyboard and sentence windows 113
  - B.3.1 Writing formulas 113
  - B.3.2 Commenting your sentences 114
  - B.3.3 Creating a list of sentences 114
  - B.3.4 Moving from sentence to sentence 114
  - B.3.5 Deleting sentences 115
  - B.3.6 Typing symbols from the keyboard 115
  - B.3.7 Cutting, copying, and pasting 116
  - B.3.8 Printing 116
- B.4 The evaluation box / sentence inspector 116
  - B.4.1 Verifying syntax and truth 116
- B.5 Playing the game 117
  - B.5.1 Picking blocks and sentences 118
  - B.5.2 Backing up and giving up 118
  - B.5.3 When to play the game 119
General Index 121
File Index 125

1/1/2008

Tarski's World: Revised and Expanded

Contents