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language fol itself, these two methods, the method of proof and the method
of counterexample, form the principal subject matter of this book.

Essential instructions about homework exercises

This book came packaged with software that you must have to use the book.
In the software package, you will ¬nd a CD-ROM containing four computer
applications”Tarski™s World, Fitch, Boole and Submit”and a manual that Tarski™s World, Fitch,
Boole and Submit
explains how to use them. If you do not have the complete package, you will
not be able to do many of the exercises or follow many of the examples used in
the book. The CD-ROM also contains an electronic copy of the book, in case
you prefer reading it on your computer. When you buy the package, you also
get access to the Grade Grinder, an Internet grading service that can check the Grade Grinder
whether your homework is correct.
About half of the exercises in the ¬rst two parts of the book will be com-
pleted using the software on the CD-ROM. These exercises typically require
that you create a ¬le or ¬les using Tarski™s World, Fitch or Boole, and then
submit these solution ¬les using the program Submit. When you do this, your
solutions are not submitted directly to your instructor, but rather to our grad-

Essential instructions about homework exercises
6 / Introduction

ing server, the Grade Grinder, which assesses your ¬les and sends a report to
both you and your instructor. (If you are not using this book as a part of a
formal class, you can have the reports sent just to you.)
Exercises in the book are numbered n.m, where n is the number of the
chapter and m is the number of the exercise in that chapter. Exercises whose
solutions consist of one or more ¬les that you are to submit to the Grade
‚ vs.  Grinder are indicated with an arrow (‚), so that you know the solutions are
to be sent o¬ into the Internet ether. Exercises whose solutions are to be
turned in (on paper) to your instructor are indicated with a pencil (). For
example, Exercises 36 and 37 in Chapter 6 might look like this:
6.36 Use Tarski™s World to build a world in which the following sentences
‚ are all true. . . .
6.37 Turn in an informal proof that the following argument is logically
 valid. . . .
The arrow on Exercise 6.36 tells you that the world you create using
Tarski™s World is to be submitted electronically, and that there is nothing
else to turn in. The pencil on Exercise 6.37 tells you that your solution should
be turned in directly to your instructor, on paper.
Some exercises ask you to turn in something to your instructor in addition
to submitting a ¬le electronically. These are indicated with both an arrow and
a pencil (‚|). This is also used when the exercise may require a ¬le to be
submitted, but may not, depending on the solution. For example, the next
problem in Chapter 6 might ask:
6.38 Is the following argument valid? If so, use Fitch to construct a formal
‚| proof of its validity. If not, explain why it is invalid and turn in your
explanation to your instructor.

Here, we can™t tell you de¬nitely whether you™ll be submitting a ¬le or
turning something in without giving away an important part of the exercise,
so we mark the exercise with both symbols.
By the way, in giving instructions in the exercises, we will reserve the word
“submit” for electronic submission, using the Submit program. We use “turn
submitting vs. turning
in exercises in” when you are to turn in the solution to your instructor.
When you create ¬les to be submitted to the Grade Grinder, it is important
that you name them correctly. Sometimes we will tell you what to name the
¬les, but more often we expect you to follow a few standard conventions. Our
naming conventions are simple. If you are creating a proof using Fitch, then
naming solution ¬les
you should name the ¬le Proof n.m, where n.m is the number of the exercise. If
you are creating a world or sentence ¬le in Tarski™s World, then you should call

Essential instructions about homework exercises / 7

it either World n.m or Sentences n.m, where n.m is the number of the exercise.
Finally, if you are creating a truth table using Boole, you should name it
Table n.m. The key thing is to get the right exercise number in the name,
since otherwise your solution will be graded incorrectly. We™ll remind you of
these naming conventions a few times, but after that you™re on your own.
When an exercise asks you to construct a formal proof using Fitch, you
will ¬nd a ¬le on your disk called Exercise n.m. This ¬le contains the proof set starting proofs
up, so you should open it and construct your solution in this ¬le. This is a lot
easier for you and also guarantees that the Grade Grinder will know which
exercise you are solving. So make sure you always start with the packaged
Exercise ¬le when you create your solution.
Exercises may also have from one to three stars ( , , ), as a rough stars
indication of the di¬culty of the problem. For example, this would be an
exercise that is a little more di¬cult than average (and whose solution you
turn in to your instructor):
6.39 Design a ¬rst-order language that allows you to express the following
 English sentences. . . .


1. The arrow (‚) means that you submit your solution electronically.

2. The pencil () means that you turn in your solution to your instruc-

3. The combination (‚|) means that your solution may be either a
submitted ¬le or something to turn in, or possibly both.

4. Stars ( , , ) indicate exercises that are more di¬cult than average.

5. Unless otherwise instructed, name your ¬les Proof n.m, World n.m,
Sentences n.m, or Table n.m, where n.m is the number of the exercise.

6. When using Fitch to construct Proof n.m, start with the exercise ¬le
Exercise n.m, which contains the problem setup.

Throughout the book, you will ¬nd a special kind of exercise that we
call You try it exercises. These appear as part of the text rather than in You try it sections
the exercise sections because they are particularly important. They either
illustrate important points about logic that you will need to understand later
or teach you some basic operations involving one of the computer programs

Essential instructions about homework exercises
8 / Introduction

that came with your book. Because of this, you shouldn™t skip any of the You
try it sections. Do these exercises as soon as you come to them, if you are in
the vicinity of a computer. If you aren™t in the vicinity of a computer, come
back and do them as soon as you are.
Here™s your ¬rst You try it exercise. Make sure you actually do it, right
now if possible. It will teach you how to use Submit to send ¬les to the Grade
Grinder, a skill you de¬nitely want to learn. You will need to know your email
address, your instructor™s name and email address, and your Book ID number
before you can do the exercise. If you don™t know any of these, talk to your
instructor ¬rst. Your computer must be connected to the internet to submit
¬les. If it™s not, use a public computer at your school or at a public library.

You try it

1. We™re going to step you through the process of submitting a ¬le to the
Grade Grinder. The ¬le is called World Submit Me 1. It is a Tarski™s World
¬le, but you won™t have to open it using Tarski™s World in order to sub-
mit it. We™ll pretend that it is an exercise ¬le that you™ve created while
doing your homework, and now you™re ready to submit it. More complete
instructions on running Submit are contained in the instruction manual
that came with the software.

2. Find the program Submit on the CD-ROM that came with your book.
Submit has a blue and yellow icon and appears inside a folder called Sub-
mit Folder. Once you™ve found it, double-click on the icon to launch the

3. After a moment, you will see the main Submit window, which has a rotat-
ing cube in the upper-left corner. The ¬rst thing you should do is ¬ll in the
requested information in the ¬ve ¬elds. Enter your Book ID ¬rst, then your
name and email address. You have to use your complete email address”
for example, claire@cs.nevada-state.edu, not just claire or claire@cs”since
the Grade Grinder will need the full address to send its response back to
you. Also, if you have more than one email address, you have to use the
same one every time you submit ¬les, since your email address and Book ID
together are how Grade Grinder will know that it is really you submitting
¬les. Finally, ¬ll in your instructor™s name and complete email address. Be
very careful to enter the correct and complete email addresses!

Essential instructions about homework exercises / 9

4. If you are working on your own computer, you might want to save the
information you™ve just entered on your hard disk so that you won™t have
to enter it by hand each time. You can do this by choosing Save As. . .
from the File menu. This will save all the information except the Book ID
in a ¬le called Submit User Data. Later, you can launch Submit by double-
clicking on this ¬le, and the information will already be entered when the
program starts up.

5. We™re now ready to specify the ¬le to submit. Click on the button Choose
Files To Submit in the lower-left corner. This opens a window showing
two ¬le lists. The list on the left shows ¬les on your computer”currently,
the ones inside the Submit Folder”while the one on the right (which is
currently empty) will list ¬les you want to submit. We need to locate the
¬le World Submit Me 1 on the left and copy it over to the right.
The ¬le World Submit Me 1 is located in the Tarski™s World exercise ¬les
folder. To ¬nd this folder you will have to navigate among folders until it
appears in the ¬le list on the left. Start by clicking once on the Submit
Folder button above the left-hand list. A menu will appear and you can
then move up to higher folders by choosing their names (the higher folders
appear lower on this menu). Move to the next folder up from the Submit
Folder, which should be called LPL Software. When you choose this folder,
the list of ¬les will change. On the new list, ¬nd the folder Tarski™s World
Folder and double-click on its name to see the contents of the folder. The
list will again change and you should now be able to see the folder TW Exer-
cise Files. Double-click on this folder and the ¬le list will show the contents
of this folder. Toward the bottom of the list (you will have to scroll down
the list by clicking on the scroll buttons), you will ¬nd World Submit Me
1. Double-click on this ¬le and its name will move to the list on the right.

6. When you have successfully gotten the ¬le World Submit Me 1 on the right-
hand list, click the Done button underneath the list. This should bring you
back to the original Submit window, only now the ¬le you want to submit
appears in the list of ¬les. (Macintosh users can get to this point quickly by
dragging the ¬les they want to submit onto the Submit icon in the Finder.
This will launch Submit and put those ¬les in the submission list. If you
drag a folder of ¬les, it will put all the ¬les in the folder onto the list.)

7. When you have the correct ¬le on the submission list, click on the Sub-
mit Files button under this list. Submit will ask you to con¬rm that you
want to submit World Submit Me 1, and whether you want to send the

Essential instructions about homework exercises
10 / Introduction

results just to you or also to your instructor. In this case, select Just Me.
When you are submitting ¬nished homework exercises, you should select
Instructor Too. Once you™ve chosen who the results should go to, click
the Proceed button and your submission will be sent. (With real home-
work, you can always do a trial submission to see if you got the answers
right, asking that the results be sent just to you. When you are satis¬ed
with your solutions, submit the ¬les again, asking that the results be sent
to the instructor too. But don™t forget the second submission!)

8. In a moment, you will get a dialog box that will tell you if your submission
has been successful. If so, it will give you a “receipt” message that you can
save, if you like. If you do not get this receipt, then your submission has
not gone through and you will have to try again.

9. A few minutes after the Grade Grinder receives your ¬le, you should get
an email message saying that it has been received. If this were a real home-
work exercise, it would also tell you if the Grade Grinder found any errors
in your homework solutions. You won™t get an email report if you put in
the wrong, or a misspelled, email address. If you don™t get a report, try
submitting again with the right address.

10. When you are done, choose Quit from the File menu. Congratulations on
submitting your ¬rst ¬le.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Congratulations
Here™s an important thing for you to know: when you submit ¬les to the
Grade Grinder, Submit sends a copy of the ¬les. The original ¬les are still
what gets sent
on the disk where you originally saved them. If you saved them on a public
computer, it is best not to leave them lying around. Put them on a ¬‚oppy disk
that you can take with you, and delete any copies from the public computer™s
hard disk.

To the instructor

Students, you may skip this section. It is a personal note from us, the authors,
to instructors planning to use this package in their logic courses.

Practical matters
We use the Language, Proof and Logic package (LPL) in two very di¬erent
sorts of courses. One is a ¬rst course in logic for undergraduates with no
previous background in logic, philosophy, mathematics, or computer science.

To the instructor / 11


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