You need the slash (/) to separate sentences from justifications. A justification is typically one or more line numbers, followed by a rule name.

The rule names are very simple in The Logic Book and in the program. The natural deduction system uses the connective followed by "i" or "e" (or "I" or "E") for "introduction" or "elimination" respectively. So ">I" is Conditional Introduction, "vE" is Disjunction Elimination, "Vi" is Universal Introduction, and so on. Primary assumptions in the derivation are justified with a "P", and auxiliary assumptions in a subderivation are justified with "A".

Often the user can enter much less than the full input string above. Often all you need to type is a slash and a rule name, or a slash, a line number or two, and a rule name. Both programs will try to generate from the line numbers you cite the sentence that would be produced by applying the rule that you cite. Bertie3 "templates" can be generated by typing in nothing more than a slash and a rule name, though if you see one or two sentences that would be useful in generating the target sentence using the rule you have in mind, it is a good idea to cite them. Those cited sentences will be incorporated into the template.

Some Examples of Using Bertie3

Let’s suppose you just want to practice some derivations using the problem sets which come with Bertie. Start the program by double-clicking the MS-DOS shortcut in the program folder (default is c:\Logic). After getting past the title screen hit ALT-P to get the Problem menu. Choose Get next. You will be given a choice of problem sets to load, choose Beginning sentential derivations. You will see a derivation with two primary assumptions listed at top, a goal sentence at bottom, and all the normal scope lines; your cursor is just to the right of the goal sentence. Let’s suppose you want to pursue a goal-analysis (bottom-up) approach—later we’ll look at top-down (hitting Page UP or Page Down keys will switch you between bottom-up and top-down).

Looking at this goal sentence and the primary assumptions, it’s pretty obvious your last step will be an application of ^I. But you don’t know what the numbers of the lines will be, so just type /^i Hit enter. (the slash is always used before a justification). Bertie will insert the justification, and insert the appropriate sub-goals with lower-case letters instead of line numbers; your cursor is now at the lower sub-goal. This sentence obviously comes from 2 by ^E. So type /2 ^e Hit enter. Bertie inserts the justification. Use your arrow key to move up to the other subgoal. Now this will clearly be gotten by ^E from D ^ K so type /^e Hit enter. Bertie inserts an appropriate conjunction as sub-goal (with K as one conjunct and «A» as a metavariable for the unknown other conjunct). Normally you’d just backspace over the metavariable and type in the appropriate other conjunct, but in this case the conjunction is in the wrong order, so backspace across the whole thing and then type D^K/1^e Hit enter. In many cases you can leave out the spaces (but not when citing two line numbers). Bertie will insert the line and its justification, and, since you have linked the bottom to the top, it will complete the derivation by inserting the appropriate line numbers to the left and in the justifications. The bottom line of the screen will congratulate you. To move on to the next problem hit any key and press enter.

Let’s try this one top-down. As before, you start at bottom at the goal-sentence. Hit Page Up to get into top-down mode. You are now in line 3 just under the primary assumptions. You’ll want to start a sub-derivation. Type L/a Hit enter. The ‘a’ is to tell Bertie you are making an assumption for a subderivation. Bertie will insert the proper scope line for the subderivation. Your next step is >E from 1 and 3. You could type J /1 3 >e, but since there is only one possible result of applying that rule to those lines, you can get away with typing just /1 3 >e Hit enter. Repeat this for /2 4 >e Hit enter. You are now done with your subderivation, but you have to end (discharge) it, so type dis (for ‘discharge’. Hit enter (I’ll stop saying that now). You are now back out on the main scope line, ready to cite the whole subderivation for >I. I want you to make a mistake here. Type L^A/3-5>i Bertie will tell you you’ve attempted a “Misapplication of rule”. You do not need to retype the whole line. Just use your arrow keys to go back and delete the ^ replacing it with a >. You’re done.

Here are some further issues.

If you want to skip ahead in the series of problems (they get harder as you go along), instead of selecting Get next from the Problem menu, select Pro n. Bertie will then ask you for a number and take you to that number problem in the problem set. Or type pro n on an empty line to go to problem n. This is useful if you have already done some of the problems, and you want to start where you left off.

If you hit ALT-H you get the Hints menu (heLp menu is ALT-L). This will allow you to get a hint at the bottom of the screen (up to three), see the next few lines of the stored solution, or (Uncle!) see the whole solution. Alternatively, you can type hint line n, or uncle on an empty derivation line. This will not work on homework problems or sample problems you input. We’ll look at these in a minute.

Sometimes, especially if you’re moving between bottom-up and top-down approaches, you may find that you have a lettered-line (part of a goal-analysis template) which matches one of the numbered lines above. You can link the two by using the arrow keys to get the cursor onto the lettered-line, hitting the Home key twice, and entering the line number it matches. Bertie will rewrite the derivation, compressing the lines.

Let’s suppose you want to do some exercises out of the book. Hit ALT-P choose New or type new on a blank line. You will see a main scope line with no primary assumptions and no goal sentence. The cursor is at bottom of screen. Simply type in your goal sentence and hit enter. The cursor now appears at line 1 of the derivation. If there are primary assumptions, then type the first on line 1 with /p as your justification (‘p’ for primary assumption). Repeat with any other primary assumptions. Once you get all the primary assumptions in, you can proceed as before doing bottom-up or top-down.

How can I use this thing to do/submit my homework? First you will have to enter each homework problem as described in the previous paragraph. Then you can do the problem in Bertie. There are then a number of ways you can submit your work.

1. Hand-copy each derivation after you complete it.

2. Print each derivation after you complete it. When you are done with a derivation, instead of choosing Get next or New choose File | Print. After some prompts, this should print out the derivation you just finished. Then you can start a new derivation. I have found that this feature works in my office, but not at home—something about how the printers are configured—so I can’t guarantee this will work.

3. Save each derivation after you complete it, for later printing or emailing. When you are done with the first derivation, instead of choosing Get next or New choose File | Save. Tell Bertie y you do want to continue. Bertie will ask you for a drive letter. You’ll probably want to choose the same drive you installed Bertie on (usually c), if you do, then the file will be saved in the same directory you installed to. So let’s assume you installed in the default directory, and you tell Bertie the c drive. Bertie next asks for a file name, I suggest your initials then ‘hw’ and then 2, or 3, etc. and then ‘.txt’; so for me that would be pghw2.txt Read the message and then tell Bertie y Bertie will ask you for a title. This title will appear in the text file just above the derivation you are saving, so I suggest you use the title to say which problem it is. E.g., 5.4E #1b The save file you specify will be used for all other saves during that Bertie session, but you will need to choose File | Save and specify a title for that derivation each time you complete a derivation. If you quit Bertie before finishing your homework, then the next time you use Bertie you can specify the same file name and Bertie will append your new derivations to the old ones. Having completed your derivations and quit Bertie, you can open the text file in any text editor and print it out. Alternatively you could either include it in or attach it to an email to me.

HELP!?

As always, feel free to use my office hours, make an appointment, or email me.

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