Boole is an application that makes it easy to construct truth tables. We begin with instructions on how to start and stop Boole, and explain the basic layout of the screen.
- Getting Started
- Writing and editing tables
- Specifying your assessment
- Verifying your table
- Saving or printing your table
The Boole application is contained inside the folder called Boole Folder. When Boole is running, you will see (from top to bottom) the menu bar, a wider, gray “tool bar,” a narrow pink “assessment pane,” and finally a large, mostly blank area for constructing truth tables, called the “table pane.” Here are the basic facts to remember about each of these.
The menusBoole has the following menus:
File: This menu lets you start new truth tables, open existing tables, save tables, and print tables.
Edit: This is the customary edit menu allowing you to cut, copy and paste items in truth tables.
Table: This menu contains commands for adding new columns, for verifying your table, and for generating reference columns automatically.
Window: This menu gives you access to various Boole files you have open.
The strip containing logical symbols and predicates located at the top of the proof window is called the “tool bar.” It is analogous to the Keyboard window in Tarski's World, and very similar to the tool bar in Fitch. Moving your cursor over an item on the tool bar turns it into a button. Clicking on the button enters the symbol or predicate, if the insertion point is located in one of the sentence fields at the top of your table. The portion of the tool bar containing predicates can be scrolled back and forth using the double-arrow buttons on the tool bar.
On the far right of the tool bar are six buttons for use in constructing and checking tables. The function of these buttons is as follows:
Delete Column: This button deletes the sentence column that contains the insertion point. It will delete the sentence at the top of the column and all associated truth value columns under that sentence. You will have a chance to cancel the deletion after you click the button.
Build Reference Columns: This button can be used after you have entered one or more target sentences on the right side of your table. If you choose this button, Boole will automatically create all of the reference columns needed for your table. You should use this feature only if the exercise says that you can, since otherwise the Grade Grinder will complain that you did not create your own reference columns. Learning how to create reference columns is part of what you must master when learning to build truth tables.
Fill Reference Columns: This button fills in the truth values under the reference columns for you. Like the preceding button, you should only use this if the exercise says that you can, since filling in the reference columns is another crucial skill to master in building truth tables.
Verify Row: Clicking this button will verify the correctness and completeness of a single row of your truth table.
Verify Table: Clicking this button will verify the correctness and completeness of your entire table.
Verify Assessment: This button verifies the correctness of your table (as does Verify Table), but also checks to see whether your assessment is correct.
The assessment pane is similar to the goal pane in Fitch. This is where you look to see whether your truth table is correctly constructed. It also contains a button that allows you to assess the target sentence or sentences in your table. When you click the Assessment button, you are presented with a list of possible assessments. For example, if you are asked to determine whether a sentence is a tautology, you can specify whether or not it is. If you are asked to determine whether a sentence is a tautological consequence of other sentences, you can specify this here as well.
The table paneThe large, mostly white area is where you construct truth tables. A thin horizontal line divides the headings of the columns from the truth value columns. A thick vertical line divides the reference columns from the body of the table. When the insertion point is in the heading area, you can enter target sentences on the right or reference sentences on the left. New sentence columns are added using the commands Add Column After or Add Column Before from the Table menu. Once sentences are entered, truth values can be entered in the appropriate places under those sentences.
Adjusting the table paneThe table pane is divided into two parts: the reference columns on the left and the target columns on the right. These are separated by a vertical divider. Often when you open or construct a table, you will not be able to see all of the columns on one or the other side. You can adjust the overall size of your window in the usual way, and you can also change the position of the divider by grabbing it and dragging to the left or right.
Writing and editing tablesThere are three steps in creating a truth table: specifying the target sentence (or sentences), building the reference columns, and filling in the truth values. Once a table is complete, it can be used to assess the logical properties of the target sentences.
Entering target sentencesTo enter a target sentence, the insertion point must be blinking in the upper right section of the table. If it is not, click in this area to place the insertion point where you want it. Then enter the desired sentence using the tool bar or keyboard. To type the logical symbols from the keyboard, refer to the table of keyboard equivalents. Notice that as you enter the sentence, the sentence number above the sentence changes color. If the sentence is ill-formed, the number is red; when it is well-formed, it turns green.
If you are constructing a joint truth table for two or more sentences, you will need to choose Add Column After or Add Column Before from the Table menu to add a new target sentence to your table.
Another way to enter sentences is by copying them from Tarski's World or Fitch and pasting them into the appropriate place in Boole.
Creating reference columnsThere are two ways to create reference columns: you can do it by hand or you can have Boole do the work for you. You should always do the work yourself unless the exercise or your instructor gives you permission to let Boole build the reference columns for you.
To enter a reference sentence, click at the top of the first column to the left of the thick dividing line. Then enter the desired atomic sentence. (Boole will allow you to enter any formula in a reference column. The number above the sentence will be red if the sentence is ill formed and blue if it is not atomic.) To add additional reference sentences, choose Add Column After or Add Column Before from the Table menu, and enter the sentence.
If you want Boole to build the reference columns for you, click on the button Build Ref Cols on the tool bar. This will generate the necessary reference columns for the target sentences currently appearing on the right. If Boole generates the reference columns, they will be numbered =1=, =2=, etc; if you build them, they will be numbered (1), (2), etc.
Filling in truth valuesTo fill in truth values in your table, click in the desired column and type T or F. (You can also type “1” for T and either “0” or “2” for F, if you find this more convenient.) After the letter is entered, the insertion point will move down one row in the same column. If you are working in a column on the right side of the table, Boole will highlight the values elsewhere in the table that the current value depends on. In other words, Boole implements the “two finger” method described in the textbook.
Boole will also fill in truth values in the reference columns of a table automatically, should you so desire. Only do this if the exercise or your instructor says that you can. (The Grade Grinder will complain if you do this without permission.) To fill them in automatically, click Fill Ref Cols on the tool bar.
In its default mode, Boole will fill in values column by column. That is, when you type a T or F, the insertion point will move down one row so that you can fill in the next value in the column. If you prefer filling in your table row by row, choose By Row in the Edit menu. In Row mode, Boole will move the insertion point to the next column after you type a truth value.
Specifying your assessmentTypically you will be asked to use truth tables to determine whether a sentence is a tautology, whether two sentences are tautologically equivalent, or whether a sentence is a tautological consequence of others. Thus after you have constructed your truth table, you will need to specify the relevant assessment of the sentence or sentences in your table. To do this, click on the Assessment button in Boole's assessment pane. This will open a window allowing you to specify your assessment.
Verifying your tableThere are three commands available for verifying portions of your table: Verify Row, Verify Table, and Verify Assessment. These are available both from the Table menu and on the tool bar.
- Verify Row will verify the correctness and completeness of a single row of your truth table. It checks the row that contains the insertion point. If the row has all the necessary reference columns and all the values in the row are filled in, a + will appear next to Complete? in the assessment pane. If the values filled in under the target sentence are correct, a + will appear next to Correct? in the assessment pane.
- Verify Table will verify the correctness and completeness of your entire table. It checks whether you have all the necessary reference columns, whether these contain all the required truth combinations, and finally, whether the values specified under the target sentence are correct. If the table has been completely filled out and the values are all correct, check marks will appear next to Correct? and Complete? in the assessment pane.
- Verify Assessment verifies the correctness of your table (as does Verify Table), but also checks to see whether your assessment is correct. Before it can do this, you must specify an assessment, as described above.
To save your table, choose Save or Save As... from the File menu. If you are submitting a table to the Grade Grinder, you should name it Table n.m, where n.m is the number of the exercise.
To print a table, choose Print from the File menu. When you do this, you will be given the standard print dialog box. Once you have chosen any printer options you want to use, click on the Print button in the dialog box.
