Socrates User's Guide

# SOCRATES USER'S GUIDE

## Version 0.6.4

### By Robert C. Koons and David V. Newman © 1995

##### Intended for use of students enrolled in Philosophy logic courses at the University of Texas at Austin. Unauthorized use or duplication is prohibited.

1. Introduction
2. Getting Started
1. Starting Socrates
3. Files: Opening, Saving, Closing
4. Navigating through a Table
5. Editing: Cut & Paste, Undo & Redo
6. Logical Moves: The Entry, SC, PC, and MC Menus
7. Annotations: Editing and Removing
8. Appearance: The Font and Size Menus
3. Sentential Logic
1. Entering premises and conclusions
2. Entering sentences of sentential logic
3. The structure of the table: left and right sides
4. The intuitive meanings of the connectives
5. Inference moves in sentential logic
6. Closing paths in sentential logic
2. By bridging open sub-tables
7. Closing the table in sentential logic
8. Open, complete tables in sentential logic
4. Predicate Logic (with Identity)
1. Entering sentences of predicate logic
2. The intuitive meanings of the quantifiers
3. Inference moves in predicate logic
4. Closing paths and closing the table in predicate logic
5. Identity
1. Performing substitutions
2. Use of the law of excluded middle
3. Closing paths through denied self-identity
6. Open, complete tables in predicate logic
5. Modal Logic
1. Entering sentences of modal logic
2. Intuitive meanings of the box and diamond
3. Inference rules in modal logic
4. Closing paths and closing the table in modal logic
5. Identity in modal logic
6. Modal Conditional Logic
1. Entering sentences of modal conditional logic
2. The intuitive meanings of the modal conditionals
3. Inference rules in modal conditional logic
4. Closing paths and closing the table in conditional modal logic
5. Complete, open tables
7. Defeasible Logic
1. Closing paths by anomaly elimination
2. Varieties of defeasible logics
8. Appendix: Keyboard Shortcuts

Introduction

Socrates is a software application for the Macintosh computer developed at the University of Texas at Austin. It is intended to assist the learning of formal logic. It has been designed to be compatible with the semantic table approach taken by Jaakko Hintikka and James Bachman in their introductory text, What If...? Toward Excellence in Reasoning (Mayfield Publishing, Mountain View, California, 1991), but it can also be used as a free-standing resource for any introductory course in formal logic.. Socrates is a flexible tool that enables the user to analyze any argument that can be expressed using one of the languages that it understands. It is not limited to some fixed stock of examples. It is so rapid and accurate that it can assist even advanced students in the analysis of complex arguments, yet is so easy to use that it is accessible to the beginner. Socrates is not limited to the resources of the sentential calculus, or ever those of the predicate calculus (first-order logic). It can be used to analyze arguments couched in terms of modalities like necessity and possibility. This so-called "modal logic" has been studied by logicians since the Greek philosopher Aristotle, and it has experienced a remarkable renaissance since the late 1950's. Moreover, Socrates can be used to analyze reasoning involving various forms of hypothetical reasoning, including systems of "common sense" or defeasible reasoning that have been developed by researchers in the area of artificial intelligence in the last 15 years. The result is an engine for analyzing a wide range of logical inferences and arguments found in many disciplines and applications.

1. Getting Started

Socrates runs on the Apple Macintosh computer (Mac Plus and higher using System 6.0.5 or higher). To use Socrates, you should be familiar with the basic operation of the Macintosh, including clicking and dragging with the mouse, and using menus. The Socrates application includes the following files and folders:
1. The Socrates application itself (whose icon is illustrated in Figure 1).
2. A font suitcase containing the Terlingua, Salt Flat and Pittsburgh fonts.

Figure 1.

The fonts in the suitcase should be installed on the Macintosh that you are using. If you are using System 6, you can use the DA/Font mover to add the fonts to the System file, or you can use some other font utility to install these fonts. If you are using System 7, you may simply drag the fonts into the Fonts folder within the System Folder.

1.1 Starting Socrates

Find the icon for Socrates – a picture of a hand holding a pencil to a table divided into columns (illustrated above in Figure 1). Double-click on the icon, or click on the icon and select “Open” from the file menu. After a moment, the window for Socrates will appear on your screen. When it starts, Socrates will open an empty document, as shown below in Figure 2.

At the top of the screen, you will see the usual Apple, File, and Edit menus as well as six new menus: Entry, SC, PC, MC, Font, and FontSize. The menu bar is illustrated immediately below in Figure 2. You can pull down each menu to see what it contains.
Figure 2.

1.3 Files: Opening, Saving, Closing

Most of the commands in the File menu are standard Macintosh File menu commands.
• New - Creates a new document.
• Open - Opens an existing document.
• Save - Saves the topmost document to a file. You may not overwrite any files that were not created by the Socrates program.
• Save As - Saves the topmost document to a file, prompting for a new file name.
• Save As MacDraw - Saves the topmost document as a PICT document, suitable for use with most drawing programs (e.g. MacDraw, SuperPaint, etc.).
• Close - Closes the topmost document. If you have changed the contents of the document, you will be asked if you want to save the document before closing it.
• Quit - Quits the application. You will be asked if you wish to save any changes to open documents.

1.4 Navigating through a Table

One can navigate through a Socrates table in one of two ways:
• by means of the mouse, or
• by means of the keyboard arrows.
When using the mouse, one simply moves the cursor to the formula to be selected and clicks the mouse button. Once a formula on the table has been selected, one can move to other formulas by means of the keyboard arrows, moving either up, down, to the left or the right, depending on the key being used.

1.5 Editing: Cut & Paste, Undo & Redo

Most of the Edit menu commands are standard Macintosh Edit menu commands. However, the Undo and Redo commands implement infinite undo and redo.
• Undo - Undoes the most recent change made to the topmost document. Once a change is undone, subsequent use of Undo undoes the changes made previous to the most recent change, in reverse chronological order.
• Redo - Redoes the most recently undone change to the topmost document. Once a change is redone, subsequent use of Redo redoes the previous most recent undone changes, in reverse chronological order. However, when a new command is selected from the Move menu, Redo cannot be used.
• Copy - Copies the selected formula, or, if no formula is selected, copies the entire table as a picture that can be pasted into another application.
• Cut - Not enabled except for use with a desk accessory. However, the command-key equivalent (CMD-X) works in all dialogs where text is entered.
• Paste - Not enabled except for use with a desk accessory. However, the command-key equivalent (CMD-V)works in all dialogs where text is entered.
• Show Clipboard - Shows the contents of the clipboard in a window.

1.6 Logical Moves: The Entry, SC, PC, and MC Menus

These menus allow you to build a semantic tableaux and evaluate the argument that it represents for the logical propertie of validity and other related properties. The commands in the SC, PC, and MC menus change the contents of the topmost document. These menus deal with the Sentential Calculus, the Predicate Calculus, and the Modal Calculus respectively. Most commands in the SC and PC menus are described in sections 2 and 3 below. In general, they allow you to simplify logical formulae or alter them so that they can be simplified by other commands. Those commands in the MC menu are described in later sections (for the most part, in sections 4, 5 and 6).The Entry menu contains the following items, which are discussed in the indicated sections:
CommandSection
Close Path2.6, 3.5.3, 4.4, 6.1
Close Table2.7, 4.4
Edit Title1.6
Edit Comment1.6
Remove Title1.6
Remove Comment1.6
List Unbridged Subtables2.7

The SC menu represents the logical moves that may be made on formulas in the language of the Sentential Calculus and the languages of the Predicate and Modal Calculi. It consists of the following items:
CommandSection
Decompose Conjunction 2.5
Decompose Disjunction 2.5
Decompose Conditional 2.5
Decompose Biconditional 2.5
Remove Double Denial 2.5
Alter Denied Conjunction 2.5
Alter Denied Disjunction 2.5
Alter Denied Conditional 2.5
Alter Denied Biconditional 2.5
Modus Ponens 2.5
Law Of Excluded Middle 3.5.2

Moves that may be performed on arguments represented in the language of the Predicate Calculus or the Modal Calculus, but not the Sentential Calculus are in the PC menu. The PC menu consists of the following items:
CommandSection
Perform Substitution 3.5.1
Instantiate Universal Variable 3.3
Instantiate Existential Variable 3.3
Alter Denied Quantifier 3.3

The commands in the MC menu correspond to moves that apply to arguments expressed in the language of the Modal Calculus (including nonmonotonic expressions). These moves do not apply to the Sentential or the Predicate Calculi. The MC menu consists of the following items:
CommandSection
Decompose Necessity 4.3
Decompose Possibility 4.3
Decompose Box-Arrow 5.3
Decompose Diamond-Arrow 5.3
Alter Denied Modal 4.3
Alter Denied Nonmonotonic 5.3
Box-Definition 5.3
Diamond-Definition 5.3
Modal Law Of Excluded Middle 4.5

1.7 Annotations: Editing and Removing

Socrates documents may be annotated with a title and a comment. The title appears at the top of the document, above the logical table. The comment appears at the bottom of the document, below the table. Four menu items in the Entry menu allow you to change the title and comment of a document.
• Edit Title - This command allows you to enter a new title for the document or edit an existing title. Within the dialog box, the standard Macintosh editing command keys work, and one may type a carriage return by typing option-return. Typing a return closes the dialog box, saving the title (this is the same as clicking the “OK” button with the mouse). Typing command-period (CMD-.) closes the dialog box without saving the title (this is the same as clicking the “Cancel” button).
• Edit Comment - This command works just as the Edit Title command does, except that it allows you to edit the comment of a document rather than the title.
• Remove Title - This command removes the title from a document.
• Remove Comment - This command removes the comment from a document.

1.8 Appearance: The Font and Size Menus

The appearance of a Socrates document may also be changed by changing the typeface and the size of the typeface used in the document. This is accomplished using the Font and FontSize menus, which change the font or font size of the entire document. The Font menu restricts you to those fonts that have the logical characters that Socrates requires organized in the way that Socrates requires.The FontSize menu allows you to directly select a number of standard font sizes, and it allows you to type in any other font size up to 1024 by using the Other… menu item. You can also change the font size up and down in one point increments by using the Larger and Smaller menu items. The current font size is indicated by a check mark beside that size, or by a number in parentheses next to the Other… menu item.

2. Propositional Logic

2.1 Entering premises and conclusions

In order to use Socrates to analyze a piece of reasoning or an argument, you must enter the premises (the information available or assumed to be true) and the conclusion (the thesis or proposition which may or may not follow logically from the premises). To enter premises and conclusions, you must use the first two items on the Entry menu.

• Add Premise - Prompts for a formula, and adds it to the topmost document as a premise. The dialog in which the formula is entered is illustrated in Figure 3.

Figure 3.

The dialog includes four major elements. The formula entry area is the large box; the formula to be entered can be edited within this box. The buttons immediately below this area allow the user to enter logical characters into the formula at the insertion point; some of these characters are not easily accessible from the keyboard. The top row of characters and the first character on the bottom row are all that is required for problems in the Sentential and Predicate Calcului; the second row of characters are needed for analyses of arguments using modal and nonmonotonic logics. The special logical symbols for sentential logic can also be produced by the following key combinations:
CommandKey Combination
¬ Option-shift-hyphen
Option-v
Option-e, a
Option-i, a

• Add Conclusion - Prompts for a formula, and adds it to the topmost document as a conclusion. The dialog presented by this command is identical to that presented by the Add Premise menu item.

2.2 Entering sentences of sentential logic

To add premises and conclusions successfully, you must enter grammatical formulas into the dialog box of the Add Premise or Add Conclusion commands. For that part of logic known as "sentential logic," the permissible or grammatical formulas for Socrates are governed by rules that codify and regularize the practice of the Hintikka/Bachman text. These rules can be summarized as follows:

1. Any capital letter A, B, … Z, followed by any number of primes ('), is a well-formed sentence.
2. If è and ê are well-formed sentences, so are: —è, (è&ê), (è_ê), (èáê), and (èâê).
3. All of the well-formed sentences of sentential logic can be formed by repeated applications of rules 1 and 2.

Note that parentheses are added whenever one of the four "binary" connectives, &, _, á, and â, are used to combine two sentences into a new, compound sentence. This is the only time such parentheses can be added. Since Socrates possesses limited intelligence, it cannot guess what you really meant to say. Thus, you must be careful to follow the rules literally and precisely. You may not arbitrarily add or omit parentheses or other symbols. Thus, the following strings of characters are not well-formed: (—A) —(A) (A) ((A)_(B)) A&B (A&B) á A In contrast, the following are well-formed sentences of sentential logic: ((A&B)_(BáA)) ——(—Aâ — (B_—A)) ————A (A_(A&(AâA))) There should always be exactly as many left parentheses in a sentence as there are right parentheses, and there should be exactly one pair of parentheses for each binary connective.

2.3 The structure of the table: left and right sides