SYMBOLIC LOGIC: THE COURSE

The entire course is organized in five modules.  Essential material is presented with a dark red background.  Supplemental material  is presented with a dark blue background.  Parallel SLIPS lessons are presented with a dark brown background.  Parallel material from other sources (sometimes rather advanced) is presented with a dark green background.  Review and practice exercises are presented with a deep orange background.  Proficiency tests are presented with a purple background.
 

How to study for this course:

Any introductory course in symbolic logic will deal with symbolization, testing for validity, and presenting derivations.  The differences among courses, however, may appear far greater than they are in other areas of study, and some of this depends on whether the course is seen as a part of a mathematics or computer science program or as part of a philosophy program.  After teaching this course for more than twenty years, I have added some wrinkles of my own, particularly in the use of postfix literal notation and in the discussion of expanding symbolic logic to more than two-value (true or false) systems.   Several years ago I developed SLIPS as a hypertext or webpage introduction to symbolic logic, and I still find much of the material useful in approaching the concepts of symbolic logic (much as I did in a textbook, now out of print, entitled Symbolic Logic: A Conceptual Approach).

While the material on these pages is self-contained, some students may find it helpful to work with one or another text that covers the same topics.  The main difficulty in doing this is that there are differences in symbolization and in the approach to a proof system, so it is necessary to make constant adaptations.  An additional difficulty is that I follow Bertrand Russell in introducing a predicate notation at the same time as a propositional notation, but I delay discussing the use of quantifiers.

In the modules below, I would recommend working from left to right along the top row, then going back  into material from other rows as it appears helpful or interesting.  I tend to discourage printing out the pages for study: in some cases, where there is interactive material, printouts will be virtually useless, and unless the printout is in color a great deal is lost for any of these pages.
 
 
 

MODULE 1:  Basic Symbolization
The properties of effective games Using both postfix and infix symbolization Propositional variables and connectives Predicate variables Logical relationships Using truth tables
The 19th century background of symbolic logic Using PLN Variables and signals Alternate connectives Truth-functional relationships
Syntax and semantics Effective symbolization Using X and Y as signals Gates in electronic circuits
Additional material on propositional logic Proficiency test
Schaum: 44-55 Schaum: 130-142 Schaum: 55-60 Schaum: 60-64
MODULE 2:  Quantification and Direct Derivations
Using quantifiers Effective symbolization for monadic expressions Direct inferences Direct derivations Exchanging wff's Proficiency test
Terms used in predicate logic More about predicate logic Beginning with derivations Inferences and equivalences
Something about Prolog and other computing languages
Schaum: 130-142 Schaum: 81-87 
note differences in what is labeled v elim
Schaum: 81-87 Schaum: 81-87, 103
MODULE 3:  Testing for Validity
Defining validity Truth table testing Additional quantifier rules Using consistency trees Converting to DNF and CNF Proficiency test
Deductive reasoning Using algebraic notation The new name rule Consistency trees with quantifiers Horn formulas
Using truth table tests Decision procedures
Algebraic notation
Schaum: 23-31 Schaum: 60-68 Schaum: 68-77, 150-158
MODULE 4:  Additional Derivation Techniques and Multiple Quantifiers
Indirect derivations Hypothetical (conditional) derivations Dyadic expressions Multiple Quantifiers Drills on symbolization Proficiency test
Indirect derivations Conditional derivations Examples for multiply quantified sentences Drills on derivations
Schaum: 87-97 Schaum: 87-97 Special problems in symbolization
Schaum: 130-142
MODULE 5:  Additional Predicate Symbolization
Prenex expressions Expressing identity The decidability (computability) problem Boolean algebra A three-value logic Proficiency test 
 
Schaum: 158-162