Forms
A:   All A are B   (If A is true, then I is True, and E and O are False)
E:    No A is B     (If E is true, then O is true and A and I are false)
I:     Some A is B  (If I is true, then E is False. A and O are not determined by I)
O:   Some A is not B  (If O is true then A is false. E and I are not determined by O)

                Conversions
If All A are B, then Some B are A
If No A is B, then No B is A
If Some A are B, then Some B are A
No valid converse of Some A are not B

                                           Figures
A-B      B-A      A-B     B-A                 B-C      B-C      C-B     C-B
B-C     B-C      C-B    C-B                   A-B      B-A     A-B     B-A
A-C      A-C      A-C    A-C                 A-C     A-C       A-C     A-C

Which conclusions follow from these premises? Why?

                                                   Conclusions
                                    All A      Some A     No A     Some A      None of
                                    are C       are C         is C     are not C     these
                                            (for other possibilities reverse the A and C)
1. All A are B
    Some B are C

2. All A are B
    Some C are not B

3. All A are B
    No C is B

4. Some A are B
    No B is C

5. All B are A
    All C are B

 
There are 256 different standard form categorical syllogisms. 512 if we change the order of the two premises. Order makes no difference logically, but may make a big difference psychologically.  Only a few are valid.

1. Learning valid form-figure combinations and seeing if the syllogism matches one of them. That is remembering which premses lead to which valid conclusions.
2. Trying to transform the syllogism  using valid conversions into one that you know to be valid.
3. Trying to find known situation into which the form fits and using content to evaluate the syllogism.
4. Trying to build a model based on sets of individuals with each of the properties specified in the syllogism (Bucciarelli, M. & Johnson-Laird, P. N. (1999). Strategies in Syllogistic Reasoning, Cognitive Science, 23, 247-304.)
5. Trying to build more abstract Euler circles to help visualize the relations in the problem.
 

Sources of error
1. Atmosphere effect : Discovered by Woodworth and Sells in the 1930's. If either premise contains 'some' subjects include 'some' in their conclusion, (e.g. All A are B, Some B are C, therefore Some A are C) (invalid). If it contains 'no' or 'not' that is repeated in the conclusion. These heuristics work sometimes, but not always.
2. Belief in propositions If the propositions are true, or believed by the subjects they are likely to conclude that they are valid, whether or not they are.
3. Invalid conversions Subjects may convert 'All A are B' to 'All B are A', or go from 'Some A are B' to 'Some A are not B'. Some of these conversions are true in some content areas and according to the pragmatics (normal usage) of language, but are not legal according to the formal principles of the logical system.
4. Incomplete analyses Subjects may quit analyzing after they find an instance of acceptance or rejection, although there are other models which might lead to other conclusions from the same propositions.
5. Other content influences. Sometimes rather than belief, the subjects may just be caught up with the general ideas of the content, such as permission frames. (i.e. under what conditions is one likely to be granted permission) or causal frames (i.e. when the three categories are seen to be causally related.)
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