Psy 416: Reasoning and
Problem Solving Fall 1998
Lecture 6: Form, logic, and logical reasoning
Associated with this topic is a Primer
on Logic. Click here to see it.
1. Logical appraisal
When a person says or writes something there are many
different ways in which her performance may be judged. Did she say something
nice? Did she speak well? Did she articulate clearly? Could I understand
what she meant to say? Has she used apt metaphors? We may take any number
of different stances to her discourse. Among these is a logical stance.
We may examine the logical structure of her discourse
and evaluate whether it can withstand logical analysis. We can evaluate
to what extent the conclusions she draws are justified by her premises.
Logic is reasoning based on the idea that often if some
statement or set of statements is true, some other possible statements
must also be true, others may be true and may be false, and still others
must be false. We all probably reason this way some of the time.
For example, if you knew the following
two statements to be true:
(1a) If a person does not practice, he or she will not
become an accomplished pianist.
(1b) Susan took piano lessons for years, but she never
practiced.
you could conclude
(1c) Susan is not an accomplished pianist.
II. A widespread AI, Cognitive Psychology,
and Cognitive Science principle is that there are well-specifiable procedures
which represent the way that people think. These involve applying logic
type rules to a formal representation base. The study of reasoning in this
case is the discovery of the form of the representation and the rules of
inference that people use.
1. Incoming information is transformed into a symbolic
representation of the implied proposition. There are certain formal ways
in which propositions are interrelated and conclusions are derived. These
are implemented by the application of logic like rules. In information
processing systems they are the application of efficient procedures which
represent algorithms or heuristics.
2. Errors occur when a) there is an error in the representation,
or b) the derivation is not completed.
3. A problem of application is: it is not always clear
how to get from premises to representations, nor for some problems, what
the derivation rules are.
III. Alternative Working Hypotheses are often
based on mental models --(these come in different variants, lists of tokens,
Venn diagrams, images of the details of the propositions described (e.g.
Johnson-Laird, 1983, Mental Models, Harvard Univ. Press)
1. Mental models are one way that people tend to solve
(logic) problems:
(a) attempt to build a mental (or external) structural
representation (=model) of the relevant content information in the premises,
(b) interrogate the model to see whether the conclusion
is already contained there.
2. Reasoning may fail when:
(a) mental model does not accurately reflect premises
(b) mental model of premises is not integrated accurately--e.g.
representation of earlier premises may not be remembered while later premises
are added
(c) mental model of premises is not remembered during
conclusion evaluation
(d) interrogation is not accurately completed.
3. Problems:
(a) There is no single universal structure for mental
models of propositions.
(b) It is not always clear what the relevant components
are.
(c) It is not obvious how to model some meanings; some
meanings are very difficult to model using certain model schemata.
(d) It is not always clear how people may interrogate
the model, nor is it always clear how to use the model to draw valid conclusions.
IV. Logical reasoning seems to be secondary
to reasoning from content which may be based on previous knowledge or even
innate tendencies to use certain reasoning schemas.
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