Notes on Logic
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.
Examples from the Wason Problem

Tversky and Kahneman Introduced certain heuristics for solving problems and making decisions.
Represetativeness: the reasoner evaluates how similar the example is to the category that is involved in the decision. The likelihood is boften based on this similarity regardless of other factors.
Binomial, Linda example, etc.

Framing of the problem. The decision maker makes her decisions dependent upon which aspects of the possible results are in the focus of attention and what the base of comparison is.
Losing money
Possible deaths