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| For all of the reasons mentioned above, and for the sake of a more compact illustration of the in and outs of a typical propositional equation reasoning system (PERS), let's now take up a much simpler example of a contingent proposition: | | For all of the reasons mentioned above, and for the sake of a more compact illustration of the in and outs of a typical propositional equation reasoning system (PERS), let's now take up a much simpler example of a contingent proposition: |
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− | o-----------------------------------------------------------o
| + | <pre> |
− | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| + | o-----------------------------------------------------------o |
− | | ` ` ` ` ` ` ` ` ` ` ` ` q o ` o r ` ` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | |
− | | ` ` ` ` ` ` ` ` ` ` ` ` ` | ` | ` ` ` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` ` ` q o ` o r ` ` ` ` ` ` ` ` ` ` ` ` | |
− | | ` ` ` ` ` ` ` ` ` ` ` ` p o ` o p ` ` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` ` ` ` | ` | ` ` ` ` ` ` ` ` ` ` ` ` ` | |
− | | ` ` ` ` ` ` ` ` ` ` ` ` ` `\ /` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` ` ` p o ` o p ` ` ` ` ` ` ` ` ` ` ` ` | |
− | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` @ ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` ` ` ` `\ /` ` ` ` ` ` ` ` ` ` ` ` ` ` | |
− | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` @ ` ` ` ` ` ` ` ` ` ` ` ` ` ` | |
− | | ` ` ` ` ` ` ` ` ` ` `(p (q)) (p (r))` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | |
− | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| + | | ` ` ` ` ` ` ` ` ` ` `(p (q)) (p (r))` ` ` ` ` ` ` ` ` ` ` | |
− | o-----------------------------------------------------------o
| + | | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | |
| + | o-----------------------------------------------------------o |
| + | </pre> |
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| For the sake of simplicity in discussing this example, I will revert to the existential interpretation (''Ex'') of logical graphs and their corresponding parse strings. | | For the sake of simplicity in discussing this example, I will revert to the existential interpretation (''Ex'') of logical graphs and their corresponding parse strings. |
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− | Under ''Ex'' the expression "(p (q))(p (r))" interprets as the vernacular expression "''p'' implies ''q'' and ''p'' implies ''r''", in symbols, {''p'' ⇒ ''q''} ∧ ''p'' ⇒ ''r'', so this is the reading that we'll want to keep in mind for the present. | + | Under ''Ex'' the expression <math>(p\ (q))(p\ (r))\!</math> interprets as the vernacular expression <math>p\ \operatorname{implies}\ q\ \operatorname{and}\ p\ \operatorname{implies}\ r,</math> in symbols, <math>\{ p \Rightarrow q \} \land \{ p \Rightarrow r \},</math> so this is the reading that we'll want to keep in mind for the present. |
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| Where brevity is required, and it occasionally is, we may invoke the propositional expression "(p (q))(p (r))" under the name "''f''" by making use of the following definition: "f = (p (q))(p (r))". | | Where brevity is required, and it occasionally is, we may invoke the propositional expression "(p (q))(p (r))" under the name "''f''" by making use of the following definition: "f = (p (q))(p (r))". |