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sav08:propositional_logic_syntax [2008/03/11 14:36] vkuncak |
sav08:propositional_logic_syntax [2008/03/18 13:54] vkuncak |
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F ::= V \mid {\it false} \mid {\it true} \mid (F \land F) \mid (F \lor F) \mid (\lnot F) \mid (F \rightarrow F) \mid (F \leftrightarrow F) | F ::= V \mid {\it false} \mid {\it true} \mid (F \land F) \mid (F \lor F) \mid (\lnot F) \mid (F \rightarrow F) \mid (F \leftrightarrow F) | ||
\] | \] | ||
- | We denote the set of all propositional formulas given by the above grammar by ${\cal F}$. This is a countable set: we can order all formulas in this set in a sequence (for example, by writing them down in binary alphabet and sorting the resulting strings alphabetically). | + | We denote the set of all propositional formulas given by the above grammar by ${\cal F}$. Each propositional formula is a finite sequence of symbols. The set ${\cal F}$ is a countable set: we can order all formulas in this set in a sequence (for example, by writing them down in binary alphabet and sorting the resulting strings alphabetically). |
Omitting parantheses: | Omitting parantheses: | ||
- | * $\land$, $\lor$ commutative | + | * $\land$, $\lor$ associative |
* priorities, from strongest-binding: $(\lnot)\ ;\ (\land, \lor)\ ;\ (\rightarrow, \leftrightarrow)$ | * priorities, from strongest-binding: $(\lnot)\ ;\ (\land, \lor)\ ;\ (\rightarrow, \leftrightarrow)$ | ||
When in doubt, use parenthesis. | When in doubt, use parenthesis. |