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sav08:propositional_logic_syntax [2008/03/18 14:00] vkuncak |
sav08:propositional_logic_syntax [2009/04/08 18:34] philippe.suter |
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| We denote the set of all propositional formulas given by the above [[:Notes on Context-Free Grammars|context-free grammar]] by ${\cal F}$. Each propositional formula is a finite sequence of symbols, given by the above context-free grammar. 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). | We denote the set of all propositional formulas given by the above [[:Notes on Context-Free Grammars|context-free grammar]] by ${\cal F}$. Each propositional formula is a finite sequence of symbols, given by the above context-free grammar. 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 parentheses: |
| * $\land$, $\lor$ associative | * $\land$, $\lor$ associative | ||
| * priorities, from strongest-binding: $(\lnot)\ ;\ (\land, \lor)\ ;\ (\rightarrow, \leftrightarrow)$ | * priorities, from strongest-binding: $(\lnot)\ ;\ (\land, \lor)\ ;\ (\rightarrow, \leftrightarrow)$ | ||