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sav08:propositional_logic_syntax [2008/03/10 19:33] vkuncak |
sav08:propositional_logic_syntax [2008/03/18 11:10] vkuncak |
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| 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. | ||
| Line 15: | Line 15: | ||
| Notation: when we write $F_1 \equiv F_2$ this means that $F_1$ and $F_2$ are identical formulas (with identical syntax trees). For example, $p \land q \equiv p \land q$, but it is not the case that $p \land q \equiv q \land p$. | Notation: when we write $F_1 \equiv F_2$ this means that $F_1$ and $F_2$ are identical formulas (with identical syntax trees). For example, $p \land q \equiv p \land q$, but it is not the case that $p \land q \equiv q \land p$. | ||
| - | In [[Isabelle theorem prover]] we use this ++++ASCII notation for Propositional Logic| | + | In [[Isabelle theorem prover]] we use this ++++ASCII notation for First-Order Logic| |
| \[ | \[ | ||
| \begin{array}{c|c} | \begin{array}{c|c} | ||
| Line 38: | Line 38: | ||
| \[\begin{array}{l} | \[\begin{array}{l} | ||
| FV(p) = \{ p \}, \mbox{ for } p \in V \\ | FV(p) = \{ p \}, \mbox{ for } p \in V \\ | ||
| + | FV(\lnot F) = FV(F) \\ | ||
| FV(F_1 \land F_2) = FV(F_1) \cup FV(F_2) \\ | FV(F_1 \land F_2) = FV(F_1) \cup FV(F_2) \\ | ||
| FV(F_1 \lor F_2) = FV(F_1) \cup FV(F_2) \\ | FV(F_1 \lor F_2) = FV(F_1) \cup FV(F_2) \\ | ||
| - | FV(\lnot F) = FV(F) \\ | ||
| FV(F_1 \rightarrow F_2) = FV(F_1) \cup FV(F_2) \\ | FV(F_1 \rightarrow F_2) = FV(F_1) \cup FV(F_2) \\ | ||
| FV(F_1 \leftrightarrow F_2) = FV(F_1) \cup FV(F_2) \\ | FV(F_1 \leftrightarrow F_2) = FV(F_1) \cup FV(F_2) \\ | ||