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--- sav08:propositional_logic_syntax [2008/03/18 11:10]
vkuncak
+++ sav08:propositional_logic_syntax [2008/03/18 14:00]
vkuncak
@@ Line 6: / Line 6: @@
    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 [[: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:
@@ 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 $p \land q \equiv q \land p$.
-In [[Isabelle theorem prover]] we use this ++++ASCII notation for First-Order Logic|
+In [[Isabelle theorem prover]] we use this ++++ASCII notation for Propositional Logic|
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