# Propositional Logic Reduction Operator

So, I'm working with Knowledge Based Agents in an AI class, and we're deriving a proposition given a logic base in CNF. I've derived $\neg G$ using proof by resolution in the following partial chain: $$G \rightarrow (\neg A \vee F \vee \neg G) \wedge (\neg B \vee F \vee \neg G) \rightarrow \cdots$$ Given $G$, $(\neg A \vee F \vee \neg G) \wedge (\neg B \vee F \vee \neg G)$ reduces to $(\neg A \vee F) \wedge (\neg B \vee F)$ which simplifies to $(\neg A \wedge \neg B) \vee F$. Is there a logic symbol to show a reduction, or should I just keep it in English?

• Is F a variable, or a truth-value representing "false"? I immediately took it to denote a contradictory statement, but please clarify it you meant for $F$ to be a variable. Sep 25, 2016 at 17:38
• F is just a variable, I apologize for the confusion.
– HDM
Sep 25, 2016 at 19:06

Some people use the $\LaTeX$ symbol \rightsquigarrow "$\large\rightsquigarrow$" for some kind of reduction. There is probably no universal convention, so you should define whatever notation you use.