Design a propositional logic system that could be used to model this: $1.(10$ points$)$ Create the relevant symbols and explain their meaning. $2.(20$ points$)$ List relevant axioms and explain their meaning. $3.(5$ points$)$ List relevant sentences that encode the start of the game. $4.(5$ points$)$ Formulate an assertion to indicate success $($which we would use, together with the knowledge base KB composed of your axioms and sentences above, to formulate a plan, by calling Ask$($KB$,$$)).$ Apply to the particular case where the gold is at location $3.$ Running SATplan on your KB with a suitable goal would produce a plan $($sequence of actions$)$ that achieves the goal, if such a plan exists $($and assuming you correctly formulated your KB$),$ but this would involve many symbols and sentences and it would be too complicated. Instead, just play out two scenarios where the agent acts in two ways: $5.(10$ points$)$ Give, for times $0$ to $4,$ the truth values of all symbols $($including the percepts$)$ for a successful agent behavior $($the agent takes a sequence of actions that lead to getting the gold$).$ You must obtain the values by applying your axioms to your initial state formulation $($not by guessing what the values should be$).$ Tabulate them like this $($where $0$ and $1$ stand for false and true, respe