Inference & production-system drills

Build a forward-chaining derivation (Q8), a DFS inference tree (Q6), and contrast data- vs goal-driven control (Q2).

Three exam tasks, one engine

A production system is rules + working memory + a recognize–act cycle. The same rule base can be run in two directions, and the exam tests both plus the contrast between them.

Q2 — data-driven vs goal-driven

	Data-driven (forward chaining)	Goal-driven (backward chaining)
Start from	the known facts	the goal to prove
Match rules by their	premises (conditions)	conclusions (actions)
Each step	fires a rule, adds its conclusion to working memory	turns a rule's premises into subgoals
Stops when	no new fact can be derived (fixpoint)	the goal traces back to known facts
Best when	few facts, many possible conclusions; "what follows from this data?"	a specific goal, the data set is large; "is this goal provable?"

Rule of thumb: choose the direction with the smaller branching factor — work from whichever end has fewer choices.

Q8 — forward chaining to a fixpoint

Using the cat/dog/mouse KB from L10.1 with facts ${d o g_ab se n t, c a t_n o t_s l ee p in g}$ , repeatedly fire any rule whose premises are all known, add the conclusion, and loop until a full pass derives nothing new (the fixpoint):

dog absent + cat not sleeping ⇒ derive cat_absent.
dog absent + cat absent ⇒ derive mouse_present.
Next pass adds nothing new ⇒ fixpoint, stop.

Every rule firing is one application of modus ponens; forward chaining is just modus ponens run to exhaustion.

Q6 — the DFS inference tree

Backward chaining proves a goal depth-first over the rules. The exam's playground KB:

$r ainin g \land t e m p_co l d \to pl a y g r o u n d_e m pt y$
$pl a y in g_v i d eo g am e \to k i d s_n o t_o u t s i d e$
$k i d s_n o t_o u t s i d e \to (v i d eo g am es \lor a t_sc h oo l)$
$n o t_sc h oo l_d a y \to (o u t s i d e \lor v i d eo g am es)$
$k i d s_n o t_o u t s i d e \to pl a y g r o u n d_e m pt y$

Facts: $n o t_sc h oo l_d a y$ , $pl a y in g_v i d eo g am e$ . Prove playground_empty, numbering rules in trial order:

Goal playground_empty. Rule 1 concludes it ⇒ try rule 1; its premises $r ainin g, t e m p_co l d$ are not facts and unprovable ⇒ fail, backtrack.
Rule 5 also concludes playground_empty ⇒ try rule 5; subgoal kids_not_outside.
Rule 2 concludes kids_not_outside ⇒ its premise playing_videogame is a fact ⇒ succeed.
kids_not_outside proved ⇒ playground_empty proved via rules [5, 2].

The and/or structure: each rule conclusion is an OR-choice (rule 1 or rule 5 could establish the goal); each rule's premises are AND-subgoals (all must hold). DFS tries OR-children left to right, backtracking on failure.

This shape is what Q6 is graded on — the <em>trial</em> sequence, not just the proof. Rule 1 is tried first and dies (neither raining nor temp_cold is a fact or provable), DFS backtracks to rule 5, and rule 2 lands on the fact: proved via rules [5, 2]. Each rule concluding the goal is an OR-choice; each rule’s premises are AND-subgoals.