The epistemic closure is that:

If S knows (if p then q) then (If S knows p then S knows q).

In Nozick's Truth-Tracking Analysis

S knows p if and only if

• p is true
• S believes that p
• If p were false, S would not believe that p
• If p were true, S would believe that p

The counter model here I mean something might includes

• W (a nonempty set of worlds),

• R (a relation over W), and

• I(SxW) (where I is the interpretation function I:(s,w)->{0,1}, where S is the set of sentense letters. This should tells us whether a sentense letter is true or not true in a world.)

To show the epistemic closure is not valid under Nozick's system, we simply find a counter model with world w s.t. the negation of epistemic closure is true in this world.

I tried to do this by myself, but I didn't figure out Nozick's semantics by reading his philosophical explansion

for example

• How did Nozick define the valuation of the belief operator
• For the relation of worlds, what rules they must obey? (are they transitive, or symmetric etc.)
• What's the valuation of Nozick's counterfactual conditionals

(I know Nozick's system of counterfactual conditionals were different from Stalnaker and Lewis.)

What Nozick said on page 173 is that

This point is brought out especially clearly in recent 'possible-worlds' accounts of subjunctives: The subjunctive is true when (roughly) in all those worlds in which p holds true that are closest to the actual world, q also is true (Examine those worlds in which p holds true closest to the actual world, and see if q holds true in all these.)

To me, this really sounds like Stalnaker's account of subjunctive conditionals:

That p subjunctive implies q is true in w if and only if for all worlds x, [if p is true in x and for all world y (if p true in y then x sees y under relation Rw)], then x true in q.

Could someone explain Nozick's semantics to me in details?

Any help or suggestion would be appreciated.