Type identity would obtain if and only if every mental event type were identical to some physical event type or other.
By using the f and g notations as in Corollary 1, Property 2 holds if and only if the joint event of holds, which is true because of the non-negativity of α,β∈ [ 0,1].
For it seems straightforward to claim that the latter two sentences are true if and only if the states or events in question correspond with reality.
Also, we could say that a true belief p is reliably formed if and only if based on an event that usually would occur only if p (or a p-type belief) were true.
Token identity would obtain if and only if every particular mental event (this pain I feel now after stubbing my toe, that pain you feel now in your forehead), is identical to a particular brain event, which might be this firing of c-fibers in my head, that firing of c-fibers in yours.
Given a patient, any follow-up myopathy event was included as a new case event if and only if there is a washout period (i.e., 6 months of no drug exposure) after the previous myopathy event.
An agent entertains an actual belief that a certain event occurs if and only if she has reason to believe that the event occurs and such event is in her awareness set at the world under consideration.
So changes are real if and only if they are logically independent events in the world's history.
One might have thought that a focus on individual events is more appropriate: an event E is causally determined if and only if there exists a set of prior events {A, B, C …} that constitute a (jointly) sufficient cause of E. Then if all or even just most events E that are our human actions are causally determined, the problem that matters to us, namely the challenge to free will, is in force.
Halpern and Pearl retain the basic counterfactual notion that one event c (or state of affairs) causes another event e if and only if there is a counterfactual dependence between the two events, such that if c had not occurred, then e would not have occurred.
Then event C causes event E if and only if there is a chain C, D1, …, Dn, E such that each member in the chain (except C) is counterfactually dependent on the event before it.
