The entailment from intermediate to weak global supervenience assumes that isomorphism-based indiscernibility tracks the same modal structure as property-by-property indiscernibility, but Hazen and Parsons show these can come apart in modal logics with non-rigid domains.
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The pattern of what's possible and what's necessary in a situation or logical system.
Non-rigid domains(modal logic)
In modal logic, this refers to situations where the set of possible things changes or varies across different possible worlds (as opposed to staying the same).
entailment(Conceptualist framework)
Understood in terms of truth at a world
global supervenience(Modal supervenience relations in philosophy of mind and metaphysics)
A globally supervenes on B if and only if no two possible worlds share the same global pattern of distribution of B-properties while differing in their global pattern of distribution of A-properties.
isomorphism(The strongest structural correspondence between two many-sorted structures.)
An embedding between structures in which all defining maps are bijections.
supervenience(Philosophy of mind and reduction; contrasted with full reduction)
A relation in which mental (or higher-level) states are dependent on physiological (or lower-level) states such that any two cases with identical lower-level bases are identical in their higher-level states; a necessary but not sufficient condition for reduction.
weak supervenience(Violated by world w1 in Petrie's example)
A supervenience relation where, within a single world, no two individuals can differ in A-properties without differing in B-properties