Models of catastrophic risks can be conjunctive or disjunctive. A conjunctive risk model is one in which the disaster is caused by the co-occurrence of multiple conditions ($D=C_1\cap \dots \cap C_k$). In a conjunctive model, the probability of the disaster is less than or equal to the probabilities of the individual conditions. By contrast, a disjunctive risk model is one in which the disaster occurs as a result of any of several conditions holding ($D=C_1\cup \dots \cup C_k$). In a disjunctive model, the probability of the disaster is greater than or equal to the probabilities of the individual conditions.

Examples of conjunctive and disjunctive risk models of AI risk:

• Joseph Carlsmith's models existential risk from power-seeking AI conjunctively, i.e. as the intersection of six conditions, all of which must be true for the existential catastrophe to occur.^[1]
• By contrast, Nate Soares's models AGI risk disjunctively, i.e. as the union of multiple conditions, any of which can cause existential catastrophe.^[2]

Both types of models are simplifying assumptions. In reality, a disaster can be caused by multiple conditions that interact conjunctively and disjunctively. For example, a disaster $D$ could occur if conditions $C_1$ and $C_2$ are true, or if condition $C_3$ is true: $D=(C_1\cap C_2)\cup C_3$.