Handbook of Automated Reasoning

2.15. Example

Consider the trivial bounds where LB(( $\mathcal{D},W$ ),FS) is the empty set and UB(( $\mathcal{D},W$ ),FS) is the whole language, a default theory $\mathcal{D}$ = {:p/p}, W = {¬p} and a set FS = {not(¬p)}. Clearly, the second condition for conflict does not hold: FS covers negations of every justification in $\mathcal{D}$ , not(¬p) ¬ FS but ¬p ∈