For twenty years, the accepted wisdom was that interval-based semantics for Metric Temporal Logic is strictly more expressive than pointwise semantics. The hierarchy was clear: evaluating temporal formulas at arbitrary time points captures more properties than evaluating them only at event positions.
Foughali shows the hierarchy is wrong. Interval-based and pointwise semantics are incomparable.
The original result establishing the hierarchy contained a flaw. The proof assumed properties of the evaluation that don't hold in the standard models (finite or non-Zeno infinite timed executions) that practitioners actually use. In these models, there exist properties expressible in pointwise semantics that interval-based semantics cannot capture, and vice versa.
The incomparability means there is no “better” semantics — each captures temporal properties the other misses. This has practical consequences for verification: the choice of semantics determines what your specification language can say, and properties verified under one semantics may not even be expressible under the other.
To bridge the gap, Foughali introduces a mixed semantics that embeds both the pointwise and interval-based variants. The mixed semantics evaluates at both event positions and arbitrary time points, recovering the full expressive power of each within a single framework.
A twenty-year-old expressiveness result, corrected. The assumed hierarchy between two fundamental approaches to temporal reasoning collapses into incomparability. The resolution is not to choose one but to combine both.