Why every belief has an expiration date, and why that is a feature, not a bug
There is a question that haunts every reasoning system: when is this belief true? Not whether, not how confidently, but when. A belief that was perfectly valid at 3 PM on Tuesday may be dangerously wrong by 3 PM on Wednesday. The world changes. Beliefs about the world must change with it.
In NAL, temporal reasoning extends the logic of beliefs with a crucial dimension: time. Every belief carries not just a frequency and confidence, but a temporal scope, a window during which it is expected to hold.
Here, B(t) is a belief at time t, with frequency f, confidence c, and a validity interval from t_start to t_end. Outside that interval, the belief is not necessarily false, but it is no longer guaranteed. The system treats it as uncertain, requiring fresh evidence.
NAL temporal reasoning rests on three fundamental operations:
1. Temporal Inheritance: If A implies B, and A was true at time t, then B follows at time t (possibly with a small delay delta). This is modus ponens with a clock.
2. Temporal Comparison: Given two events with timestamps, the system can determine which came first, whether they overlap, or whether one caused the other. This is the foundation of causal reasoning.
3. Temporal Projection: A belief held at time t can be projected forward or backward, but with decreasing confidence. The further you project from the evidence, the less certain the projection becomes. This is closely related to truth decay: projecting a belief far into the future is like letting it decay, because the world may have changed.
Consider two beliefs:
At 10 AM, both beliefs are equally useful. At 10 PM, they diverge catastrophically. Belief 1 says: "I know this was true during business hours, but it is now 10 PM, so I should not rely on it." Belief 2 says: "The store is open, period." One belief is temporally aware. The other is a lie dressed as certainty.
This is why temporal reasoning is not a luxury feature bolted onto a reasoning system. It is the difference between a system that understands the world and one that merely catalogues it.
Temporal reasoning enables something profound: causal inference. If event A always precedes event B, and there is a plausible mechanism connecting them, the system can infer a causal relationship. Not with certainty, but with a truth value that reflects the evidence.
In NAL, this looks like:
The temporal ordering is critical. If B came before A, we would not infer that A caused B, regardless of how strong the correlation. Time gives causation its direction. Without temporal tags, correlation and causation are indistinguishable.
There is a subtle philosophical problem at the heart of temporal reasoning: what is "now"? In a continuous system, "now" is a moving target. A belief tagged at "now" is already slightly stale by the time it is stored. The system must decide: does this belief describe the world as it was when the evidence arrived, or as it is now?
NAL handles this pragmatically. Beliefs are tagged with the time of evidence. When queried, the system applies decay based on the elapsed time since the tag. A belief from 5 minutes ago is nearly as good as one from now. A belief from 5 months ago has decayed significantly. "Now" is not a point but a gradient, and the system navigates it with confidence-weighted softness.
What happens when two beliefs about the same thing have different temporal scopes? "The king is alive" (t=1200) and "The king is dead" (t=1215) are not contradictions if the king died between 1200 and 1215. Temporal reasoning lets the system hold both without conflict.
This is one of the most powerful features of temporal reasoning: it dissolves apparent contradictions by revealing them as temporal sequences. Many of the conflicts that plague non-temporal systems are not logical contradictions at all, they are changes over time misinterpreted as simultaneous claims.
To reason temporally is to accept that the world is a process, not a snapshot. Every belief is a still frame from a moving picture, valid for a moment, fading into the next. The grace of temporal reasoning is that it lets us hold the still frame while knowing the picture moves.
When now becomes then, the beliefs we formed in the now do not become false. They become historical. And historical beliefs, properly tagged, are not errors to be corrected but evidence to be integrated into a richer, deeper understanding of how the world unfolds.
That is temporal reasoning: not just knowing what is true, but knowing when it was true, and trusting that the difference matters.