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SKILL.md: Temporal Interval Reasoning (Allen 1983)

When to Use This Skill

Load this skill when you encounter:

Do not use if you only need to compare two absolute timestamps with no uncertainty — plain arithmetic suffices.

Decision Points

New Temporal Assertion Added

IF assertion conflicts with existing constraints:
    → Detect empty arc label during propagation
    → HALT immediately, report inconsistent interval pair
    → Do NOT continue with inconsistent state

IF assertion is consistent:
    → Run constraint propagation from affected arcs
    → Update labels by intersecting transitivity consequences
    → Continue until no more refinements possible

Handling Temporal Uncertainty

IF evidence only supports multiple relations:
    → Maintain full disjunctive label {before, meets, overlaps}
    → Never collapse to single relation without evidence
    → Log when/why constraint set narrows

IF forced to act under uncertainty:
    → Use disjunctive label as-is for planning
    → Tag any assumptions as defeasible
    → Avoid premature commitment

Scoping Temporal Reasoning

IF dealing with events at vastly different timescales:
    → Identify reference interval hierarchy (year→month→day)
    → Reason within each cluster separately
    → Create explicit bridge constraints at boundaries
    → Avoid flattening everything into one global graph

IF local reasoning feels sufficient:
    → Verify query scope matches reference interval level
    → Propagate only within relevant cluster
    → Escalate cross-cluster only when dependency detected

State Persistence

IF state continues with no explicit end bound:
    → Apply persistence default AND mark as defeasible
    → Any future end-bound assertion overrides default
    → Never treat persistence assumption as hard constraint

IF explicit temporal bound provided:
    → Override any existing persistence defaults
    → Propagate new constraint normally

Failure Modes

Detection Rules:

• If you see timestamps without duration → Point-ification
• If you see single relation chosen arbitrarily → Premature Commitment
• If propagation cost grows with total KB size → Global Propagation Bomb
• If reasoning continues after empty label → Empty Label Denial
• If new temporal facts get rejected → Persistence Rigidity

Worked Examples

Example 1: Meeting Schedule Conflict Detection

Scenario: Adding "Team Review" to calendar that already has "Client Call" and "Engineering Standup"

Initial State:

Client Call (I₁): [10:00, 11:00]
Engineering Standup (I₂): [11:30, 12:00]
Known: I₁ {before} I₂

New Assertion: Team Review (I₃): [10:45, 11:15]

Expert Reasoning Trace:

1. Classify new relations:

   • I₃ vs I₁: starts at 10:45, I₁ ends at 11:00 → {overlaps}
   • I₃ vs I₂: ends at 11:15, I₂ starts at 11:30 → {before}

2. Constraint propagation:

   • From I₁ {before} I₂ and I₃ {overlaps} I₁
   • Transitivity: overlaps ∘ before = {before, overlaps, meets, starts, during}
   • New constraint: I₃ {before, overlaps, meets, starts, during} I₂
   • Intersect with I₃ {before} I₂: label becomes {before}

3. Consistency check: All labels non-empty → Schedule is feasible but has overlap

Novice Would Miss:

• Might not check I₃ overlap with I₁ creates resource conflict
• Might not verify transitivity maintains consistency
• Might not distinguish "feasible ordering" from "no resource conflicts"

Expert Catches:

• Overlap detection flagged immediately via relation classification
• Propagation verifies global consistency maintained
• Clear distinction between temporal feasibility and resource availability

Example 2: Process Phase Dependencies

Scenario: Deployment pipeline with uncertain task completion times

Initial State:

Build Phase (B): duration unknown, must finish before Deploy
Test Phase (T): overlaps with end of Build, duration uncertain  
Deploy Phase (D): starts after both B and T complete

Constraint Network:

T {overlaps, finishes} B  (Test can finish with or before Build)
B {before, meets} D       (Build must complete before Deploy)
T {before, meets} D       (Test must complete before Deploy)

New Information: "Test found critical bug, extending by 2 hours"

Expert Reasoning:

1. Update affects scope: Test extension pushes T endpoint later
2. Propagation: If T {finishes} B originally, now T {overlaps} B (extends past Build end)
3. Check consistency: T {overlaps} B still allows B {before, meets} D and T {before, meets} D
4. Result: Deployment delayed but pipeline logic intact

Novice Would Miss:

• Might assume Test completion doesn't affect Build-Deploy dependency
• Might not propagate Test extension through to Deploy timing
• Might treat "Test extends" as isolated fact rather than constraint network update

Expert Catches:

• Recognizes Test-Build relation must be re-evaluated
• Propagates timing implications through full constraint network
• Maintains uncertainty appropriately (Deploy could start immediately after Build OR after extended Test)

Quality Gates

Temporal reasoning task is complete when:

• All intervals represented with explicit start/end bounds (no point events)
• Every interval pair has non-empty arc label from the 13-relation vocabulary
• Constraint propagation run to completion (no pending transitivity updates)
• All disjunctive labels honestly reflect current evidence (no arbitrary commitments)
• Reference interval hierarchy established for multi-scale reasoning
• Persistence defaults tagged as defeasible where applicable
• Inconsistency detection verified (empty labels caught and reported)
• Cross-reference scope bridges explicitly defined
• All temporal assertions traced to evidence source
• Query scope matches reasoning granularity level

NOT-FOR Boundaries

Do NOT use Allen's interval algebra for:

• Simple timestamp comparison → Use arithmetic: if (t1 < t2)
• Metric duration calculation → Use calendar arithmetic: end_date - start_date
• Real-time scheduling optimization → Use constraint satisfaction with numeric domains
• Probabilistic temporal inference → Use temporal probabilistic networks
• Continuous time dynamics → Use differential equations
• High-frequency event streams → Use stream processing frameworks

Delegate instead:

• For metric constraints: Use constraint-satisfaction-with-numeric-domains
• For probabilistic temporal reasoning: Use bayesian-temporal-networks
• For real-time systems: Use rate-monotonic-scheduling
• For continuous dynamics: Use temporal-logic-model-checking
• For event stream processing: Use complex-event-processing

Allen excels at: Qualitative temporal reasoning under uncertainty with incremental knowledge updates and hierarchical scope management.