implement_plan_micro

Formal Specification

Multimodal Logic Integration

Five modal logics via fusion with bridge principles:

• JL: Justification Logic - evidence-backed claims
• IEL: Inferential Erotetic Logic - question handling
• TEL: Temporal Epistemic Logic - phase sequencing
• SDL: Standard Deontic Logic - obligations/permissions
• DEL: Dynamic Epistemic Logic - action modalities

Justification Logic (JL)

# Justification terms
[h]:context(task_n)                    # Handoff h justifies task context
[v]:verified(phase_n)                  # Verification v justifies completion
[p]:plan(tasks)                        # Plan p justifies task list

# Evidence production
[read(f)]exists e. [e]:content(f)
[verify(c)]exists v. [v]:pass(c) | [v]:fail(c)

# Handoff chain: evidence propagates
[h_n]:complete(task_n) -> [h_{n+1}]:context(task_{n+1})
proceed(task) <-> exists h. [h]:validated

Inferential Erotetic Logic (IEL)

# Mode and blocker questions
?{direct, orchestration}               # Mode selection
?{continue, retry, ask_user}           # Blocker resolution
mismatch(plan, reality) -> ?{how_proceed}
no_validation -> ?{run_validation_first}

Temporal Epistemic Logic (TEL)

# File reading constraints
[](mentioned(f) -> <>read_fully(f))           # Eventually read
[](mentioned(f) -> not spawn U read_fully(f)) # No spawn until read
[](partial_read(f) -> false)                  # Partial reads forbidden

# Phase sequencing
[](phase(n) -> P(phase(n-1) & verified(n-1))) # Verified before next
[](automated_pass -> <>manual_verify)         # Automated gates manual
[](manual_pass(n) -> <>phase(n+1))            # Manual gates next phase

# Handoff persistence
[](handoff_created(h) -> []exists_on_disk(h)) # Survives compaction

# Termination
<>(all_complete | abandoned)

Standard Deontic Logic (SDL)

# Reading obligations
O(read_fully(plan))
O(read_fully(f)) <- mentioned_in_plan(f)
O(check_existing_checkmarks)
F(partial_read)

# Verification obligations
O(run_automated) <- impl_complete
O(pause_for_manual) <- automated_pass
O(present_manual_checklist)
F(checkoff_manual) <- not user_confirmed

# Mode selection
O(orchestration) <- tasks >= 4
P(direct) <- tasks <= 3
O(respect_user_preference)

# Orchestration obligations
O(read_previous_handoff) <- exists_handoff(task_{n-1})
O(create_handoff) <- agent_completes
O(update_ledger) <- task_complete
F(batch_tasks)                                # One agent per task
F(proceed_on_mismatch) <- not user_guidance