Symbolic Reasoning with Role-Filler Binding

Topics: Role-filler binding, structured representations, reasoning, analogy Time: 20 minutes Prerequisites: 00_quickstart.py, 18_encoders_graph.py Related: 24_app_working_memory.py, 25_app_integration_patterns.py

This example demonstrates symbolic reasoning using role-filler binding in hyperdimensional computing. Role-filler binding is a fundamental technique for representing structured knowledge, enabling AI systems to perform complex reasoning tasks.

Key concepts: - Role-filler binding: bind(role, filler) separates structure from content - Frame-based representations: Templates with variable slots - Variable binding: Bind abstract concepts to concrete instances - Analogical reasoning: Transfer structure between domains - Query answering: Retrieve fillers by unbinding roles

This approach enables human-like reasoning about structured knowledge, essential for natural language understanding, planning, and problem solving.

from holovec import VSA
from holovec.retrieval import ItemStore

print("=" * 70)
print("Symbolic Reasoning with Role-Filler Binding")
print("=" * 70)
print()

# Create model
model = VSA.create('FHRR', dim=10000, seed=42)

# ============================================================================
# Demo 1: Sentence Understanding with Role-Filler Binding
# ============================================================================
print("=" * 70)
print("Demo 1: Sentence Understanding")
print("=" * 70)

# Define semantic roles
print("\nDefining semantic roles:")
agent = model.random(seed=100)
action = model.random(seed=101)
patient = model.random(seed=102)
instrument = model.random(seed=103)
location = model.random(seed=104)
time = model.random(seed=105)

print("  Roles: agent, action, patient, instrument, location, time")

# Encode entities and concepts
print("\nEncoding entities:")
john = model.random(seed=200)
mary = model.random(seed=201)
hammer = model.random(seed=202)
nail = model.random(seed=203)
workshop = model.random(seed=204)
morning = model.random(seed=205)

# Encode actions
hit = model.random(seed=300)
build = model.random(seed=301)

print("  Entities: john, mary, hammer, nail, workshop, morning")
print("  Actions: hit, build")

# Sentence 1: "John hit the nail with a hammer in the workshop"
print("\n" + "=" * 70)
print("Encoding: 'John hit the nail with a hammer in the workshop'")
print("=" * 70)

sentence1_bindings = [
    model.bind(agent, john),
    model.bind(action, hit),
    model.bind(patient, nail),
    model.bind(instrument, hammer),
    model.bind(location, workshop),
]

sentence1 = model.bundle(sentence1_bindings)

print("\nRole-filler bindings:")
print("  agent ⊗ john")
print("  action ⊗ hit")
print("  patient ⊗ nail")
print("  instrument ⊗ hammer")
print("  location ⊗ workshop")

# Query: Who performed the action?
print("\nQuery: Who performed the action?")
agent_result = model.unbind(sentence1, agent)
print(f"  Similarity to john: {float(model.similarity(agent_result, john)):.3f}  ← Agent")
print(f"  Similarity to mary: {float(model.similarity(agent_result, mary)):.3f}")

# Query: What was used as instrument?
print("\nQuery: What was used as instrument?")
instrument_result = model.unbind(sentence1, instrument)
print(f"  Similarity to hammer: {float(model.similarity(instrument_result, hammer)):.3f}  ← Instrument")
print(f"  Similarity to nail:   {float(model.similarity(instrument_result, nail)):.3f}")

# Query: Where did this happen?
print("\nQuery: Where did this happen?")
location_result = model.unbind(sentence1, location)
print(f"  Similarity to workshop: {float(model.similarity(location_result, workshop)):.3f}  ← Location")
print(f"  Similarity to morning:  {float(model.similarity(location_result, morning)):.3f}")

print("\nKey observation:")
print("  - Each role can be queried independently")
print("  - Structure (roles) is separate from content (fillers)")

# ============================================================================
# Demo 2: Frame-Based Representations
# ============================================================================
print("\n" + "=" * 70)
print("Demo 2: Frame-Based Event Representations")
print("=" * 70)

# Define frame template for "commercial transaction"
print("\nDefining 'Commercial Transaction' frame:")
buyer = model.random(seed=110)
seller = model.random(seed=111)
goods = model.random(seed=112)
payment = model.random(seed=113)
amount = model.random(seed=114)

print("  Roles: buyer, seller, goods, payment, amount")

# Encode specific transactions
print("\nEncoding specific transactions:")

# Transaction 1: Alice bought a book from Bob for $20
alice = model.random(seed=210)
bob = model.random(seed=211)
book = model.random(seed=212)
twenty_dollars = model.random(seed=213)

transaction1_bindings = [
    model.bind(buyer, alice),
    model.bind(seller, bob),
    model.bind(goods, book),
    model.bind(amount, twenty_dollars),
]
transaction1 = model.bundle(transaction1_bindings)

print("  Transaction 1: Alice bought a book from Bob for $20")

# Transaction 2: Bob bought a laptop from Charlie for $500
charlie = model.random(seed=214)
laptop = model.random(seed=215)
five_hundred = model.random(seed=216)

transaction2_bindings = [
    model.bind(buyer, bob),
    model.bind(seller, charlie),
    model.bind(goods, laptop),
    model.bind(amount, five_hundred),
]
transaction2 = model.bundle(transaction2_bindings)

print("  Transaction 2: Bob bought a laptop from Charlie for $500")

# Query: What did Alice buy?
print("\n" + "=" * 70)
print("Query: What did Alice buy?")
print("=" * 70)

# Filter transactions where Alice is buyer
alice_as_buyer = model.bind(buyer, alice)
print("\nStep 1: Find transactions where Alice is buyer")
sim_t1 = float(model.similarity(transaction1, alice_as_buyer))
sim_t2 = float(model.similarity(transaction2, alice_as_buyer))
print(f"  Transaction 1 similarity: {sim_t1:.3f}  ← Alice is buyer")
print(f"  Transaction 2 similarity: {sim_t2:.3f}")

# Get goods from Alice's transaction
print("\nStep 2: Extract goods from Alice's transaction")
goods_result = model.unbind(transaction1, goods)
print(f"  Similarity to book:   {float(model.similarity(goods_result, book)):.3f}  ← Answer")
print(f"  Similarity to laptop: {float(model.similarity(goods_result, laptop)):.3f}")

# Query: Who sold to Bob?
print("\n" + "=" * 70)
print("Query: Who sold to Bob?")
print("=" * 70)

# Filter transactions where Bob is buyer
bob_as_buyer = model.bind(buyer, bob)
print("\nStep 1: Find transactions where Bob is buyer")
sim_t1_bob = float(model.similarity(transaction1, bob_as_buyer))
sim_t2_bob = float(model.similarity(transaction2, bob_as_buyer))
print(f"  Transaction 1 similarity: {sim_t1_bob:.3f}")
print(f"  Transaction 2 similarity: {sim_t2_bob:.3f}  ← Bob is buyer")

# Get seller from Bob's transaction
print("\nStep 2: Extract seller from Bob's transaction")
seller_result = model.unbind(transaction2, seller)
print(f"  Similarity to alice:   {float(model.similarity(seller_result, alice)):.3f}")
print(f"  Similarity to bob:     {float(model.similarity(seller_result, bob)):.3f}")
print(f"  Similarity to charlie: {float(model.similarity(seller_result, charlie)):.3f}  ← Answer")

print("\nKey observation:")
print("  - Frame templates provide reusable structure")
print("  - Multiple instances share same frame structure")
print("  - Enables structured knowledge queries")

# ============================================================================
# Demo 3: Variable Binding and Substitution
# ============================================================================
print("\n" + "=" * 70)
print("Demo 3: Variable Binding and Pattern Matching")
print("=" * 70)

# Create abstract pattern: "X gives Y to Z"
print("\nCreating abstract pattern:")
print("  Pattern: 'X gives Y to Z'")

giver = model.random(seed=120)
gift = model.random(seed=121)
receiver = model.random(seed=122)
gives_action = model.random(seed=302)

# Create pattern template
pattern_template = model.bundle([
    model.bind(agent, giver),
    model.bind(action, gives_action),
    model.bind(patient, gift),
    model.bind(receiver, receiver),
])

print("  Roles: giver, gift, receiver")

# Concrete instances
print("\nConcrete instances:")

# Instance 1: "Alice gives a book to Bob"
instance1_bindings = [
    model.bind(giver, alice),
    model.bind(gift, book),
    model.bind(receiver, bob),
]
instance1 = model.bundle(instance1_bindings)
print("  Instance 1: 'Alice gives a book to Bob'")

# Instance 2: "John gives a hammer to Mary"
instance2_bindings = [
    model.bind(giver, john),
    model.bind(gift, hammer),
    model.bind(receiver, mary),
]
instance2 = model.bundle(instance2_bindings)
print("  Instance 2: 'John gives a hammer to Mary'")

# Extract variable bindings from instance 1
print("\n" + "=" * 70)
print("Extracting variable bindings from Instance 1:")
print("=" * 70)

giver_i1 = model.unbind(instance1, giver)
gift_i1 = model.unbind(instance1, gift)
receiver_i1 = model.unbind(instance1, receiver)

print(f"\n  giver: alice    (sim={float(model.similarity(giver_i1, alice)):.3f})")
print(f"  gift: book      (sim={float(model.similarity(gift_i1, book)):.3f})")
print(f"  receiver: bob   (sim={float(model.similarity(receiver_i1, bob)):.3f})")

# Substitute variables: Replace Alice with John in instance 1
print("\n" + "=" * 70)
print("Variable substitution: Replace Alice with John")
print("=" * 70)

print("\nStep 1: Unbind Alice from giver role")
unbind_alice = model.unbind(instance1, model.bind(giver, alice))

print("Step 2: Bind John to giver role")
new_instance = model.bind(unbind_alice, model.bind(giver, john))

print("Step 3: Extract new giver")
new_giver = model.unbind(new_instance, giver)

print(f"\nNew giver similarity:")
print(f"  john:  {float(model.similarity(new_giver, john)):.3f}  ← Substituted")
print(f"  alice: {float(model.similarity(new_giver, alice)):.3f}")

print("\nKey observation:")
print("  - Variables can be extracted and rebound")
print("  - Enables pattern matching and substitution")

# ============================================================================
# Demo 4: Analogical Reasoning
# ============================================================================
print("\n" + "=" * 70)
print("Demo 4: Analogical Reasoning")
print("=" * 70)

# Create analogy: "hand is to arm as foot is to leg"
print("\nAnalogy: 'hand is to arm as foot is to leg'")
print("  Structure: part-of relationship")

# Define part-whole relation
part_of = model.random(seed=400)

# Source domain: hand-arm
hand = model.random(seed=500)
arm = model.random(seed=501)
source_relation = model.bind(model.bind(hand, part_of), arm)

print("\n  Source: hand is part_of arm")

# Target domain: foot-leg
foot = model.random(seed=502)
leg = model.random(seed=503)
target_relation = model.bind(model.bind(foot, part_of), leg)

print("  Target: foot is part_of leg")

# Test analogy: Given hand-arm and foot, find leg
print("\n" + "=" * 70)
print("Analogical inference: Given 'hand-arm' and 'foot', find '?'")
print("=" * 70)

# Create source structure
source = model.bind(model.bind(hand, part_of), arm)

# Create target structure with foot
target_query = model.bind(foot, part_of)

# Bundle all known relations
knowledge = model.bundle([source_relation, target_relation])

# Query: What is foot part of?
answer = model.unbind(model.unbind(knowledge, foot), part_of)

print("\nSimilarity to body parts:")
print(f"  hand: {float(model.similarity(answer, hand)):.3f}")
print(f"  arm:  {float(model.similarity(answer, arm)):.3f}")
print(f"  foot: {float(model.similarity(answer, foot)):.3f}")
print(f"  leg:  {float(model.similarity(answer, leg)):.3f}  ← Analogical answer!")

print("\nKey observation:")
print("  - Structural relationships can be transferred across domains")
print("  - Analogical reasoning emerges from compositional operations")

# ============================================================================
# Demo 5: Complex Query Answering with ItemStore
# ============================================================================
print("\n" + "=" * 70)
print("Demo 5: Complex Query Answering")
print("=" * 70)

# Build a knowledge base of facts
print("\nBuilding knowledge base with multiple facts:")

# Create ItemStore for entity lookups
entities_store = ItemStore(model)
entities_store.add("alice", alice)
entities_store.add("bob", bob)
entities_store.add("charlie", charlie)
entities_store.add("john", john)
entities_store.add("mary", mary)

# Keep dict for direct lookups
entities_dict = {
    "alice": alice,
    "bob": bob,
    "charlie": charlie,
    "john": john,
    "mary": mary
}

# Facts:
facts = []

# alice likes bob
likes = model.random(seed=401)
facts.append(model.bind(model.bind(alice, likes), bob))
print("  Fact 1: alice likes bob")

# bob likes charlie
facts.append(model.bind(model.bind(bob, likes), charlie))
print("  Fact 2: bob likes charlie")

# charlie likes alice (cycle!)
facts.append(model.bind(model.bind(charlie, likes), alice))
print("  Fact 3: charlie likes alice")

# john is_friend_of mary
is_friend_of = model.random(seed=402)
facts.append(model.bind(model.bind(john, is_friend_of), mary))
print("  Fact 4: john is_friend_of mary")

# Bundle into knowledge base
kb = model.bundle(facts)
print("\nKnowledge base created")

# Query 1: Who does Bob like?
print("\n" + "=" * 70)
print("Query 1: Who does Bob like?")
print("=" * 70)

bob_likes = model.unbind(model.unbind(kb, bob), likes)
result = entities_store.query(bob_likes, k=1)  # Returns list of (label, similarity) tuples
answer1, sim1 = result[0]  # Extract first result
print(f"  Answer: {answer1} (similarity={sim1:.3f})")

# Query 2: Who likes Alice?
print("\n" + "=" * 70)
print("Query 2: Who likes Alice? (reverse query)")
print("=" * 70)

# For reverse query, need to find who has alice as target
# Check each entity
print("\nChecking each entity:")
for name in ["alice", "bob", "charlie"]:
    entity = entities_dict[name]
    query = model.unbind(model.unbind(kb, entity), likes)
    sim_alice = float(model.similarity(query, alice))
    marker = "  ← Answer!" if sim_alice > 0.3 else ""
    print(f"  {name} likes ?: similarity to alice = {sim_alice:.3f}{marker}")

print("\nKey observation:")
print("  - ItemStore enables efficient entity retrieval")
print("  - Complex queries combine unbinding with similarity search")
print("  - Knowledge base supports bidirectional queries")

# ============================================================================
# Summary
# ============================================================================
print("\n" + "=" * 70)
print("Summary: Symbolic Reasoning Key Takeaways")
print("=" * 70)
print()
print("✓ Role-filler binding: Separates structure from content")
print("✓ Frame-based representation: Reusable templates with variable slots")
print("✓ Variable binding: Extract and substitute fillers")
print("✓ Analogical reasoning: Transfer structure across domains")
print("✓ Complex queries: Combine unbinding with ItemStore lookups")
print()
print("Core pattern:")
print("  1. Define roles: abstract slots (agent, patient, location, ...)")
print("  2. Bind fillers: concrete instances to roles")
print("  3. Bundle: combine all role-filler pairs")
print("  4. Query: unbind roles to retrieve fillers")
print("  5. Reason: compose operations for complex inferences")
print()
print("Applications:")
print("  - Natural language understanding: Semantic role labeling")
print("  - Knowledge representation: Frames, scripts, schemas")
print("  - Planning: Action representations with preconditions/effects")
print("  - Cognitive modeling: Human-like structured reasoning")
print()
print("Advantages of HDC approach:")
print("  - Noise tolerance: Graceful degradation")
print("  - Compositional: Build complex from simple operations")
print("  - Distributed: No brittle symbolic pointers")
print("  - Brain-like: Biologically plausible representations")
print()
print("Next steps:")
print("  → 24_app_working_memory.py - Reasoning with cleanup")
print("  → 25_app_integration_patterns.py - Combine symbolic + subsymbolic")
print("  → 18_encoders_graph.py - Graph encoding foundations")
print()
print("=" * 70)