🧠 Advanced Reasoning Systems
Advanced reasoning systems combine symbolic AI, causal inference, and meta-learning to create AI that can understand cause-and-effect relationships, perform logical deduction, and quickly adapt to new domains with minimal data.
Symbolic AI
Logic-based reasoning and knowledge representation
Causal Inference
Understanding cause-and-effect from observational data
Meta-Learning
Learning to learn - rapid adaptation to new tasks
Choose Reasoning Domain
Symbolic AI & Logic
Knowledge representation, inference engines, and logical reasoning systems
Complexity:High
Implementation:6-12 months
Causal Inference
Understanding cause-and-effect relationships from observational data
Complexity:Very High
Implementation:8-18 months
Meta-Learning
Learning to learn - quick adaptation to new tasks with minimal data
Complexity:Very High
Implementation:12-24 months
Symbolic AI & Logic
Key Applications
Expert Systems
Automated Theorem Proving
Knowledge Graphs
Rule-based AI
Implementation Metrics
94.2%
Inference Accuracy
87.5%
Knowledge Grounding
📚 Symbolic Reasoning Engine
import numpy as np
from typing import Dict, List, Set, Tuple, Optional
from dataclasses import dataclass
from enum import Enum
import networkx as nx
class LogicalOperator(Enum):
AND = "∧"
OR = "∨"
NOT = "¬"
IMPLIES = "→"
BICONDITIONAL = "↔"
EXISTS = "∃"
FORALL = "∀"
@dataclass
class Predicate:
name: str
arguments: List[str]
negated: bool = False
def __str__(self):
args_str = "(" + ", ".join(self.arguments) + ")"
prefix = "¬" if self.negated else ""
return f"{prefix}{self.name}{args_str}"
@dataclass
class Rule:
premises: List[Predicate]
conclusion: Predicate
confidence: float = 1.0
def __str__(self):
premises_str = " ∧ ".join(str(p) for p in self.premises)
return f"{premises_str} → {self.conclusion}"
class SymbolicReasoningEngine:
"""
Advanced symbolic reasoning system with logical inference,
knowledge representation, and explanation capabilities.
"""
def __init__(self):
self.knowledge_base: Set[Predicate] = set()
self.rules: List[Rule] = []
self.inference_history: List[Dict] = []
self.explanation_tree = nx.DiGraph()
def add_fact(self, fact: Predicate, confidence: float = 1.0):
"""Add a fact to the knowledge base with confidence."""
self.knowledge_base.add(fact)
self.explanation_tree.add_node(str(fact),
type='fact',
confidence=confidence)
def add_rule(self, rule: Rule):
"""Add an inference rule to the system."""
self.rules.append(rule)
def ground_symbols(self, natural_language: str) -> List[Predicate]:
"""
Convert natural language to logical predicates.
This is a simplified version - real systems use sophisticated NLP.
"""
predicates = []
# Simple pattern matching for demonstration
if "bird" in natural_language.lower():
if "can fly" in natural_language.lower():
predicates.append(Predicate("CanFly", ["x"]))
predicates.append(Predicate("Bird", ["x"]))
if "penguin" in natural_language.lower():
predicates.append(Predicate("Penguin", ["x"]))
predicates.append(Predicate("Bird", ["x"]))
predicates.append(Predicate("CanFly", ["x"], negated=True))
return predicates
def unify(self, p1: Predicate, p2: Predicate) -> Optional[Dict[str, str]]:
"""
Unification algorithm for predicate matching.
Returns substitution if unification succeeds.
"""
if p1.name != p2.name or p1.negated != p2.negated:
return None
if len(p1.arguments) != len(p2.arguments):
return None
substitution = {}
for arg1, arg2 in zip(p1.arguments, p2.arguments):
# Variable (starts with lowercase) vs constant unification
if arg1.islower() and not arg2.islower():
if arg1 in substitution and substitution[arg1] != arg2:
return None
substitution[arg1] = arg2
elif arg2.islower() and not arg1.islower():
if arg2 in substitution and substitution[arg2] != arg1:
return None
substitution[arg2] = arg1
elif arg1 != arg2:
return None
return substitution
def forward_chaining(self, max_iterations: int = 100) -> List[Predicate]:
"""
Forward chaining inference algorithm.
Derives new facts from existing knowledge and rules.
"""
new_facts = []
iterations = 0
while iterations < max_iterations:
iteration_facts = []
for rule in self.rules:
# Try to match all premises
substitutions = [{}]
for premise in rule.premises:
new_substitutions = []
for substitution in substitutions:
instantiated_premise = self.apply_substitution(
premise, substitution)
# Check if premise matches any fact in KB
for fact in self.knowledge_base:
unification = self.unify(instantiated_premise, fact)
if unification is not None:
# Combine substitutions
combined_sub = {**substitution, **unification}
new_substitutions.append(combined_sub)
substitutions = new_substitutions
if not substitutions:
break
# Apply rule if all premises matched
for substitution in substitutions:
conclusion = self.apply_substitution(
rule.conclusion, substitution)
if conclusion not in self.knowledge_base:
self.knowledge_base.add(conclusion)
iteration_facts.append(conclusion)
new_facts.append(conclusion)
# Add to explanation tree
self.explanation_tree.add_node(
str(conclusion),
type='derived',
confidence=rule.confidence
)
if not iteration_facts:
break
iterations += 1
return new_facts
# Usage Example
def demonstrate_symbolic_reasoning():
"""Demonstrate the symbolic reasoning system."""
engine = SymbolicReasoningEngine()
# Add facts to knowledge base
engine.add_fact(Predicate("Bird", ["Tweety"]))
engine.add_fact(Predicate("Penguin", ["Pingu"]))
engine.add_fact(Predicate("Bird", ["Pingu"]))
# Add rules
engine.add_rule(Rule(
premises=[Predicate("Bird", ["x"])],
conclusion=Predicate("CanFly", ["x"]),
confidence=0.9
))
# Perform forward chaining
new_facts = engine.forward_chaining()
print(f"Derived {len(new_facts)} new facts")
return {
"facts_derived": len(new_facts),
"knowledge_base_size": len(engine.knowledge_base)
}
🧠 Key Insight: Symbolic reasoning systems excel at logical deduction, explanation generation, and handling structured knowledge domains where explicit reasoning rules are important.
🌐 Causal Inference Engine
import numpy as np
import pandas as pd
from typing import Dict, List, Tuple, Optional, Set
from dataclasses import dataclass
from scipy import stats
import networkx as nx
from sklearn.linear_model import LinearRegression
@dataclass
class CausalEdge:
"""Represents a causal relationship between variables."""
cause: str
effect: str
strength: float
confidence: float
mechanism: str = "unknown"
class CausalGraph:
"""Directed Acyclic Graph (DAG) for causal relationships."""
def __init__(self):
self.graph = nx.DiGraph()
self.confounders: Dict[Tuple[str, str], Set[str]] = {}
def add_causal_edge(self, edge: CausalEdge):
"""Add a causal edge to the graph."""
self.graph.add_edge(edge.cause, edge.effect,
strength=edge.strength,
confidence=edge.confidence,
mechanism=edge.mechanism)
def get_confounders(self, treatment: str, outcome: str) -> Set[str]:
"""Identify confounding variables using backdoor criterion."""
confounders = set()
# Find all paths from treatment to outcome
try:
paths = list(nx.all_simple_paths(self.graph, treatment, outcome))
# Identify backdoor paths (paths that go into treatment)
for node in self.graph.nodes():
if (node != treatment and node != outcome and
nx.has_path(self.graph, node, treatment) and
nx.has_path(self.graph, node, outcome)):
confounders.add(node)
except nx.NetworkXNoPath:
pass
return confounders
class CausalInferenceEngine:
"""
Advanced causal inference system implementing multiple methods
for causal discovery, effect estimation, and counterfactual reasoning.
"""
def __init__(self):
self.causal_graph = CausalGraph()
self.data: Optional[pd.DataFrame] = None
self.discovered_edges: List[CausalEdge] = []
def load_data(self, data: pd.DataFrame):
"""Load observational data for causal analysis."""
self.data = data
def pc_algorithm(self, alpha: float = 0.05) -> CausalGraph:
"""
PC algorithm for causal discovery from observational data.
Implements constraint-based causal structure learning.
"""
if self.data is None:
raise ValueError("No data loaded")
variables = list(self.data.columns)
n_vars = len(variables)
# Initialize complete undirected graph
graph = nx.Graph()
graph.add_nodes_from(variables)
# Add all possible edges
for i in range(n_vars):
for j in range(i + 1, n_vars):
graph.add_edge(variables[i], variables[j])
# Phase 1: Remove edges based on conditional independence tests
max_conditioning_set_size = min(n_vars - 2, 3) # Limit for efficiency
for conditioning_size in range(max_conditioning_set_size + 1):
edges_to_remove = []
for edge in list(graph.edges()):
var1, var2 = edge
# Find all possible conditioning sets
neighbors = set(graph.neighbors(var1)) | set(graph.neighbors(var2))
neighbors.discard(var1)
neighbors.discard(var2)
if len(neighbors) >= conditioning_size:
from itertools import combinations
for conditioning_set in combinations(neighbors, conditioning_size):
# Test conditional independence
p_value = self._conditional_independence_test(
var1, var2, list(conditioning_set))
if p_value > alpha:
edges_to_remove.append(edge)
break
# Remove edges that failed independence test
for edge in edges_to_remove:
if graph.has_edge(*edge):
graph.remove_edge(*edge)
# Phase 2: Orient edges to create DAG
dag = self._orient_edges(graph)
# Convert to causal graph
causal_graph = CausalGraph()
for edge in dag.edges():
causal_edge = CausalEdge(
cause=edge[0],
effect=edge[1],
strength=self._estimate_edge_strength(edge[0], edge[1]),
confidence=0.8 # Simplified confidence estimate
)
causal_graph.add_causal_edge(causal_edge)
self.causal_graph = causal_graph
return causal_graph
def estimate_treatment_effect(self, treatment: str, outcome: str,
confounders: List[str] = None) -> Dict:
"""
Estimate causal effect using adjustment for confounders.
"""
if confounders is None:
confounders = list(self.causal_graph.get_confounders(treatment, outcome))
# Simple linear regression with confounders
features = [treatment] + confounders
X = self.data[features]
y = self.data[outcome]
reg = LinearRegression().fit(X, y)
treatment_effect = reg.coef_[0] # Coefficient of treatment
# Estimate confidence interval (simplified)
residuals = y - reg.predict(X)
mse = np.mean(residuals ** 2)
se = np.sqrt(mse / len(y))
ci_lower = treatment_effect - 1.96 * se
ci_upper = treatment_effect + 1.96 * se
return {
"treatment_effect": treatment_effect,
"confidence_interval": [ci_lower, ci_upper],
"confounders_adjusted": confounders,
"r_squared": reg.score(X, y)
}
def counterfactual_reasoning(self, individual_data: Dict,
treatment: str, outcome: str,
treatment_value: float) -> Dict:
"""
Perform counterfactual reasoning: What would have happened
if this individual received a different treatment?
"""
# Simplified counterfactual estimation
# Real implementation would use more sophisticated methods
# Create counterfactual scenario
counterfactual_data = individual_data.copy()
counterfactual_data[treatment] = treatment_value
# Use learned model to predict counterfactual outcome
features = [col for col in self.data.columns if col != outcome]
X_train = self.data[features]
y_train = self.data[outcome]
reg = LinearRegression().fit(X_train, y_train)
current_features = [individual_data[var] for var in features]
counterfactual_features = [counterfactual_data[var] for var in features]
actual_prediction = reg.predict([current_features])[0]
counterfactual_prediction = reg.predict([counterfactual_features])[0]
return {
"actual_outcome": individual_data.get(outcome, "unknown"),
"predicted_outcome": actual_prediction,
"counterfactual_outcome": counterfactual_prediction,
"treatment_effect": counterfactual_prediction - actual_prediction,
"treatment_changed": {
"from": individual_data[treatment],
"to": treatment_value
}
}
# Usage Example
def demonstrate_causal_inference():
"""Demonstrate the causal inference system."""
# Generate synthetic data
np.random.seed(42)
n_samples = 1000
# True causal model: Z -> X -> Y, Z -> Y
Z = np.random.normal(0, 1, n_samples) # Confounder
X = 2 * Z + np.random.normal(0, 0.5, n_samples) # Treatment
Y = 1.5 * X + 3 * Z + np.random.normal(0, 0.3, n_samples) # Outcome
data = pd.DataFrame({'Z': Z, 'X': X, 'Y': Y})
# Initialize causal inference engine
engine = CausalInferenceEngine()
engine.load_data(data)
# Discover causal structure
causal_graph = engine.pc_algorithm(alpha=0.05)
# Estimate treatment effect
treatment_effect = engine.estimate_treatment_effect('X', 'Y', ['Z'])
return {
"discovered_edges": len(causal_graph.graph.edges()),
"treatment_effect": treatment_effect
}
🌐 Key Insight: Causal inference enables understanding cause-and-effect relationships, crucial for making informed decisions and policy recommendations from observational data.
🎯 Meta-Learning Framework
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
from typing import Dict, List, Tuple, Optional, Callable
from dataclasses import dataclass
from abc import ABC, abstractmethod
import copy
@dataclass
class Task:
"""Represents a learning task with training and test data."""
name: str
X_train: np.ndarray
y_train: np.ndarray
X_test: np.ndarray
y_test: np.ndarray
task_type: str = "classification" # or "regression"
class MetaLearner(ABC):
"""Abstract base class for meta-learning algorithms."""
@abstractmethod
def meta_train(self, tasks: List[Task]) -> Dict:
"""Train the meta-learner on a distribution of tasks."""
pass
@abstractmethod
def adapt(self, task: Task, num_adaptation_steps: int = 5) -> nn.Module:
"""Adapt to a new task with few examples."""
pass
class MAML(MetaLearner):
"""
Model-Agnostic Meta-Learning (MAML) implementation.
Learns good parameter initialization for fast adaptation.
"""
def __init__(self, model: nn.Module, inner_lr: float = 0.01,
meta_lr: float = 0.001):
self.model = model
self.inner_lr = inner_lr
self.meta_lr = meta_lr
self.meta_optimizer = optim.Adam(self.model.parameters(), lr=meta_lr)
def inner_loop(self, task: Task, num_steps: int = 5) -> Tuple[nn.Module, float]:
"""
Perform inner loop adaptation on a single task.
Returns adapted model and final loss.
"""
# Create a copy of the model for adaptation
adapted_model = copy.deepcopy(self.model)
# Convert data to tensors
X_train = torch.FloatTensor(task.X_train)
y_train = torch.FloatTensor(task.y_train)
# Inner loop optimization
inner_optimizer = optim.SGD(adapted_model.parameters(), lr=self.inner_lr)
for step in range(num_steps):
inner_optimizer.zero_grad()
predictions = adapted_model(X_train)
if task.task_type == "classification":
loss = nn.CrossEntropyLoss()(predictions, y_train.long())
else:
loss = nn.MSELoss()(predictions.squeeze(), y_train)
loss.backward()
inner_optimizer.step()
return adapted_model, loss.item()
def meta_train(self, tasks: List[Task], num_epochs: int = 1000) -> Dict:
"""
Meta-training using MAML algorithm.
"""
meta_losses = []
for epoch in range(num_epochs):
epoch_meta_loss = 0.0
# Sample batch of tasks
task_batch = np.random.choice(tasks, size=min(8, len(tasks)), replace=False)
meta_gradients = []
for task in task_batch:
# Inner loop: adapt to task
adapted_model, _ = self.inner_loop(task, num_steps=5)
# Compute meta-loss on query set
X_test = torch.FloatTensor(task.X_test)
y_test = torch.FloatTensor(task.y_test)
meta_predictions = adapted_model(X_test)
if task.task_type == "classification":
meta_loss = nn.CrossEntropyLoss()(meta_predictions, y_test.long())
else:
meta_loss = nn.MSELoss()(meta_predictions.squeeze(), y_test)
# Compute gradients w.r.t. original parameters
meta_gradients.append(torch.autograd.grad(
meta_loss, self.model.parameters(), retain_graph=True))
epoch_meta_loss += meta_loss.item()
# Meta-update: average gradients and update original model
self.meta_optimizer.zero_grad()
for i, param in enumerate(self.model.parameters()):
# Average gradients across tasks
avg_grad = torch.stack([grads[i] for grads in meta_gradients]).mean(dim=0)
param.grad = avg_grad
self.meta_optimizer.step()
avg_meta_loss = epoch_meta_loss / len(task_batch)
meta_losses.append(avg_meta_loss)
if epoch % 100 == 0:
print(f"Epoch {epoch}, Meta-loss: {avg_meta_loss:.4f}")
return {
"meta_losses": meta_losses,
"final_meta_loss": meta_losses[-1],
"num_epochs": num_epochs
}
def adapt(self, task: Task, num_adaptation_steps: int = 5) -> nn.Module:
"""
Adapt the meta-learned model to a new task.
"""
adapted_model, final_loss = self.inner_loop(task, num_adaptation_steps)
return adapted_model
class MetaLearningFramework:
"""
Comprehensive meta-learning framework with multiple algorithms
and evaluation capabilities.
"""
def __init__(self):
self.meta_learners: Dict[str, MetaLearner] = {}
self.task_generator = TaskGenerator()
self.evaluation_results = {}
def register_meta_learner(self, name: str, meta_learner: MetaLearner):
"""Register a meta-learning algorithm."""
self.meta_learners[name] = meta_learner
def generate_task_distribution(self, num_tasks: int = 100) -> List[Task]:
"""Generate a distribution of related tasks."""
return self.task_generator.generate_sine_wave_tasks(num_tasks)
def few_shot_evaluation(self, meta_learner: MetaLearner,
test_tasks: List[Task],
shots: List[int] = [1, 5, 10]) -> Dict:
"""
Evaluate meta-learner on few-shot learning tasks.
"""
results = {}
for num_shots in shots:
shot_results = []
for task in test_tasks:
# Create few-shot version of task
if len(task.X_train) >= num_shots:
# Sample few-shot support set
indices = np.random.choice(len(task.X_train),
size=num_shots, replace=False)
few_shot_task = Task(
name=f"{task.name}_{num_shots}shot",
X_train=task.X_train[indices],
y_train=task.y_train[indices],
X_test=task.X_test,
y_test=task.y_test,
task_type=task.task_type
)
# Adapt and evaluate
adapted_model = meta_learner.adapt(few_shot_task)
# Evaluate on test set
X_test = torch.FloatTensor(task.X_test)
y_test = torch.FloatTensor(task.y_test)
with torch.no_grad():
predictions = adapted_model(X_test)
if task.task_type == "classification":
pred_labels = torch.argmax(predictions, dim=1)
accuracy = (pred_labels == y_test.long()).float().mean().item()
shot_results.append(accuracy)
else:
mse = nn.MSELoss()(predictions.squeeze(), y_test).item()
shot_results.append(mse)
results[f"{num_shots}_shot"] = {
"mean": np.mean(shot_results),
"std": np.std(shot_results),
"individual_results": shot_results
}
return results
class TaskGenerator:
"""Generate synthetic tasks for meta-learning experiments."""
def generate_sine_wave_tasks(self, num_tasks: int) -> List[Task]:
"""Generate regression tasks based on sine waves with different parameters."""
tasks = []
for i in range(num_tasks):
# Random sine wave parameters
amplitude = np.random.uniform(0.1, 5.0)
frequency = np.random.uniform(0.5, 2.0)
phase = np.random.uniform(0, 2 * np.pi)
# Generate data
X_train = np.random.uniform(-5, 5, (20, 1))
y_train = amplitude * np.sin(frequency * X_train.flatten() + phase)
X_test = np.random.uniform(-5, 5, (20, 1))
y_test = amplitude * np.sin(frequency * X_test.flatten() + phase)
# Add noise
y_train += np.random.normal(0, 0.1, y_train.shape)
y_test += np.random.normal(0, 0.1, y_test.shape)
task = Task(
name=f"sine_task_{i}",
X_train=X_train,
y_train=y_train,
X_test=X_test,
y_test=y_test,
task_type="regression"
)
tasks.append(task)
return tasks
# Usage Example
def demonstrate_meta_learning():
"""Demonstrate the meta-learning framework."""
# Create simple neural network for MAML
model = nn.Sequential(
nn.Linear(1, 40),
nn.ReLU(),
nn.Linear(40, 40),
nn.ReLU(),
nn.Linear(40, 1)
)
# Initialize meta-learning framework
framework = MetaLearningFramework()
# Create meta-learners
maml = MAML(model, inner_lr=0.01, meta_lr=0.001)
framework.register_meta_learner("MAML", maml)
# Generate tasks
train_tasks = framework.generate_task_distribution(num_tasks=50)
test_tasks = framework.generate_task_distribution(num_tasks=20)
# Meta-train MAML
maml_results = maml.meta_train(train_tasks, num_epochs=500)
# Evaluate few-shot performance
evaluation_results = framework.few_shot_evaluation(
maml, test_tasks, shots=[1, 5, 10])
return {
"meta_training_loss": maml_results["final_meta_loss"],
"few_shot_evaluation": evaluation_results,
"num_train_tasks": len(train_tasks),
"num_test_tasks": len(test_tasks)
}
🎯 Key Insight: Meta-learning enables rapid adaptation to new tasks with minimal data, crucial for building AI systems that can quickly learn new skills and domains.
📚 Advanced Reasoning Systems Resources
Symbolic AI & Knowledge Representation
- • Russell & Norvig: Artificial Intelligence - A Modern Approach (Logical Agents)
- • Description Logic and Semantic Web Technologies
- • Prolog Programming and Logic Programming Paradigms
- • Ontology Engineering and Knowledge Graphs
Causal Inference Methods
- • Judea Pearl: Causality - Models, Reasoning, and Inference
- • The Book of Why: The New Science of Cause and Effect
- • DoWhy Python Library for Causal Inference
- • PC Algorithm and Constraint-based Causal Discovery
Meta-Learning Algorithms
- • Model-Agnostic Meta-Learning (MAML) Papers
- • Prototypical Networks for Few-shot Learning
- • Learning to Learn: Gradient Descent by Gradient Descent
- • Meta-Learning with Memory-Augmented Neural Networks
Advanced Reasoning Applications
- • Automated Theorem Proving Systems
- • Planning and Scheduling in AI
- • Commonsense Reasoning and Knowledge Bases
- • Explainable AI and Interpretable Machine Learning
💡 Advanced Reasoning Mastery Path
Theoretical Foundations
- • First-order logic and predicate calculus
- • Causal graphical models and do-calculus
- • Bayesian reasoning and uncertainty
- • Computational learning theory
Practical Applications
- • Expert systems and knowledge-based AI
- • Policy evaluation and recommendation systems
- • Few-shot learning for new domains
- • Automated scientific discovery
📝 Advanced Reasoning Systems Quiz
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