Reasoning Paradigms to AI Implementations
| Reasoning Paradigm | Core Principles | AI Implementation | Examples/Technologies |
|---|---|---|---|
| 1. Classical Deductive Reasoning | Identity, Non-Contradiction, Excluded Middle, Valid Inference, Truth Preservation | Symbolic logic systems; rule-based engines; logic programming | Prolog, Datalog, Theorem Provers (e.g., Coq, Isabelle), SAT/SMT solvers, OWL reasoners (e.g., Pellet) |
| 2. Probabilistic Reasoning | Probability coherence, Bayes’ Rule, Total Evidence, Updating, Calibration | Probabilistic graphical models, Bayesian networks, probabilistic programming | PyMC, Stan, Edward, TensorFlow Probability, DeepProbLog, Bayesian networks in diagnostics |
| 3. Defeasible / Non-Monotonic Reasoning | Defeasibility, Specificity, Priority of Recent Info, Consistency Maintenance | Default reasoning systems; non-monotonic logics; belief revision systems | Answer Set Programming (ASP), Circumscription, Reiter’s Default Logic, Truth Maintenance Systems |
| 4. Abductive Reasoning | Best Explanation, Simplicity, Coherence with Evidence, Explanatory Power | Model selection, hypothesis generation, explanation-based learning (EBL) | Logic-based abduction in AI (e.g., abductive logic programming), Explainable AI (XAI), COMET (commonsense) |
| 5. Analogical Reasoning | Structural Similarity, Relevance of Mapping, Systematicity | Structure-mapping engines, embedding-based similarity, case-based reasoning (CBR) | SME (Structure-Mapping Engine), CBR systems in law/medicine, analogy modules in neural networks |
| 6. Causal Reasoning | Temporal Precedence, Interventions, Counterfactuals, Covariation | Causal models, structural causal models (SCMs), counterfactual simulators | Judea Pearl’s do-calculus, CausalNex (Python), Microsoft’s DoWhy, GNN-based causal discovery |
| 7. Commonsense / Intuitive Reasoning | Heuristics, Typicality, Availability, Satisficing, Gradience | Knowledge graphs, script-based models, pretrained language models with implicit knowledge | ConceptNet, ATOMIC, COMET, GPT-4, LLaMA 3, PaLM-E, DeepMind’s AlphaCode reasoning under heuristics |
| 8. Neural and Deep Learning-Based Reasoning | Gradient reasoning, representation learning, pattern extraction | Neural networks with attention, transformers, self-consistency sampling, chain-of-thought prompting | GPT-4, Claude, Gemini, Tree-of-Thoughts (ToT), ReAct, Toolformer, CoT prompting in LLMs |
| 9. Hybrid Neuro-Symbolic Reasoning | Symbolic-connectionist integration, discrete-continuous interface | Models that combine neural representations with symbolic logic or rules | DeepProbLog, Logic Tensor Networks, Neuro-Symbolic Concept Learner, OpenCog, IBM’s Neuro-Symbolic AI |
| 10. Decision-Theoretic Reasoning | Utility Maximization, Trade-offs, Expected Value, Cost of Actions | Markov Decision Processes (MDPs), Reinforcement Learning, POMDPs | AlphaZero, MuZero, OpenAI Gym environments, Bandit Algorithms, Dyna-Q, Deep Q-Networks (DQNs) |
| 11. Ethical and Moral Reasoning | Moral principles, trade-offs, harm minimization, deontic logic | Simulated moral dilemmas, multi-objective decision-making, rule-based ethical modules | MIT Moral Machine simulations, Moral Choice Machine, deontic logics in robotics and autonomous vehicle AI |
Detailed Notes by Paradigm
1. Classical Deductive Reasoning in AI
- Implemented through symbolic AI, where rules and facts are explicitly represented.
- Used in expert systems, semantic web ontologies, and automated theorem provers.
- Limitations include brittleness and poor handling of uncertainty.
2. Probabilistic Reasoning
- Central to machine learning, especially in domains with noise or uncertainty (e.g., sensor fusion).
- Uses Bayesian networks, hidden Markov models, and variational inference.
- Employed in NLP (e.g., topic modeling), medical diagnosis, and robotics.
3. Defeasible Reasoning
- Common in legal AI, real-world planning, and uncertain environments.
- Logic programming languages like Answer Set Programming allow retractable assumptions.
- Useful when knowledge is incomplete or evolving.
4. Abductive Reasoning
- Models used to infer causes or hypotheses from effects.
- Often employed in diagnosis systems, scientific discovery models, and explanation-based learning.
- Forms part of explainable AI when models generate natural-language justifications for predictions.
5. Analogical Reasoning
- Simulated using embedding similarity in vector space (e.g., cosine similarity in word2vec).
- CBR systems rely on retrieving and adapting solutions from previous similar cases.
- Also found in analogy-based tutoring systems and educational software.
6. Causal Reasoning
- Growing rapidly with causal discovery algorithms, interventional models, and counterfactual simulators.
- Key in fairness, interpretability, and robustness of AI systems.
- Employed in causal inference pipelines for economics, epidemiology, and social sciences.
7. Commonsense Reasoning
- AI systems trained on structured knowledge bases and narrative structures.
- Emerging LLMs like GPT-4 demonstrate implicit commonsense via massive pretraining.
- Used in story completion, dialogue systems, and robot planning.
8. Neural-Based Reasoning
- Transformers (e.g., GPT, BERT) use self-attention to simulate reasoning sequences.
- Techniques like chain-of-thought (CoT) and tree-of-thoughts explicitly model reasoning steps.
- Self-consistency sampling improves robustness of model-generated answers.
9. Neuro-Symbolic Reasoning
- Integrates symbolic logic with neural nets for interpretable and flexible reasoning.
- Useful in vision-language reasoning, theorem proving with learned guidance, and semantic parsing.
10. Decision-Theoretic Reasoning
- Employed in reinforcement learning (RL) to model agents optimizing long-term rewards.
- Algorithms include Q-learning, policy gradients, and Monte Carlo Tree Search.
- Critical in game AI (e.g., AlphaGo), robotics, and autonomous systems.
11. Ethical and Moral Reasoning
- Simulated via value alignment models, ethical rule-checking systems, or trade-off-based multi-objective optimization.
- Still an active area of research, especially in autonomous vehicles, AI governance, and AI for law.
Summary
AI systems today implement a wide variety of reasoning types, each grounded in different foundational principles:
- Symbolic systems reflect formal deductive logic.
- Probabilistic systems manage uncertainty and update beliefs.
- Connectionist systems extract patterns and latent reasoning from data.
- Hybrid systems combine these approaches for robustness and interpretability.
- Ethical reasoning systems simulate value-based and constrained decision-making.
Understanding how each reasoning paradigm maps to technical systems provides insight into AI model behavior, capabilities, and limitations — essential for researchers, engineers, and ethicists designing intelligent systems.