I. Classical Logical Reasoning (Deductive)
- Modus Ponens
Description: If A → B and A is true, then B follows.
Applications: Formal logic systems, theorem proving, expert systems. - Modus Tollens
Description: If A → B and ¬B, then infer ¬A.
Applications: Automated reasoning, error detection, rule-based AI. - Syllogistic Reasoning
Description: Deductive reasoning using categorical premises, e.g., all A are B, C is A → C is B.
Applications: Legal reasoning, semantic reasoning in NLP. - Propositional Logic
Description: Logic involving truth-functional operators (¬, ∧, ∨, →, ↔).
Applications: Digital circuit design, logic programming. - Predicate Logic (First-order logic)
Description: Extends propositional logic with quantifiers and predicates.
Applications: Knowledge representation, semantic web, theorem proving. - Higher-order Logic
Description: Quantifies over predicates or functions, not just individuals.
Applications: Formal mathematics, type theory, advanced proof systems. - Modal Logic
Description: Handles necessity and possibility using modal operators.
Applications: AI planning, verification, belief modeling. - Temporal Logic
Description: Adds time modalities (always, eventually, etc.) to logic.
Applications: Formal verification, real-time systems, temporal databases. - Deontic Logic
Description: Formalizes obligations, permissions, and prohibitions.
Applications: Ethical AI, law modeling, policy checking. - Automated Theorem Proving
Description: Algorithms that prove mathematical/logical statements using formal systems.
Applications: Formal methods, logic engines, mathematics.
II. Probabilistic Reasoning
- Bayesian Inference
Description: Updates beliefs based on new evidence using Bayes’ theorem.
Applications: Diagnostics, spam filters, medical AI. - Bayesian Networks
Description: Graphical models representing probabilistic dependencies among variables.
Applications: Causal reasoning, decision support, risk analysis. - Hidden Markov Models (HMMs)
Description: Probabilistic models with hidden states and observable outputs.
Applications: Speech recognition, bioinformatics, time-series analysis. - Markov Networks
Description: Undirected probabilistic graphical models capturing joint distributions.
Applications: Image processing, contextual reasoning. - Monte Carlo Inference
Description: Uses random sampling to approximate probabilistic inference.
Applications: Uncertainty modeling, physics simulations. - Variational Inference
Description: Approximates intractable distributions via optimization.
Applications: Bayesian deep learning, topic modeling. - Probabilistic Programming
Description: Incorporates random variables into programming languages for model definition.
Applications: Probabilistic simulations, automated model building. - Bayesian Occam’s Razor
Description: Penalizes models with more assumptions unless strongly supported by data.
Applications: Model selection, scientific discovery.
III. Defeasible and Non-monotonic Reasoning
- Defeasible Logic
Description: Reasoning that allows conclusions to be retracted in light of new evidence.
Applications: Legal AI, commonsense reasoning. - Default Logic
Description: Allows use of defaults in the absence of conflicting information.
Applications: Legal reasoning, expert systems. - Circumscription
Description: Prefers minimal models consistent with known information.
Applications: Commonsense AI, non-monotonic knowledge bases. - Belief Revision (AGM Theory)
Description: Framework for changing beliefs systematically when new information contradicts old.
Applications: Knowledge bases, epistemic logic. - Answer Set Programming (ASP)
Description: Logic programming paradigm for solving combinatorial problems with stable models.
Applications: Planning, scheduling, knowledge representation.
IV. Abductive Reasoning
- Abductive Logic Programming
Description: Infers the best explanation for observations.
Applications: Fault diagnosis, natural language understanding. - Explanation-Based Learning (EBL)
Description: Uses generalizations of explanations from specific examples to learn.
Applications: Machine learning, XAI. - Hypothesis Ranking
Description: Orders possible explanations by likelihood or simplicity.
Applications: Scientific modeling, AI explainability. - Minimal Explanation Principle
Description: Prefers explanations that account for observations with fewest assumptions.
Applications: Cognitive science, automated discovery.
V. Analogical Reasoning
- Structure-Mapping Theory
Description: Infers analogies based on matching relational structure, not just surface similarity.
Applications: Educational AI, analogy-based problem solving. - Case-Based Reasoning (CBR)
Description: Solves new problems by adapting past solutions to similar situations.
Applications: Legal AI, diagnostics. - Analogy by Embedding Similarity
Description: Uses high-dimensional vector similarity to model analogical closeness.
Applications: NLP, recommendation systems.
VI. Causal Reasoning
- Structural Causal Models (SCMs)
Description: Graphical models with directed edges representing causal relationships.
Applications: Epidemiology, economics, policy analysis. - Interventional Reasoning (do-calculus)
Description: Computes the effect of external interventions on a system.
Applications: Causal inference, experiment design. - Counterfactual Reasoning
Description: Explores “what if” scenarios by modifying past events in models.
Applications: Law, ethics, causal analysis. - Causal Discovery Algorithms
Description: Learns causal structure from observational or interventional data.
Applications: Scientific discovery, fairness in AI.
VII. Commonsense and Intuitive Reasoning
- Script-Based Reasoning
Description: Uses stereotyped sequences of events (scripts) for inference.
Applications: Narrative understanding, dialogue systems. - ConceptNet-Based Reasoning
Description: Uses large-scale commonsense knowledge graphs for inference.
Applications: Chatbots, context-aware systems. - Prototype-Based Reasoning
Description: Uses typical examples rather than formal definitions to make inferences.
Applications: Categorization, informal reasoning. - Heuristic Reasoning
Description: Uses simplified strategies or rules of thumb.
Applications: Decision-making under time constraints. - Fast and Frugal Trees
Description: Decision trees with minimal depth for quick judgments.
Applications: Emergency decision-making, cognitive modeling.
VIII. Symbolic and Knowledge-Based Reasoning
- Ontology-Based Reasoning
Description: Uses formal representations of concepts and their relations.
Applications: Semantic web, knowledge graphs. - Semantic Reasoning Engines
Description: Deduce new knowledge from structured vocabularies and taxonomies.
Applications: Medical informatics, information integration. - Production Rules
Description: If-then rules representing knowledge.
Applications: Expert systems, planning.
IX. Neural and Deep Learning-Based Reasoning
- Transformer Attention Mechanisms
Description: Learns dependencies across input positions for reasoning.
Applications: LLMs, vision transformers. - Chain-of-Thought (CoT) Prompting
Description: Guides LLMs to reason step-by-step before final answers.
Applications: Math word problems, logic puzzles. - Tree-of-Thoughts (ToT)
Description: Explores reasoning paths as a tree structure with evaluation.
Applications: Planning, multi-step reasoning. - Graph-of-Thoughts
Description: Generalizes ToT with non-linear reasoning graphs.
Applications: Complex problem-solving, agent systems. - Self-Consistency Decoding
Description: Samples multiple reasoning paths and selects the most consistent answer.
Applications: Robust question answering. - Meta-CoT
Description: Uses a second-level reasoning model to supervise CoT.
Applications: Meta-reasoning, verification. - Self-Ask Prompting
Description: Prompts the model to ask and answer sub-questions.
Applications: Multi-hop QA. - ReAct (Reason + Act)
Description: Combines reasoning traces with real-time tool use.
Applications: Agent systems, web automation.
IX. Neural and Deep Learning-Based Reasoning
- Auto-CoT Prompting
Description: Automatically generates chain-of-thought examples from questions for model fine-tuning.
Applications: LLM training, zero-shot reasoning improvement. - LogiCoT (Logical Chain-of-Thought)
Description: Incorporates formal logical constraints into chain-of-thought reasoning.
Applications: Symbol-sensitive reasoning, verifiable logic inference. - Toolformer Agents
Description: AI models that learn when and how to use external tools during reasoning.
Applications: API-driven agents, dynamic workflows. - Retrieval-Augmented Reasoning (RAG)
Description: Uses external documents or knowledge bases to support reasoning.
Applications: Question answering, research assistants. - In-Context Learning with Demonstrations
Description: LLMs learn reasoning patterns by observing few-shot examples within a prompt.
Applications: Classification, decision-making under minimal supervision. - Graph Neural Reasoning
Description: Learns over graph structures, capturing entity and relationship semantics.
Applications: Molecule modeling, social network reasoning. - Latent Space Reasoning
Description: Logical operations or inference performed in a continuous latent embedding space.
Applications: Language modeling, symbolic regression. - Contrastive Reasoning via Embeddings
Description: Models learn to reason by distinguishing similar from dissimilar cases.
Applications: Retrieval, entailment tasks. - Visual CoT (Multimodal Chain-of-Thought)
Description: Combines image and text inputs for step-wise visual reasoning.
Applications: VQA (visual question answering), robotics. - Cross-modal Reasoning
Description: Performs inference across vision, audio, language, etc., jointly.
Applications: Multimodal assistants, embodied agents.
X. Hybrid Neuro-Symbolic Reasoning
- Neuro-Symbolic Concept Learner
Description: Learns symbolic representations from raw data for structured reasoning.
Applications: Visual understanding, interpretable AI. - Logic Tensor Networks (LTNs)
Description: Integrates logic rules with neural representations using differentiable logic.
Applications: Scene understanding, knowledge base completion. - Neural Theorem Provers
Description: Combines learning with symbolic deduction in proof tasks.
Applications: Mathematics, logic verification. - DeepProbLog
Description: Combines deep learning with probabilistic logic programming.
Applications: Visual reasoning, program synthesis. - Scallop (Differentiable Datalog)
Description: Declarative probabilistic reasoning via differentiable Datalog execution.
Applications: Interpretable program learning, knowledge-intensive NLP. - Neuro-Symbolic Relational Learning
Description: Learns relational facts and their logical rules simultaneously.
Applications: Ontology reasoning, inductive logic programming. - Symbolic AI-Augmented Planning
Description: Combines logic-based planning with LLMs or neural predictors.
Applications: Agent coordination, robotics. - Symbolic Regression
Description: Learns interpretable mathematical expressions that fit observed data.
Applications: Scientific discovery, formula extraction.
XI. Decision-Theoretic and Reinforcement Reasoning
- Markov Decision Processes (MDPs)
Description: Models agents acting in stochastic environments with states and rewards.
Applications: Control systems, reinforcement learning. - Partially Observable MDPs (POMDPs)
Description: Extends MDPs to handle uncertainty in state observation.
Applications: Autonomous navigation, medical decision-making. - Deep Reinforcement Learning (DRL)
Description: Learns policies via neural networks from interaction with environments.
Applications: Games (e.g., Go), robotics, finance. - Model-Based RL
Description: Builds internal models of environment dynamics to plan actions.
Applications: Sample-efficient learning, control. - Policy Gradient Methods
Description: Directly optimizes the agent’s policy via gradient descent.
Applications: Continuous action spaces, robotics. - Reward Shaping and Inverse RL
Description: Infers reward functions from observed behaviors.
Applications: Human imitation, ethical alignment. - RLHF (Reinforcement Learning with Human Feedback)
Description: Uses human preference data to guide learning.
Applications: LLM fine-tuning, safe AI. - DPO (Direct Preference Optimization)
Description: Optimizes AI models directly from ranked preference data.
Applications: Preference-based language generation. - Multi-agent Game-Theoretic Reasoning
Description: Models interactions among multiple decision-making agents.
Applications: Economics, competitive AI agents.
XII. Meta-Reasoning and Self-Reflective Architectures
- Meta-CoT Reasoning
Description: Higher-level reasoning system evaluates or corrects another’s reasoning chain.
Applications: Self-verification, robustness. - Self-Reflective Agents
Description: AI systems that reason about their own beliefs, goals, and actions.
Applications: Ethical agents, planning under uncertainty. - Debate-Driven Reasoning (AI Debate)
Description: Multiple models argue contrasting viewpoints to improve reliability.
Applications: Alignment, truth-seeking. - Auto-Verification Agents
Description: Models that reason about the validity of their own outputs.
Applications: Fact-checking, scientific research. - Long Context Memory Reasoning
Description: Uses extended memory (100K+ tokens) to maintain coherent reasoning.
Applications: Legal document understanding, historical analysis. - Reasoning with External Memory Systems
Description: Uses databases or vector stores to store and retrieve intermediate inferences.
Applications: Agent memory, augmented LLMs.
XIII. Cutting-Edge and Novel Reasoning Frameworks
- Tree of Thoughts (ToT) Search Algorithms
Description: Multi-step exploration with pruning and selection strategies.
Applications: Creative problem solving, planning. - Graph of Thoughts
Description: Captures reasoning paths as interconnected graphs, not linear chains.
Applications: Scientific workflows, multi-goal agents. - Function-Calling LLMs
Description: Reason by delegating sub-problems to code or external APIs.
Applications: Developer agents, simulation pipelines. - Q-Learning with Reasoning Traces
Description: Combines step-wise explanation with Q-value estimation.
Applications: Transparent reinforcement learning. - Multimodal Reasoning Transformers
Description: Integrates images, audio, and text for joint inference.
Applications: Assistive AI, VQA, robotics. - Multi-Agent Planning Architectures
Description: Distributes reasoning across agents coordinating to solve sub-tasks.
Applications: Simulation, cooperative AI. - AlphaGeometry
Description: LLM-guided symbolic reasoning in mathematical geometry.
Applications: Geometry solvers, STEM education. - Gradient-Logic Networks
Description: Combines gradients with symbolic logic inference.
Applications: Explainable neural-symbolic AI. - Value Learning for Moral Reasoning
Description: Infers moral principles from behavior or instructions.
Applications: Ethics, alignment. - Sparse Attention Reasoning Models
Description: Uses sparse context to focus reasoning on key parts of input.
Applications: Scalable transformers, efficiency. - Memory-Compressed Reasoning Transformers
Description: Reduces context complexity while maintaining logical flow.
Applications: Edge devices, long-context inference. - Self-Improving LLMs via Reflection
Description: AI models that adjust prompts or sampling based on self-evaluation.
Applications: Autonomous tutors, debugging. - Contrastive CoT
Description: Generates contrasting reasoning paths to reinforce correct inference.
Applications: Error analysis, model robustness. - Recurrent LLM Architectures
Description: Iteratively refines answers through reasoning steps.
Applications: Long conversations, multi-stage planning. - Adaptive Step Reasoning
Description: Dynamically chooses number of reasoning steps needed.
Applications: Efficiency in large model deployments. - Debate + Voting Models
Description: Generates multiple candidate arguments and selects via voting.
Applications: Legal AI, opinion summarization. - Planning-Driven LLM Agents
Description: Integrates planning algorithms (like A*) with language reasoning.
Applications: Robotics, task completion agents.