130+ Distinct Reasoning Methods and Frameworks Used In AI and Cognitive Science

AI & Cognitive Science Reasoning Methods

Probabilistic and Statistical Reasoning

• Bayesian Inference
  • Example: Updating the probability of a disease given a positive test result, incorporating prior knowledge of disease prevalence.
  • Steps: 1. Define prior probabilities based on existing knowledge. 2. Collect likelihoods from new evidence. 3. Apply Bayes’ theorem to compute posterior probabilities. 4. Interpret the updated beliefs.
• Bayesian Networks
  • Example: Modeling dependencies in medical diagnosis, where symptoms depend on underlying diseases.
  • Steps: 1. Identify variables and their dependencies. 2. Construct a directed acyclic graph (DAG). 3. Assign conditional probability tables (CPTs). 4. Perform inference using algorithms like variable elimination.
• Dynamic Bayesian Networks
  • Example: Tracking object positions over time in video surveillance.
  • Steps: 1. Extend a Bayesian network with temporal slices. 2. Define transition models between time steps. 3. Incorporate observations. 4. Use filtering or smoothing for inference.
• Hidden Markov Models (HMMs)
  • Example: Speech recognition, where hidden states represent phonemes and observations are audio features.
  • Steps: 1. Define states, transition probabilities, and emission probabilities. 2. Use the forward algorithm for likelihood computation. 3. Apply Viterbi for most likely state sequence. 4. Train with Baum-Welch (EM algorithm).
• Markov Random Fields / Markov Networks
  • Example: Image segmentation, where pixel labels depend on neighboring pixels.
  • Steps: 1. Define an undirected graph with nodes as variables. 2. Specify potential functions for cliques. 3. Normalize to get joint probabilities. 4. Use Gibbs sampling for inference.
• Monte Carlo Methods (MCMC, Importance Sampling)
  • Example: Estimating the value of π by sampling points in a square and circle.
  • Steps: 1. Define the target distribution. 2. Generate samples using Markov chains (e.g., Metropolis-Hastings). 3. Compute expectations from samples. 4. Assess convergence.
• Variational Inference
  • Example: Approximating posterior in topic modeling like LDA.
  • Steps: 1. Choose a variational family (e.g., mean-field). 2. Optimize ELBO using coordinate ascent or gradient descent. 3. Update parameters iteratively. 4. Use the approximation for predictions.
• Probabilistic Programming
  • Example: Modeling coin flips with uncertainty in fairness using languages like Pyro.
  • Steps: 1. Define a probabilistic model with priors and likelihoods. 2. Condition on observed data. 3. Run inference engines (e.g., MCMC or VI). 4. Sample from the posterior.
• Gaussian Processes for reasoning under uncertainty
  • Example: Predicting function values in regression, like stock prices.
  • Steps: 1. Specify a mean function and kernel. 2. Compute the covariance matrix. 3. Condition on observations for posterior. 4. Make predictions with uncertainty.
• Bayesian Occam’s Razor / Model Selection
  • Example: Choosing between polynomial models for data fitting, favoring simpler ones.
  • Steps: 1. Compute marginal likelihoods for models. 2. Compare using Bayes factors. 3. Select the model with highest evidence. 4. Validate on holdout data.
• Probabilistic Soft Logic
  • Example: Reasoning over noisy knowledge bases, like social network relations.
  • Steps: 1. Define weighted logical rules. 2. Relax to continuous truths. 3. Optimize the most probable explanation. 4. Infer using gradient-based methods.
• Probabilistic Relational Models
  • Example: Modeling student performance across courses with relational dependencies.
  • Steps: 1. Define entities and relations. 2. Specify probabilistic dependencies. 3. Aggregate over relations. 4. Perform joint inference.
• Hierarchical Bayesian Models
  • Example: Multi-level regression for grouped data, like schools in districts.
  • Steps: 1. Define hyperpriors for group parameters. 2. Specify individual-level models. 3. Use MCMC for posterior sampling. 4. Interpret shrinkage effects.
• Particle Filtering (Sequential Monte Carlo)
  • Example: Robot localization in dynamic environments.
  • Steps: 1. Initialize particles with weights. 2. Predict using motion model. 3. Update weights with observations. 4. Resample particles.
• Expectation-Maximization (EM) for latent variable models
  • Example: Clustering with Gaussian Mixture Models.
  • Steps: 1. Initialize parameters. 2. E-step: Compute responsibilities. 3. M-step: Update parameters. 4. Iterate until convergence.
• Deep Probabilistic Models (e.g., Variational Autoencoders)
  • Example: Generating images with latent variables in VAEs.
  • Steps: 1. Define encoder and decoder networks. 2. Optimize ELBO with reparameterization. 3. Train via backpropagation. 4. Sample from latent space.
• Statistical Relational Learning
  • Example: Link prediction in graphs with probabilistic rules.
  • Steps: 1. Represent data as relational structures. 2. Learn statistical patterns. 3. Use inference for predictions. 4. Evaluate on relational tasks.
• Probabilistic Logic Networks
  • Example: Combining logic rules with probabilities for knowledge graphs.
  • Steps: 1. Define logical atoms and rules. 2. Assign probabilities. 3. Build a network for inference. 4. Query using propagation.

Non-Monotonic and Defeasible Reasoning

• Defeasible Logic
  • Example: Legal reasoning where rules like “birds fly” can be defeated by “penguins don’t.”
  • Steps: 1. Define strict and defeasible rules. 2. Specify superiority relations. 3. Apply team defeat for conclusions. 4. Resolve conflicts.
• Default Logic
  • Example: Assuming “students are adults” unless specified otherwise.
  • Steps: 1. Define defaults with prerequisites and justifications. 2. Generate extensions. 3. Check consistency. 4. Select applicable defaults.
• Circumscription
  • Example: Minimizing abnormalities in “all birds fly except exceptions.”
  • Steps: 1. Define predicates to minimize. 2. Add circumscription axioms. 3. Use second-order logic for entailment. 4. Infer minimal models.
• Belief Revision (AGM Theory)
  • Example: Updating beliefs when new evidence contradicts, like retracting “all swans are white.”
  • Steps: 1. Represent beliefs as a set. 2. Apply expansion, contraction, revision operators. 3. Ensure postulates (e.g., success, inclusion). 4. Select minimal change.
• Autoepistemic Logic
  • Example: Self-referential beliefs like “I believe it’s raining if I don’t believe otherwise.”
  • Steps: 1. Use modal operators for beliefs. 2. Compute stable expansions. 3. Check consistency with assumptions. 4. Infer from expansions.
• Argumentation Frameworks (Dung’s Theory)
  • Example: Debating policies where arguments attack each other.
  • Steps: 1. Define arguments and attacks. 2. Compute extensions (e.g., grounded, stable). 3. Use semantics for acceptability. 4. Resolve disputes.
• Prioritized Default Reasoning
  • Example: Handling exceptions with priorities, like “fly unless injured” over general rules.
  • Steps: 1. Assign priorities to defaults. 2. Order activations. 3. Apply highest priority first. 4. Resolve inconsistencies.
• Non-Monotonic Description Logics
  • Example: Ontology reasoning with overrides, like “employees are taxed unless students.”
  • Steps: 1. Extend DL with non-monotonic operators. 2. Define typicality or defaults. 3. Compute rational closures. 4. Infer under exceptions.
• Preference-Based Reasoning
  • Example: Decision-making with ranked options, like preferring cheaper flights.
  • Steps: 1. Define preference relations. 2. Model as partial orders. 3. Use optimization for selection. 4. Handle incomparabilities.
• Defeasible Argumentation in AI
  • Example: Multi-agent negotiation where arguments can be undercut.
  • Steps: 1. Build argument trees. 2. Evaluate defeat relations. 3. Use dialectical semantics. 4. Determine winning arguments.
• Formal Argumentation for Dialogue Systems
  • Example: Chatbots debating user queries with supporting evidence.
  • Steps: 1. Define dialogue protocols. 2. Generate and attack arguments. 3. Track commitments. 4. Conclude based on burden of proof.
• Dynamic Epistemic Logic
  • Example: Modeling knowledge updates in puzzles like Muddy Children.
  • Steps: 1. Use Kripke models for knowledge. 2. Apply update operators (e.g., announcements). 3. Compute new accessibility relations. 4. Query epistemic formulas.

Abductive and Explanatory Reasoning

• Abductive Logic Programming
  • Example: Diagnosing faults in circuits by hypothesizing causes.
  • Steps: 1. Define background knowledge and abducibles. 2. Generate hypotheses to explain observations. 3. Check consistency and minimality. 4. Select best explanation.
• Explanation-Based Learning (EBL)
  • Example: Learning chess strategies from explained examples.
  • Steps: 1. Generalize from a specific example using domain theory. 2. Construct operational explanations. 3. Prune irrelevant parts. 4. Store as chunks for future use.
• Hypothesis Generation and Ranking
  • Example: Scientific discovery, generating hypotheses for data patterns.
  • Steps: 1. Enumerate possible hypotheses. 2. Score based on simplicity and fit. 3. Rank using Bayesian priors. 4. Test top ones.
• Minimal Explanation Principle
  • Example: Parsimonious diagnosis in medicine, preferring fewest causes.
  • Steps: 1. Define possible explanations. 2. Minimize the set covering observations. 3. Use Occam’s razor. 4. Validate coverage.
• Diagnostic Reasoning Models
  • Example: Troubleshooting car issues based on symptoms.
  • Steps: 1. Model system components. 2. Observe discrepancies. 3. Infer faults using consistency checks. 4. Prioritize likely diagnoses.
• Counterfactual Abduction
  • Example: “What if” scenarios in history, abducing causes for alternate outcomes.
  • Steps: 1. Define actual and counterfactual worlds. 2. Abduce changes to explain differences. 3. Use causal models. 4. Evaluate plausibility.
• Bayesian Abductive Reasoning
  • Example: Inferring hidden causes in probabilistic settings, like weather from effects.
  • Steps: 1. Define prior over hypotheses. 2. Compute likelihoods. 3. Use Bayes for posteriors. 4. Select MAP hypothesis.
• Model-Based Diagnosis
  • Example: Fault detection in software systems using behavioral models.
  • Steps: 1. Build a system model. 2. Simulate observations. 3. Find minimal hitting sets for conflicts. 4. Rank diagnoses.
• Plan Recognition via Abduction
  • Example: Inferring user intentions in assistive AI from actions.
  • Steps: 1. Define plan libraries. 2. Abduce plans explaining observed actions. 3. Score by cost or probability. 4. Predict next steps.
• Causal Abduction Models
  • Example: Abducing root causes in failure analysis.
  • Steps: 1. Use causal graphs. 2. Generate abductions along causes. 3. Check explanatory power. 4. Minimize assumptions.

Analogical and Similarity-Based Reasoning

• Structure-Mapping Theory
  • Example: Comparing solar system to atom model.
  • Steps: 1. Represent domains as relational structures. 2. Map alignments systematically. 3. Evaluate candidate inferences. 4. Score based on depth.
• Case-Based Reasoning (CBR)
  • Example: Legal precedents for new cases.
  • Steps: 1. Retrieve similar cases. 2. Reuse solutions. 3. Revise for differences. 4. Retain new case.
• Analogical Problem Solving
  • Example: Using fortress story to solve radiation tumor problem (Duncker’s).
  • Steps: 1. Encode source and target. 2. Notice analogy. 3. Map elements. 4. Adapt solution.
• Conceptual Blending
  • Example: Creating “houseboat” from house and boat concepts.
  • Steps: 1. Identify input spaces. 2. Find cross-space mappings. 3. Blend selectively. 4. Emerge new structure.
• Embedding-Based Similarity Reasoning
  • Example: Word analogies in vector spaces like king – man + woman = queen.
  • Steps: 1. Train embeddings. 2. Compute cosine similarities. 3. Perform vector arithmetic. 4. Interpret results.
• Vector Space Models for Analogy
  • Example: Image analogies using feature vectors.
  • Steps: 1. Represent items as vectors. 2. Find analogical proportions. 3. Solve for missing term. 4. Validate similarity.
• Prototype and Exemplar Reasoning
  • Example: Categorizing birds by comparing to robin prototype.
  • Steps: 1. Build prototypes from averages. 2. Compare new instances. 3. Classify by similarity. 4. Update with exemplars.
• Relational Similarity Computation
  • Example: Comparing company structures.
  • Steps: 1. Extract relations. 2. Compute graph similarities. 3. Use metrics like edit distance. 4. Rank matches.
• Graph Matching for Analogy
  • Example: Molecular analogies in chemistry.
  • Steps: 1. Represent as graphs. 2. Find subgraph isomorphisms. 3. Align nodes and edges. 4. Infer properties.
• Metaphor and Analogy in NLP
  • Example: Detecting “time is money” in text.
  • Steps: 1. Identify source/target domains. 2. Map linguistic elements. 3. Use embeddings for detection. 4. Interpret meaning.

Causal and Counterfactual Reasoning

• Structural Causal Models (SCMs)
  • Example: Modeling smoking’s effect on lung cancer.
  • Steps: 1. Define variables and functions. 2. Represent as DAG. 3. Simulate interventions. 4. Compute effects.
• Pearl’s Do-Calculus for Interventions
  • Example: Estimating treatment effects in confounded data.
  • Steps: 1. Identify query. 2. Apply rules (insertion, action/observation exchange). 3. Reduce to observable. 4. Estimate.
• Counterfactual Inference
  • Example: “What if I had taken the other job?” simulations.
  • Steps: 1. Build causal model. 2. Abduct evidence. 3. Intervene counterfactually. 4. Predict outcomes.
• Causal Discovery Algorithms
  • Example: Learning gene regulatory networks from data.
  • Steps: 1. Assume faithfulness. 2. Use PC algorithm for skeletons. 3. Orient edges. 4. Validate.
• Granger Causality
  • Example: Testing if stock A causes stock B movements.
  • Steps: 1. Fit VAR models. 2. Test restrictions. 3. Compute F-statistics. 4. Infer directionality.
• Causal Bayesian Networks
  • Example: Risk assessment in finance.
  • Steps: 1. Build BN with causal arcs. 2. Estimate parameters. 3. Perform do-interventions. 4. Query effects.
• Causal Mediation Analysis
  • Example: Decomposing education’s effect on income via skills.
  • Steps: 1. Identify mediator. 2. Estimate direct/indirect effects. 3. Use sensitivity analysis. 4. Interpret decomposition.
• Temporal Causal Models
  • Example: Time-series causation in climate data.
  • Steps: 1. Incorporate time lags. 2. Use dynamic models. 3. Discover temporal relations. 4. Forecast interventions.
• Probabilistic Causation Models
  • Example: Probabilistic causes in quantum events.
  • Steps: 1. Define cause-effect probabilities. 2. Use INUS conditions. 3. Compute contributions. 4. Assess sufficiency.
• Learning Causal Relations from Observational Data
  • Example: Identifying confounders in epidemiology.
  • Steps: 1. Collect data. 2. Use algorithms like FCI. 3. Test independence. 4. Orient causal graph.

Commonsense and Heuristic Reasoning

• Script-Based Reasoning
  • Example: Restaurant script for ordering food sequence.
  • Steps: 1. Define event sequences. 2. Match observations to script. 3. Fill gaps. 4. Predict next events.
• Frame-Based Reasoning
  • Example: Filling slots in a “birthday party” frame.
  • Steps: 1. Activate frame with trigger. 2. Instantiate slots. 3. Infer defaults. 4. Update with evidence.
• ConceptNet and Commonsense Knowledge Graphs
  • Example: Inferring “knife cuts food” from relations.
  • Steps: 1. Query graph for relations. 2. Traverse edges. 3. Score paths. 4. Integrate into reasoning.
• Heuristic Search Algorithms (A*, Beam Search)
  • Example: Pathfinding in maps with A*.
  • Steps: 1. Define state space. 2. Use heuristic for guidance. 3. Expand nodes. 4. Select optimal path.
• Fast and Frugal Trees
  • Example: Medical decisions with simple decision trees.
  • Steps: 1. Order cues by validity. 2. Build shallow tree. 3. Decide at leaves. 4. Evaluate ecologically.
• Bounded Rationality Models
  • Example: Satisficing in shopping, choosing good enough.
  • Steps: 1. Set aspiration levels. 2. Search sequentially. 3. Stop when satisfied. 4. Choose option.
• Dual Process Models (System 1 and 2 Reasoning)
  • Example: Intuitive (System 1) vs. analytical (System 2) in puzzles.
  • Steps: 1. Engage fast heuristics. 2. Monitor for errors. 3. Switch to deliberate if needed. 4. Resolve conflicts.
• Intuitive Physics Engines
  • Example: Predicting ball trajectories in games.
  • Steps: 1. Simulate mental models. 2. Apply naive physics rules. 3. Update with observations. 4. Anticipate outcomes.
• Mental Simulation for Reasoning
  • Example: Imagining outcomes of actions in planning.
  • Steps: 1. Build mental model. 2. Run forward simulations. 3. Evaluate scenarios. 4. Select best path.
• Prototype-Based Categorization
  • Example: Classifying fruits by apple-like features.
  • Steps: 1. Compute prototype averages. 2. Measure distances. 3. Assign to closest. 4. Update prototypes.

Symbolic, Knowledge-Based, and Ontological Reasoning

• Ontology-Based Reasoning
  • Example: Classifying animals in a taxonomy.
  • Steps: 1. Define classes and properties. 2. Assert individuals. 3. Use reasoners like Pellet. 4. Infer subclass relations.
• Description Logics (DL)
  • Example: Querying knowledge bases for “parents with PhD children.”
  • Steps: 1. Define concepts and roles. 2. Build TBox and ABox. 3. Check satisfiability. 4. Perform retrieval.
• Semantic Web Reasoning (OWL, RDF)
  • Example: Inferring relations in linked data.
  • Steps: 1. Model in RDF triples. 2. Add OWL axioms. 3. Use SPARQL for queries. 4. Reason with entailment.
• Production Rule Systems
  • Example: Expert systems like if-then rules for diagnosis.
  • Steps: 1. Define rules. 2. Match facts. 3. Fire rules. 4. Update working memory.
• Logic Programming (Prolog, ASP)
  • Example: Solving puzzles with Prolog queries.
  • Steps: 1. Define facts and rules. 2. Pose queries. 3. Use backtracking. 4. Find solutions.
• Knowledge Graph Reasoning
  • Example: Pathfinding in Wikipedia links.
  • Steps: 1. Embed entities. 2. Traverse relations. 3. Predict missing links. 4. Answer queries.
• Conceptual Graphs
  • Example: Representing sentences as graphs for inference.
  • Steps: 1. Parse to concepts and relations. 2. Join graphs. 3. Project for subsumption. 4. Infer new graphs.
• Constraint Satisfaction Problems (CSP)
  • Example: Sudoku solving.
  • Steps: 1. Define variables, domains, constraints. 2. Use backtracking. 3. Apply arc consistency. 4. Find assignments.
• Automated Theorem Proving
  • Example: Proving math theorems in Coq.
  • Steps: 1. Formalize axioms. 2. Use resolution or tableaux. 3. Search proof space. 4. Verify proof.
• Deductive Databases
  • Example: Querying relational data with Datalog.
  • Steps: 1. Define rules and facts. 2. Compute fixpoints. 3. Evaluate queries. 4. Optimize with magic sets.

Neural, Deep Learning, and Representation-Based Reasoning

• Transformer Attention-Based Reasoning
  • Example: Question answering in BERT models.
  • Steps: 1. Encode inputs with attention. 2. Compute key-query similarities. 3. Aggregate values. 4. Feed to layers.
• Chain-of-Thought (CoT) Prompting
  • Example: Math problems broken into steps in LLMs.
  • Steps: 1. Prompt with “think step by step.” 2. Generate intermediate reasoning. 3. Arrive at final answer. 4. Refine if needed.
• Tree-of-Thought (ToT) Reasoning
  • Example: Exploring branches in game strategies.
  • Steps: 1. Decompose problem into tree. 2. Evaluate nodes. 3. Prune poor paths. 4. Select best chain.
• Graph Neural Networks (GNNs)
  • Example: Node classification in social networks.
  • Steps: 1. Represent graph. 2. Aggregate neighbors. 3. Update embeddings. 4. Predict labels.
• Neuro-Symbolic Reasoning
  • Example: Combining NN perceptions with symbolic rules.
  • Steps: 1. Extract features neurally. 2. Map to symbols. 3. Apply logic. 4. Backpropagate.
• Deep Reinforcement Learning Reasoning
  • Example: AlphaGo’s move selection.
  • Steps: 1. Define state-action space. 2. Train policy/value nets. 3. Simulate rollouts. 4. Update with rewards.
• Latent Space Reasoning
  • Example: Interpolating in VAEs for generation.
  • Steps: 1. Encode to latent. 2. Manipulate vectors. 3. Decode outputs. 4. Interpret changes.
• Contrastive Reasoning with Embeddings
  • Example: CLIP for image-text matching.
  • Steps: 1. Compute embeddings. 2. Maximize positive similarities. 3. Minimize negatives. 4. Infer relations.
• Multimodal Reasoning Models
  • Example: Visual question answering.
  • Steps: 1. Fuse modalities. 2. Attend cross-modally. 3. Generate responses. 4. Train end-to-end.
• Self-Consistency Sampling in LLMs
  • Example: Voting on multiple CoT paths for math.
  • Steps: 1. Sample diverse reasonings. 2. Generate answers. 3. Majority vote. 4. Select consistent one.

Hybrid and Neuro-Symbolic Approaches

• Logic Tensor Networks (LTNs)
  • Example: Satisfying fuzzy logic in knowledge bases.
  • Steps: 1. Embed symbols in tensors. 2. Define logical connectives. 3. Optimize satisfaction. 4. Query embeddings.
• DeepProbLog (Deep Probabilistic Logic Programming)
  • Example: Probabilistic reasoning over images.
  • Steps: 1. Combine neural predicates with logic. 2. Approximate inference. 3. Train with gradients. 4. Sample proofs.
• Neural Theorem Provers
  • Example: Proving lemmas with NN guidance.
  • Steps: 1. Represent proofs as sequences. 2. Predict tactics. 3. Verify symbolically. 4. Iterate.
• Differentiable Programming with Logical Constraints
  • Example: Optimizing under Sudoku constraints.
  • Steps: 1. Embed constraints differentiably. 2. Define loss. 3. Gradient descent. 4. Project to feasible.
• Symbolic Regression via Neural Networks
  • Example: Discovering equations from data.
  • Steps: 1. Generate expression trees. 2. Evaluate fitness. 3. Evolve with NN. 4. Select best formula.
• Neuro-Symbolic Relational Learning
  • Example: Learning rules from relational data.
  • Steps: 1. Extract features neurally. 2. Induce symbolic rules. 3. Refine jointly. 4. Predict relations.
• Symbolic Planning with Neural Guidance
  • Example: Robot path planning with learned heuristics.
  • Steps: 1. Use NN for state evaluation. 2. Search symbolically. 3. Combine for efficiency. 4. Execute plan.
• Neuro-Symbolic Concept Learners
  • Example: Learning visual concepts with symbols.
  • Steps: 1. Perceive features. 2. Map to concepts. 3. Reason symbolically. 4. Update mappings.
• Differentiable Answer Set Programming
  • Example: Optimizing logic programs with gradients.
  • Steps: 1. Relax ASP to continuous. 2. Define objective. 3. Differentiate semantics. 4. Optimize parameters.
• Hybrid Logical Neural Architectures
  • Example: QA systems with logic layers.
  • Steps: 1. Process input neurally. 2. Apply logical modules. 3. Fuse outputs. 4. Train hybridly.

Decision-Theoretic and Reinforcement Reasoning

• Markov Decision Processes (MDPs)
  • Example: Optimal control in grid worlds.
  • Steps: 1. Define states, actions, rewards. 2. Solve Bellman equations. 3. Compute policy. 4. Execute.
• Partially Observable MDPs (POMDPs)
  • Example: Tiger problem for uncertainty.
  • Steps: 1. Add belief states. 2. Update beliefs. 3. Approximate value iteration. 4. Select actions.
• Policy Gradient Methods
  • Example: Training agents in continuous spaces.
  • Steps: 1. Parameterize policy. 2. Sample trajectories. 3. Compute gradients. 4. Update parameters.
• Model-Based Reinforcement Learning
  • Example: Learning dynamics for planning.
  • Steps: 1. Learn transition model. 2. Simulate rollouts. 3. Optimize policy. 4. Interact with environment.
• Inverse Reinforcement Learning
  • Example: Learning rewards from expert demos.
  • Steps: 1. Observe trajectories. 2. Infer reward function. 3. Maximize likelihood. 4. Derive policy.
• Reinforcement Learning with Human Feedback (RLHF)
  • Example: Fine-tuning LLMs like ChatGPT.
  • Steps: 1. Collect preferences. 2. Train reward model. 3. Optimize policy with PPO. 4. Iterate.
• Multi-agent Reinforcement Learning
  • Example: Cooperative games like soccer.
  • Steps: 1. Define joint actions. 2. Learn decentralized policies. 3. Handle non-stationarity. 4. Coordinate.
• Reward Shaping
  • Example: Guiding agents with intermediate rewards.
  • Steps: 1. Design potential functions. 2. Add to base rewards. 3. Ensure policy invariance. 4. Train.
• Q-Learning with Explanation Traces
  • Example: Explaining why an action was chosen.
  • Steps: 1. Learn Q-values. 2. Trace updates. 3. Generate explanations. 4. Visualize traces.
• Game-Theoretic Reasoning
  • Example: Nash equilibria in auctions.
  • Steps: 1. Model as game. 2. Compute strategies. 3. Find equilibria. 4. Predict outcomes.

Meta-Reasoning, Self-Reflective, and Autonomous Reasoning

• Meta-Chain-of-Thought Reasoning
  • Example: Reflecting on CoT steps in complex problems.
  • Steps: 1. Generate initial CoT. 2. Evaluate meta-level. 3. Refine reasoning. 4. Iterate.
• Self-Reflective Agent Architectures
  • Example: Agents critiquing their own plans.
  • Steps: 1. Monitor performance. 2. Reflect on errors. 3. Adjust models. 4. Replan.
• Debate-Based Reasoning Frameworks
  • Example: Multiple LLMs debating answers.
  • Steps: 1. Generate opposing views. 2. Argue iteratively. 3. Judge winner. 4. Conclude.
• Self-Verification and Auto-Critique Models
  • Example: LLMs checking their outputs.
  • Steps: 1. Generate answer. 2. Critique for flaws. 3. Revise. 4. Verify consistency.
• Reasoning with Extended Context and Memory
  • Example: Long-term planning with memory banks.
  • Steps: 1. Store past states. 2. Retrieve relevant. 3. Integrate into context. 4. Reason.
• Reasoning with External Knowledge Stores
  • Example: Querying databases during inference.
  • Steps: 1. Identify gaps. 2. Query external. 3. Incorporate info. 4. Continue reasoning.
• Self-Improving Reasoning via Reflection
  • Example: Agents learning from failures.
  • Steps: 1. Attempt task. 2. Reflect on outcome. 3. Update heuristics. 4. Retry.
• Adaptive Reasoning Step Models
  • Example: Adjusting CoT depth based on difficulty.
  • Steps: 1. Assess complexity. 2. Choose steps. 3. Execute adaptively. 4. Optimize.
• Contrastive Chain-of-Thought Reasoning
  • Example: Comparing good vs. bad reasoning paths.
  • Steps: 1. Generate positive/negative CoTs. 2. Contrast differences. 3. Learn from contrasts. 4. Apply to new.
• Recursive Reasoning Architectures
  • Example: Solving subproblems recursively.
  • Steps: 1. Decompose. 2. Solve base cases. 3. Combine recursively. 4. Terminate.

Cutting-Edge and Novel Reasoning Frameworks

• Tree-of-Thought Search Algorithms
  • Example: Branching explorations in coding problems.
  • Steps: 1. Build thought tree. 2. Evaluate branches. 3. Search BFS/DFS. 4. Select path.
• Graph-of-Thought Reasoning
  • Example: Non-linear reasoning in knowledge synthesis.
  • Steps: 1. Nodes as thoughts. 2. Edges as relations. 3. Traverse graph. 4. Aggregate.
• Function-Calling Language Models
  • Example: LLMs calling APIs for calculations.
  • Steps: 1. Detect need. 2. Call function. 3. Integrate result. 4. Respond.
• Planning-Driven Language Models
  • Example: Generating plans before execution.
  • Steps: 1. Prompt for plan. 2. Simulate steps. 3. Execute. 4. Adjust.
• Multi-Agent Collaborative Reasoning
  • Example: Agents specializing in subtasks.
  • Steps: 1. Assign roles. 2. Communicate. 3. Collaborate. 4. Synthesize.
• Sparse Attention Reasoning Models
  • Example: Efficient long-context reasoning.
  • Steps: 1. Select key tokens. 2. Attend sparsely. 3. Compute. 4. Scale.
• Memory-Compressed Reasoning Transformers
  • Example: Summarizing history for decisions.
  • Steps: 1. Compress memory. 2. Retrieve. 3. Reason over compressed. 4. Update.
• Gradient-Logic Hybrid Networks
  • Example: Differentiable logic for optimization.
  • Steps: 1. Embed logic. 2. Apply gradients. 3. Optimize. 4. Extract rules.
• Value Learning for Moral Reasoning
  • Example: Aligning AI with human values.
  • Steps: 1. Learn from preferences. 2. Infer values. 3. Reason morally. 4. Act accordingly.
• Debate and Voting Models for AI Alignment
  • Example: Voting on safe outputs.
  • Steps: 1. Generate candidates. 2. Debate pros/cons. 3. Vote. 4. Select aligned.

Summary:

The above extended list captures 130+ distinct reasoning methods and frameworks prominent in Extended AI and Cognitive Science, now including one practical example and step-by-step application guidance for each. These enhancements aim to make the methods more actionable for implementation in domains like natural language processing, robotics, cognitive modeling, knowledge representation, and AI alignment.

Tags: ^{Bayesian Inference, Bayesian Networks, Dynamic Bayesian Networks, Hidden Markov Models, Markov Random Fields, Monte Carlo Methods, Variational Inference, Probabilistic Programming, Gaussian Processes, Bayesian Occam’s Razor, Probabilistic Soft Logic, Probabilistic Relational Models, Hierarchical Bayesian Models, Particle Filtering, Expectation-Maximization, Deep Probabilistic Models, Statistical Relational Learning, Probabilistic Logic Networks, Defeasible Logic, Default Logic, Circumscription, Belief Revision, Autoepistemic Logic, Argumentation Frameworks, Prioritized Default Reasoning, Non-Monotonic Description Logics, Preference-Based Reasoning, Defeasible Argumentation, Formal Argumentation, Dynamic Epistemic Logic, Abductive Logic Programming, Explanation-Based Learning, Hypothesis Generation, Minimal Explanation, Diagnostic Reasoning, Counterfactual Abduction, Bayesian Abductive Reasoning, Model-Based Diagnosis, Plan Recognition, Causal Abduction, Structure-Mapping Theory, Case-Based Reasoning, Analogical Problem Solving, Conceptual Blending, Embedding-Based Similarity, Vector Space Models, Prototype Reasoning, Relational Similarity, Graph Matching, Metaphor in NLP, Structural Causal Models, Do-Calculus, Counterfactual Inference, Causal Discovery, Granger Causality, Causal Bayesian Networks, Causal Mediation Analysis, Temporal Causal Models, Probabilistic Causation, Causal Relations, Script-Based Reasoning, Frame-Based Reasoning, ConceptNet, Heuristic Search, Fast and Frugal Trees, Bounded Rationality, Dual Process Models, Intuitive Physics, Mental Simulation, Prototype Categorization, Ontology-Based Reasoning, Description Logics, Semantic Web, Production Rule Systems, Logic Programming, Knowledge Graph Reasoning, Conceptual Graphs, Constraint Satisfaction, Automated Theorem Proving, Deductive Databases, Transformer Reasoning, Chain-of-Thought, Tree-of-Thought, Graph Neural Networks, Neuro-Symbolic Reasoning, Deep Reinforcement Learning, Latent Space Reasoning, Contrastive Reasoning, Multimodal Reasoning, Self-Consistency Sampling, Logic Tensor Networks, DeepProbLog, Neural Theorem Provers, Differentiable Programming, Symbolic Regression, Neuro-Symbolic Learning, Symbolic Planning, Concept Learners, Answer Set Programming, Hybrid Neural Architectures, Markov Decision Processes, POMDPs, Policy Gradient, Multi-Agent RL, Reward Shaping, Probabilistic Graphical Models, Markov Chain Monte Carlo, Importance Sampling, Sequential Monte Carlo, Variational Autoencoders, Dirichlet Processes, Beta Processes, Indian Buffet Processes, Gibbs Sampling, Belief Propagation, Junction Tree Algorithm, Loopy Belief Propagation, Stochastic Gradient MCMC, Hamiltonian Monte Carlo, Nested Sampling, Approximate Bayesian Computation, Credal Networks, Fuzzy Bayesian Inference, Non-Parametric Bayesian Models, Bayesian Model Averaging, Argumentation Semantics, Stable Extensions, Grounded Extensions, Preferred Extensions, Conflict-Free Extensions, Admissible Sets, Dialectical Frameworks, Weighted Argumentation, Value-Based Argumentation, Bipolar Argumentation, Dialogue Game Theory, Epistemic Modal Logic, Temporal Epistemic Logic, Belief Update Models, Knowledge Revision, Defeasible Rule Systems, Non-Monotonic Inference, Rational Closure, Lexicographic Closure, Abductive Reasoning Frameworks, Diagnostic Inference, Explanation Selection, Hypothesis Testing, Causal Explanation, Abductive Inference Networks, Analogical Mapping, Similarity Metrics, Exemplar-Based Models, Feature-Based Similarity, Distance-Based Reasoning, Structural Alignment, Cognitive Analogy, Metaphorical Reasoning, Relational Mapping, Causal Effect Estimation, Potential Outcomes Framework, Propensity Score Matching, Instrumental Variables, Difference-in-Differences, Causal Impact Analysis, Time-Series Causation, Mediation Models, Confounder Adjustment, Causal Graph Learning, Commonsense Knowledge Bases, Semantic Networks, Event Calculus, Situation Calculus, Default Reasoning, Qualitative Physics, Heuristic Evaluation, Cognitive Heuristics, Satisficing Models, Recognition-Primed Decision Making, Mental Models, Frame Semantics, Knowledge Representation, Ontological Inference, Semantic Reasoning, Rule-Based Systems, Datalog Reasoning, Constraint Logic Programming, Satisfiability Modulo Theories, Resolution Theorem Proving, Tableau Methods, First-Order Logic Reasoning, Higher-Order Logic, Neural Reasoning, Attention Mechanisms, Prompt Engineering, Graph-Based Reasoning, Symbolic Neural Integration, Reinforcement Learning Policies, Value Iteration, Policy Iteration, Deep Q-Learning, Actor-Critic Methods, Transfer Learning Reasoning, Meta-Learning, Self-Supervised Reasoning, Cross-Modal Reasoning, Memory-Augmented Neural Networks, Differentiable Logic, Neural-Symbolic Integration, Hybrid Reasoning Systems, Adaptive Inference, Reflective Reasoning}