[{"data":1,"prerenderedAt":1282},["ShallowReactive",2],{"subject:artificial-intelligence":3,"course-wordcounts":63,"nav:artificial-intelligence":975},{"id":4,"title":5,"blurb":6,"body":7,"brief":14,"category":46,"description":47,"draft":48,"extension":49,"meta":50,"module":11,"navigation":21,"path":51,"practice":52,"rawbody":53,"readingTime":54,"seo":57,"sources":58,"status":59,"stem":60,"summary":11,"topics":61,"__hash__":62},"course\u002F08.artificial-intelligence\u002Findex.md","Artificial Intelligence","The classical science of intelligent agents — search, logic, planning,\nprobability, and decision-making, from the Russell & Norvig canon.\n",{"type":8,"value":9,"toc":10},"minimark",[],{"title":11,"searchDepth":12,"depth":12,"links":13},"",2,[],[15,17,22,24,28,30,34,36,40,42],{"p":16},"For most of its history, artificial intelligence meant\n\u003Cstrong>search\u003C\u002Fstrong>, \u003Cstrong>logic\u003C\u002Fstrong>, and\n\u003Cstrong>reasoning\u003C\u002Fstrong> rather than learning from data — writing down\nwhat an agent knows and letting it deduce, plan, and decide what to do.\n",{"fig":18,"n":19,"caption":20,"large":21},"searchtree","001","Search: expand the frontier node by node until a path to the goal appears.\n",true,{"p":23},"The organizing idea is the \u003Cstrong>rational agent\u003C\u002Fstrong>: something that\nperceives its environment and acts to maximize its expected performance.\nEverything else is machinery for choosing the action — searching a space of\npossibilities, proving a logical consequence, or computing an expected\nutility under uncertainty.\n",{"fig":25,"n":26,"caption":27},"minimax","002","Minimax: leaf values back up as min and max to pick the best move.\n",{"p":29},"Search comes first: cast a problem as states and moves, and algorithms like\nA* find a path to the goal, guided by a heuristic that estimates the\ndistance still to go. Add an adversary and the same idea becomes the minimax\nsearch that plays chess.\n",{"fig":31,"n":32,"caption":33},"csp","003","A constraint problem: color the map so no two neighbors match.\n",{"p":35},"When the world is uncertain, logic gives way to \u003Cem>probability\u003C\u002Fem>. A\nBayesian network compresses a joint distribution over many variables into a\ngraph of local dependencies, and the same expected-utility calculus, run\nover time, becomes the Markov decision process that underlies planning and\nreinforcement learning.\n",{"fig":37,"n":38,"caption":39},"bayesnet","004","A Bayesian network: evidence enters and belief flows down the edges.\n",{"p":41},"These are the ideas that ran from the Logic Theorist to Deep Blue to the\nprobabilistic robotics of self-driving cars — the foundation the modern,\nlearning-driven era of AI was built on top of.\n",{"fig":43,"n":44,"caption":45},"resolution","005","Resolution: clauses combine and cancel down to the empty clause — a proof.\n","computer-science","Intelligence as the design of rational agents: problem-solving by search\n(uninformed, heuristic, and adversarial); constraint satisfaction; knowledge\nand reasoning in propositional and first-order logic; automated planning;\nreasoning under uncertainty with probability and Bayesian networks; sequential\ndecision-making with Markov decision processes; learning from data; and the\nfrontier of perception, robotics, and the philosophy of mind. Built on Russell\n& Norvig's _Artificial Intelligence: A Modern Approach_. Notes for this subject\nare coming soon.\n",false,"md",{},"\u002Fartificial-intelligence",[],"---\ntitle: Artificial Intelligence\nstatus: available\nblurb: |\n  The classical science of intelligent agents — search, logic, planning,\n  probability, and decision-making, from the Russell & Norvig canon.\ndescription: |\n  Intelligence as the design of rational agents: problem-solving by search\n  (uninformed, heuristic, and adversarial); constraint satisfaction; knowledge\n  and reasoning in propositional and first-order logic; automated planning;\n  reasoning under uncertainty with probability and Bayesian networks; sequential\n  decision-making with Markov decision processes; learning from data; and the\n  frontier of perception, robotics, and the philosophy of mind. Built on Russell\n  & Norvig's _Artificial Intelligence: A Modern Approach_. Notes for this subject\n  are coming soon.\nbrief:\n  - p: |\n      For most of its history, artificial intelligence meant\n      \u003Cstrong>search\u003C\u002Fstrong>, \u003Cstrong>logic\u003C\u002Fstrong>, and\n      \u003Cstrong>reasoning\u003C\u002Fstrong> rather than learning from data — writing down\n      what an agent knows and letting it deduce, plan, and decide what to do.\n  - fig: searchtree\n    n: \"001\"\n    caption: |\n      Search: expand the frontier node by node until a path to the goal appears.\n    large: true\n  - p: |\n      The organizing idea is the \u003Cstrong>rational agent\u003C\u002Fstrong>: something that\n      perceives its environment and acts to maximize its expected performance.\n      Everything else is machinery for choosing the action — searching a space of\n      possibilities, proving a logical consequence, or computing an expected\n      utility under uncertainty.\n  - fig: minimax\n    n: \"002\"\n    caption: |\n      Minimax: leaf values back up as min and max to pick the best move.\n  - p: |\n      Search comes first: cast a problem as states and moves, and algorithms like\n      A* find a path to the goal, guided by a heuristic that estimates the\n      distance still to go. Add an adversary and the same idea becomes the minimax\n      search that plays chess.\n  - fig: csp\n    n: \"003\"\n    caption: |\n      A constraint problem: color the map so no two neighbors match.\n  - p: |\n      When the world is uncertain, logic gives way to \u003Cem>probability\u003C\u002Fem>. A\n      Bayesian network compresses a joint distribution over many variables into a\n      graph of local dependencies, and the same expected-utility calculus, run\n      over time, becomes the Markov decision process that underlies planning and\n      reinforcement learning.\n  - fig: bayesnet\n    n: \"004\"\n    caption: |\n      A Bayesian network: evidence enters and belief flows down the edges.\n  - p: |\n      These are the ideas that ran from the Logic Theorist to Deep Blue to the\n      probabilistic robotics of self-driving cars — the foundation the modern,\n      learning-driven era of AI was built on top of.\n  - fig: resolution\n    n: \"005\"\n    caption: |\n      Resolution: clauses combine and cancel down to the empty clause — a proof.\n---\n",{"text":55,"minutes":56,"time":56,"words":56},"0 min 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Is Artificial Intelligence?","\u002Fartificial-intelligence\u002Ffoundations\u002Fwhat-is-ai",[977],"Eight definitions of AI fall into a two-by-two grid: think versus act, and measure success against human performance versus an ideal standard of rationality. We work through all four schools — the Turing test, cognitive modelling, the laws of thought, and the rational agent — and adopt the last as the frame for the whole course: AI is the study and design of rational agents.\n",{"title":987,"path":988,"lessonNumber":12,"topics":989,"summary":990},"The Foundations of AI","\u002Fartificial-intelligence\u002Ffoundations\u002Ffoundations-of-ai",[977],"Where the rational-agent idea came from and what surrounds it. AI inherited its core tools from eight older disciplines — philosophy, mathematics, economics, neuroscience, psychology, computer engineering, control theory, and linguistics. Its history runs in cycles of boom and winter, from the 1956 Dartmouth workshop through expert systems to the statistical turn. And the deep-learning era — AlexNet, the Transformer, GPT-3, AlphaGo — is a new way of computing the agent function at scale, not a new definition of AI.\n",{"title":992,"path":993,"lessonNumber":994,"topics":995,"summary":996},"Intelligent Agents","\u002Fartificial-intelligence\u002Ffoundations\u002Fintelligent-agents",3,[977],"An agent perceives an environment through sensors and acts on it through actuators; its behavior is an agent function mapping percept sequences to actions. A rational agent chooses, for each percept sequence, the action that maximizes its expected performance measure given its knowledge. We build the first half of the vocabulary the whole course rests on — the agent function, rationality, PEAS task specifications, and the six axes along which task environments vary.\n",{"title":998,"path":999,"lessonNumber":1000,"topics":1001,"summary":1002},"Agent Architectures","\u002Fartificial-intelligence\u002Ffoundations\u002Fagent-architectures",4,[977],"How to build a program that computes a good agent function without storing an astronomically large lookup table. Four skeleton architectures in order of increasing power — simple reflex, model-based, goal-based, and utility-based — plus the learning agent that improves any of them, the scale of world representations (atomic, factored, structured) they rest on, and how a modern language-model agent fits the same frame.\n",{"module":1004,"moduleNumber":12,"slug":1005,"lessons":1006},"Search","search",[1007,1012,1017,1022,1027,1033,1039,1045,1051,1057,1063,1069],{"title":1008,"path":1009,"lessonNumber":978,"topics":1010,"summary":1011},"Uninformed Search","\u002Fartificial-intelligence\u002Fsearch\u002Funinformed-search",[1004],"A goal-based agent that cannot see which action is best turns the problem into a state space — an initial state, a set of actions, a transition model, a goal test, and a path cost — and searches for a sequence of actions reaching the goal. We build the state-space formulation on the 8-puzzle and route-finding, give the one TREE-SEARCH \u002F GRAPH-SEARCH skeleton every algorithm specializes, and measure strategies by completeness, optimality, and complexity. This lesson develops the first two frontier disciplines — breadth-first and uniform-cost search; the rest follow in the next lesson.\n",{"title":1013,"path":1014,"lessonNumber":12,"topics":1015,"summary":1016},"Search Strategies Compared","\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-strategies-compared",[1004],"Breadth-first and uniform-cost search pay for optimality in memory. This lesson develops the strategies that trade memory for depth: depth-first search, which keeps only the current path; depth-limited and iterative-deepening search, which fix DFS's failure on infinite paths; and bidirectional search, which meets in the middle for a square-root saving. It closes by lining up all six uninformed strategies against completeness, optimality, and complexity, and tracing where the algorithms came from and where they went.\n",{"title":1018,"path":1019,"lessonNumber":994,"topics":1020,"summary":1021},"Informed Search and A*","\u002Fartificial-intelligence\u002Fsearch\u002Finformed-search",[1004],"An informed search uses a heuristic $h(n)$, an estimate of the cost from a node to the goal, to decide what to expand next. Greedy best-first search follows the heuristic blindly and gives up optimality; A* corrects it by ranking nodes on $f(n) = g(n) + h(n)$, and is optimal when the heuristic is admissible (tree search) or consistent (graph search). This lesson defines the heuristic, builds best-first search, and proves why A* is optimal, with the contour picture that explains its pruning. Where good heuristics come from is the next lesson.\n",{"title":1023,"path":1024,"lessonNumber":1000,"topics":1025,"summary":1026},"Heuristic Functions and Memory-Bounded Search","\u002Fartificial-intelligence\u002Fsearch\u002Fheuristic-functions",[1004],"A* is only as good as its heuristic, so this lesson answers where good heuristics come from: relaxed problems, whose exact solution cost is an admissible heuristic, and pattern databases, which precompute subproblem costs. It measures heuristic quality with dominance and the effective branching factor, then tackles A*'s memory problem with IDA*, RBFS, and SMA*. It closes with modern heuristic search — weighted A*, learned and disjoint pattern-database heuristics, and bidirectional A*.\n",{"title":1028,"path":1029,"lessonNumber":1030,"topics":1031,"summary":1032},"Local Search and Optimization","\u002Fartificial-intelligence\u002Fsearch\u002Flocal-search",5,[1004],"When the path to a goal is irrelevant and only the final state matters, we can discard the search tree entirely and keep just the current state, moving to a better neighbor at each step. This lesson builds the state-space landscape metaphor, works through hill climbing and the three obstacles that defeat it (local maxima, ridges, plateaus), then develops the first escapes: random restarts and simulated annealing with its temperature schedule. The population-based methods and continuous-space calculus follow in the next lesson.\n",{"title":1034,"path":1035,"lessonNumber":1036,"topics":1037,"summary":1038},"Population and Continuous Search","\u002Fartificial-intelligence\u002Fsearch\u002Fpopulation-and-continuous-search",6,[1004],"Single-state local search escapes a trap by restarting or tolerating downhill moves. This lesson develops the alternatives that keep several states at once — local beam search, which shares successors across parallel threads, and genetic algorithms, which recombine two parents through crossover and mutation — then crosses into continuous spaces, where calculus replaces the finite neighbor set: gradient ascent, line search, and Newton's method. It closes with the industrial descendants of these methods and the loop they all share.\n",{"title":1040,"path":1041,"lessonNumber":1042,"topics":1043,"summary":1044},"Adversarial Search and Games","\u002Fartificial-intelligence\u002Fsearch\u002Fadversarial-search",7,[1004],"When another agent plans against you, search becomes a game. We formalize two-player, zero-sum, perfect-information games as search problems, define the minimax value that optimal play backs up through the game tree, and give the MINIMAX algorithm that computes it. Alpha–beta pruning then cuts the cost of that search roughly in half in the exponent without changing the answer, and a heuristic evaluation function plus a cutoff test turns the exact algorithm into a real-time player that copes with the horizon effect.\n",{"title":1046,"path":1047,"lessonNumber":1048,"topics":1049,"summary":1050},"Games of Chance and Imperfect Information","\u002Fartificial-intelligence\u002Fsearch\u002Fgames-of-chance-and-imperfect-information",8,[1004],"Minimax and alpha–beta assume a deterministic game both players can see in full. Drop either assumption and search must change. This lesson adds chance nodes and the expectiminimax value for games with dice, then belief-state reasoning for partially observable games — Kriegspiel and card games — where averaging over clairvoyance both helps and misleads. It closes with the line from Deep Blue's alpha–beta to AlphaGo's learned evaluation and Monte Carlo tree search, and the provable-pruning and self-play research around each end of that story.\n",{"title":1052,"path":1053,"lessonNumber":1054,"topics":1055,"summary":1056},"Constraint Satisfaction Problems","\u002Fartificial-intelligence\u002Fsearch\u002Fconstraint-satisfaction",9,[1004],"A constraint satisfaction problem replaces the black-box state with a factored one: variables, domains, and constraints. That structure supports inference before any search runs. This lesson defines the CSP on map coloring, Sudoku, and scheduling, then develops constraint propagation: node and arc consistency, the AC-3 algorithm that makes a whole network arc-consistent, and the way one deleted value cascades across the graph to prune impossible options ahead of search.\n",{"title":1058,"path":1059,"lessonNumber":1060,"topics":1061,"summary":1062},"CSP Search and Structure","\u002Fartificial-intelligence\u002Fsearch\u002Fcsp-search-and-structure",10,[1004],"Propagation prunes a CSP but rarely finishes it, so we search. This lesson builds backtracking search over partial assignments and the general-purpose heuristics that make it fast — MRV, degree, least-constraining-value, forward checking, MAC, and intelligent backtracking. It then shows how the shape of the constraint graph controls difficulty: tree-structured problems fall in linear time, cutset conditioning handles the rest, and min-conflicts local search solves a million queens in a constant number of steps.\n",{"title":1064,"path":1065,"lessonNumber":1066,"topics":1067,"summary":1068},"Search Under Uncertainty","\u002Fartificial-intelligence\u002Fsearch\u002Fsearch-under-uncertainty",11,[1004],"Classical search assumes the agent knows the state it is in and exactly what each action does. Drop the second assumption and a plan can no longer be a fixed sequence of actions. This lesson develops the first response: AND-OR search over nondeterministic actions, which returns a branching contingency plan rather than a straight line. We build it on the erratic vacuum world, show how OR nodes (the agent's choices) alternate with AND nodes (nature's outcomes), trace the recursion that finds a plan, and handle the case where the only solution is a cyclic \"try, try again.\"\n",{"title":1070,"path":1071,"lessonNumber":1072,"topics":1073,"summary":1074},"Belief-State and Online Search","\u002Fartificial-intelligence\u002Fsearch\u002Fbelief-state-and-online-search",12,[1004],"When the agent cannot see the full state, a plan can no longer test where it actually is — it must reason over the set of states it might be in. This lesson develops belief-state search, from sensorless (conformant) planning that coerces an unknown world into a goal, through the predict-observe-update cycle of contingent planning with percepts, to online search in unknown environments, where the agent must act in order to learn. It closes with LRTA*, which refines its own heuristic as it explores, one step from reinforcement learning.\n",{"module":1076,"moduleNumber":994,"slug":1077,"lessons":1078},"Logic and Planning","logic-and-planning",[1079,1085,1090,1095,1100,1105,1110,1115,1120,1125,1130,1135],{"title":1080,"path":1081,"lessonNumber":978,"topics":1082,"summary":1084},"Logical Agents and Propositional Logic","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-logic",[1083],"Logic","A knowledge-based agent keeps a store of sentences and acts by asking it what to do. To make \"asking\" mean something we need entailment — the relation $KB \\models \\alpha$ that holds when every model of the knowledge base is a model of the query. Propositional logic gives a syntax and a truth-table semantics for which entailment is decidable. This first part builds the foundations: the agent loop, the Wumpus World, models and entailment, the connectives and truth tables, theorem proving by refutation, and the resolution rule with its CNF conversion — a single complete inference procedure for all of propositional logic.\n",{"title":1086,"path":1087,"lessonNumber":12,"topics":1088,"summary":1089},"Propositional Inference and Logical Agents","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fpropositional-inference",[1083],"Model checking and resolution decide entailment, but both can blow up. This part turns propositional logic into a practical engine and a working agent. Horn clauses give linear-time forward and backward chaining — the basis of logic programming. DPLL and WalkSAT make satisfiability testing fast in the common case. Then we make the agent situated: time-indexed fluents, the frame problem and its solution by successor-state axioms, a hybrid agent that deduces a safe map and plans a route through it, and SATPlan, which finds a plan by asking a SAT solver for a satisfying model.\n",{"title":1091,"path":1092,"lessonNumber":994,"topics":1093,"summary":1094},"First-Order Logic","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic",[1083],"Propositional logic can only say that facts hold; it cannot talk about the objects a fact is about, or state a rule once and have it cover every object. First-order logic fixes this by committing to a world of objects, relations, and functions. This first part builds the language from the ground up: the ontology it commits to, the model that gives a sentence a truth value, the syntax of terms and sentences, the two quantifiers with their standard mistakes, and equality.\n",{"title":1096,"path":1097,"lessonNumber":1000,"topics":1098,"summary":1099},"First-Order Logic in Use","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-logic-in-use",[1083],"With the language of first-order logic in hand, this part is about using it well. Database semantics trades expressive power for the convenience of a single intended model; higher-order logic shows what first-order logic gives up for decidability. Then we put the language to work: the Tell\u002FAsk interface, the kinship domain axiomatized from scratch, and the seven-step knowledge-engineering process applied to a digital circuit.\n",{"title":1101,"path":1102,"lessonNumber":1030,"topics":1103,"summary":1104},"Inference in First-Order Logic","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Finference-and-resolution",[1083],"Propositional inference lifts to first-order logic once we can make terms match. Unification is that machinery: the algorithm that finds the substitution making two expressions identical, and the basis of generalized modus ponens. This first part builds the lifted inference rules and the two chaining algorithms they drive — forward chaining, the data-driven procedure behind production systems and Datalog, and backward chaining, the goal-driven procedure behind Prolog.\n",{"title":1106,"path":1107,"lessonNumber":1036,"topics":1108,"summary":1109},"First-Order Resolution","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Ffirst-order-resolution",[1083],"Chaining is complete only for Horn knowledge bases. General first-order sentences — with disjunctive conclusions and negations — need a single sound and complete rule: resolution. This part converts arbitrary sentences to CNF by skolemizing away the existentials, lifts the resolution rule with unification, and proves entailment by refuting the negated goal. The result is the proof procedure Gödel's completeness theorem guarantees will find any entailment, together with the search strategies that make it usable.\n",{"title":1111,"path":1112,"lessonNumber":1042,"topics":1113,"summary":1114},"Classical Planning","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fclassical-planning",[1083],"Classical planning represents a problem in a factored language, PDDL: states are sets of ground fluents, and actions are lifted schemas with a precondition and an effect. That structure turns planning into search — forward through states or backward through goals — and lets a program read heuristics straight off the schemas by relaxing the problem. This first part develops the representation, the two search directions, and the domain-independent heuristics that come from ignoring preconditions or delete lists.\n",{"title":1116,"path":1117,"lessonNumber":1048,"topics":1118,"summary":1119},"Planning Heuristics and GraphPlan","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-graphs-and-graphplan",[1083],"Every relaxation heuristic can be inaccurate, and none can tell how far apart subgoals sit. The planning graph is a polynomial-size structure that does better: leveled off the problem, it yields admissible distance estimates and a record of which actions and fluents cannot coexist. This part builds the graph, reads heuristics from it, extracts plans with GraphPlan, and closes with the other classical approaches — SATPlan and partial-order planning — and the representational trade that makes all of it work.\n",{"title":1121,"path":1122,"lessonNumber":1054,"topics":1123,"summary":1124},"Planning and Acting in the Real World","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-in-the-real-world",[1083],"Classical planning's clean theory rests on four assumptions: time is ignored, actions are atomic, the world is deterministic and fully observable, and the agent is alone. This first part drops the first two. We add durations and resource constraints — turning a plan into a schedule, solved by the critical-path method and, once resources contend, by NP-hard job-shop scheduling — and let a planner reason at multiple levels of abstraction through high-level actions and their angelic reachable sets.\n",{"title":1126,"path":1127,"lessonNumber":1060,"topics":1128,"summary":1129},"Planning Under Uncertainty","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fplanning-under-uncertainty",[1083],"Classical planning assumed the world was deterministic, fully observable, and the agent alone. This part drops the last two assumptions. When the agent cannot see or predict the world, planning moves into belief-state space: sensorless plans that coerce the world into the goal without sensing, contingent plans that branch on what is sensed, and online agents that monitor and replan when execution diverges. Then we add other agents — joint plans, the coordination problem, and the conventions that let a team act without constant negotiation.\n",{"title":1131,"path":1132,"lessonNumber":1066,"topics":1133,"summary":1134},"Knowledge Representation","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Fknowledge-representation",[1083],"First-order logic gives you the language; this lesson is about what to say in it. This first part builds the content: a general upper ontology from the top down, categories as first-class objects with taxonomies and inheritance, physical composition and the count-noun\u002Fmass-noun split, events and time reified through the event calculus, and belief modeled with modal logic — the machinery for representing the world an agent reasons about.\n",{"title":1136,"path":1137,"lessonNumber":1072,"topics":1138,"summary":1139},"Reasoning Systems and Default Logic","\u002Fartificial-intelligence\u002Flogic-and-planning\u002Freasoning-systems-and-defaults",[1083],"Having represented the world, this part is about reasoning with it at scale. Semantic networks give a graphical notation with fast inheritance; description logics keep subsumption and classification tractable by design. Then we confront the fact that most useful rules hold only by default: circumscription and default logic give a logical account of nonmonotonic reasoning, and truth maintenance systems retract conclusions cleanly when the beliefs beneath them change.\n",{"module":1141,"moduleNumber":1000,"slug":1142,"lessons":1143},"Uncertainty","uncertainty",[1144,1149,1154,1159,1164,1169,1174,1179,1184,1189],{"title":1145,"path":1146,"lessonNumber":978,"topics":1147,"summary":1148},"Quantifying Uncertainty","\u002Fartificial-intelligence\u002Funcertainty\u002Fprobability-and-bayes",[1141],"Logic breaks down in any domain where the rules have exceptions you cannot enumerate — the qualification problem. Probability replaces truth values with degrees of belief that obey Kolmogorov's axioms, and the full joint distribution becomes a knowledge base from which any query is answered by summing entries: marginalization, conditioning, and normalization. Independence factors that joint into smaller pieces — the first step toward a calculus of rational belief that an agent can actually compute with.\n",{"title":1150,"path":1151,"lessonNumber":12,"topics":1152,"summary":1153},"Bayes' Rule and Naive Bayes","\u002Fartificial-intelligence\u002Funcertainty\u002Fbayes-rule-and-naive-bayes",[1141],"Bayes' rule inverts a causal model into a diagnostic one, turning \"how a cause produces its symptoms\" into \"which cause explains what I observed.\" Ignoring the prior is the base-rate fallacy behind overconfident test results. Conditional independence then lets several pieces of evidence combine by multiplying likelihood ratios instead of building an exponential joint, giving the naive Bayes model and pointing directly at Bayesian networks.\n",{"title":1155,"path":1156,"lessonNumber":994,"topics":1157,"summary":1158},"Bayesian Networks","\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks",[1141],"A Bayesian network is a directed acyclic graph of random variables in which each node carries a conditional probability table for itself given its parents. That structure factors the full joint distribution into a product of local terms, turning an exponential table into a linear one, and it makes the conditional independences of the domain explicit. We build the canonical burglary–alarm network, read compactness and d-separation off the graph, run exact inference by variable elimination, and, where that is intractable, estimate answers by sampling.\n",{"title":1160,"path":1161,"lessonNumber":1000,"topics":1162,"summary":1163},"Bayesian Networks: Inference and Relational Models","\u002Fartificial-intelligence\u002Funcertainty\u002Finference-in-bayesian-networks",[1141],"When exact inference is intractable, sampling estimates the posterior instead: prior and rejection sampling, likelihood weighting, and Gibbs\u002FMCMC, whose error shrinks as one over the square root of the sample count. The same graphical idea then lifts from a fixed set of variables to whole populations — relational and open-universe probability models write dependencies once and unroll them over objects — and we close by placing probability against the rule-based, Dempster–Shafer, and fuzzy alternatives it displaced.\n",{"title":1165,"path":1166,"lessonNumber":1030,"topics":1167,"summary":1168},"Probabilistic Reasoning over Time","\u002Fartificial-intelligence\u002Funcertainty\u002Freasoning-over-time",[1141],"A world that changes needs a state variable at every point in time. The Markov assumption cuts the dependence on history down to the previous slice, leaving a transition model and a sensor model that define a temporal Bayesian network. Four recursive tasks fall out — filtering, prediction, smoothing, and the most likely explanation — each a message passed along the sequence. We ground them in hidden Markov models and their matrix form, sketch the Kalman filter for continuous state, and reach dynamic Bayesian networks with particle filtering as the general approximate method.\n",{"title":1170,"path":1171,"lessonNumber":1036,"topics":1172,"summary":1173},"Reasoning over Time: Tracking and Data Association","\u002Fartificial-intelligence\u002Funcertainty\u002Ftracking-and-data-association",[1141],"Dynamic Bayesian networks generalize HMMs and Kalman filters to arbitrarily many state variables per slice, and when exact inference blows up, particle filtering approximates the belief state with a population of weighted samples that propagate, reweight, and resample. Tracking several objects at once adds the data-association problem — which observation came from which object — whose combinatorics defeat any exact filter, so particle filters and MCMC keep many hypotheses alive. We close with SLAM and learned state-space models.\n",{"title":1175,"path":1176,"lessonNumber":1042,"topics":1177,"summary":1178},"Making Decisions: Utility Theory","\u002Fartificial-intelligence\u002Funcertainty\u002Fmaking-decisions",[1141],"A rational agent chooses the action that maximizes expected utility — the probability of each outcome weighted by how much the agent wants it. We derive the utility function from six axioms on preferences, so maximizing expected utility is forced by consistency rather than assumed; look at risk aversion in the utility-of-money curve; package one-shot choices into decision networks; and quantify what an observation is worth with the value of information.\n",{"title":1180,"path":1181,"lessonNumber":1048,"topics":1182,"summary":1183},"Markov Decision Processes","\u002Fartificial-intelligence\u002Funcertainty\u002Fmarkov-decision-processes",[1141],"When an agent must act repeatedly in a stochastic world, a fixed plan is useless — it needs a policy, an action for every state. The Markov decision process makes this precise with a transition model, a reward, and a discount factor; the Bellman equation characterizes the optimal state utilities, and value iteration and policy iteration solve it. Partial observability lifts the problem to belief states, and bandits, Monte-Carlo tree search, and scalable POMDP solvers extend it — this is the model-known half of reinforcement learning.\n",{"title":1185,"path":1186,"lessonNumber":1054,"topics":1187,"summary":1188},"Decision Analysis: Multi-Attribute Utility and Decision Networks","\u002Fartificial-intelligence\u002Funcertainty\u002Fdecision-networks-and-game-theory",[1141],"Decision analysis takes the single-agent utility framework and makes it practical: utility over several attributes, dominance and additive value functions, influence diagrams that fold Bayesian networks together with decision and utility nodes, and the value of information that tells an agent which questions are worth asking. Structure in an agent's preferences — dominance, preferential and utility independence — collapses an exponential utility table into a few one-dimensional functions, the same move that made Bayesian networks compact.\n",{"title":1190,"path":1191,"lessonNumber":1060,"topics":1192,"summary":1193},"Game Theory and Mechanism Design","\u002Fartificial-intelligence\u002Funcertainty\u002Fgame-theory-and-mechanism-design",[1141],"When outcomes depend on other rational agents, single-agent utility maximization no longer suffices. Game theory studies decisions among agents — normal-form games, dominant strategies, Nash and maximin equilibria, and repeated games — and mechanism design runs the logic backwards, engineering rules (auctions, VCG) so that self-interested play produces a good collective outcome. Algorithmic game theory then asks whether equilibria can be computed, what selfishness costs society, and how the mechanisms deployed at internet scale actually behave.\n",{"module":1195,"moduleNumber":1030,"slug":1196,"lessons":1197},"Learning","learning",[1198,1203,1208,1213,1218,1223,1228,1233],{"title":1199,"path":1200,"lessonNumber":978,"topics":1201,"summary":1202},"Learning from Examples","\u002Fartificial-intelligence\u002Flearning\u002Flearning-from-examples",[1195],"An agent that improves with experience does not need its designer to anticipate every situation. Inductive learning takes that ambition and narrows it to one tractable problem: from labelled input-output pairs, recover a function that predicts the output for inputs never seen. This first part builds the foundation around a single organizing question — generalization — through decision trees and information gain, and the training\u002Fvalidation\u002Ftest discipline for evaluating and choosing hypotheses. A second part takes up the theory of learning and the main model families.\n",{"title":1204,"path":1205,"lessonNumber":12,"topics":1206,"summary":1207},"The Theory of Learning and Model Families","\u002Fartificial-intelligence\u002Flearning\u002Ftheory-and-model-families",[1195],"Cross-validation measures generalization but does not explain it. This part supplies the theory — PAC learning, sample complexity, and the VC dimension — that says when a hypothesis consistent with enough data is probably approximately correct, and why an unrestricted hypothesis space can never generalize. It then surveys the model families a practitioner reaches for: linear regression and gradient descent, the perceptron and logistic regression, support vector machines and the kernel trick, and ensembles by bagging and boosting — closing with what deep learning changed about the classical picture.\n",{"title":1209,"path":1210,"lessonNumber":994,"topics":1211,"summary":1212},"Learning Probabilistic Models","\u002Fartificial-intelligence\u002Flearning\u002Fprobabilistic-learning",[1195],"A [Bayesian network](\u002Fartificial-intelligence\u002Funcertainty\u002Fbayesian-networks) is useless until its numbers are filled in, and those numbers come from data. This first part casts learning itself as probabilistic inference: hypotheses carry a prior, data update it to a posterior, and predictions average over what remains. From that frame fall the standard estimators — maximum likelihood by counting, MAP with a conjugate prior, full Bayesian updating — for the case where every variable is observed. A second part takes up the harder case of hidden variables and the EM algorithm.\n",{"title":1214,"path":1215,"lessonNumber":1000,"topics":1216,"summary":1217},"Learning with Hidden Variables: The EM Algorithm","\u002Fartificial-intelligence\u002Flearning\u002Fexpectation-maximization",[1195],"Complete data can be learned by counting; real data usually hide some variables — the disease behind the symptoms, the cluster behind the points. This part develops the expectation-maximization algorithm, which learns those models by alternating an expected completion of the missing data with a re-estimation of the parameters. It works the idea through mixtures of Gaussians, Bayesian networks, and hidden Markov models, proves the monotone-likelihood guarantee from the evidence lower bound, and traces the line from EM to variational inference and the variational autoencoder.\n",{"title":1219,"path":1220,"lessonNumber":1030,"topics":1221,"summary":1222},"Reinforcement Learning","\u002Fartificial-intelligence\u002Flearning\u002Freinforcement-learning",[1195],"Reinforcement learning is an MDP with the model unknown: the agent knows neither how its actions move the world nor which states are rewarded, and must recover good behaviour from experienced transitions and rewards alone. This first part builds the classical tabular theory — passive learning (fix a policy, learn its value, by direct estimation, adaptive dynamic programming, and temporal differences) and active learning (choose actions, trade exploration against exploitation, and learn control with Q-learning and SARSA). A second part lifts it off the lookup table with function approximation and policy search.\n",{"title":1224,"path":1225,"lessonNumber":1036,"topics":1226,"summary":1227},"Reinforcement Learning: Generalization and Policy Search","\u002Fartificial-intelligence\u002Flearning\u002Fgeneralization-and-policy-search",[1195],"Tabular reinforcement learning stores one number per state, which is hopeless for backgammon or chess. This part lifts RL off the lookup table with function approximation, so that updating one state generalizes to related ones, then turns to policy search — representing and optimizing the policy directly, up to the REINFORCE policy gradient and correlated sampling. It closes with the bridge to deep reinforcement learning (deep Q-networks, actor-critic, PPO), the classic applications, and the hand-off to the dedicated RL subject.\n",{"title":1229,"path":1230,"lessonNumber":1042,"topics":1231,"summary":1232},"Knowledge in Learning","\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-in-learning",[1195],"Pure induction learns a function from labelled examples while knowing almost nothing to begin with. This first part brings prior knowledge into the loop by recasting learning as logical inference — hypotheses, examples, and classifications as sentences. It develops current-best-hypothesis search, the version space and its general\u002Fspecific boundary maintained by candidate elimination, and states the three entailment constraints that fix how background knowledge enters. A second part builds the three knowledge-based methods those constraints define.\n",{"title":1234,"path":1235,"lessonNumber":1048,"topics":1236,"summary":1237},"Knowledge-Based Learning: EBL, Relevance, and ILP","\u002Fartificial-intelligence\u002Flearning\u002Fknowledge-based-learning-methods",[1195],"Once learning is cast as logical inference, three methods follow from the three ways prior knowledge can enter. Explanation-based learning generalizes a single example by explaining it with the domain theory, gaining speed but nothing new. Relevance-based learning uses determinations to shrink the hypothesis space and converge from fewer examples. Inductive logic programming learns genuinely new first-order rules — top-down with FOIL, bottom-up by inverting resolution, even inventing new predicates — and connects to modern statistical relational and neuro-symbolic learning.\n",{"module":1239,"moduleNumber":1036,"slug":1240,"lessons":1241},"Frontiers","frontiers",[1242,1247,1252,1257,1262,1267,1272,1277],{"title":1243,"path":1244,"lessonNumber":978,"topics":1245,"summary":1246},"Vision and Perception","\u002Fartificial-intelligence\u002Ffrontiers\u002Fvision-and-perception",[1239],"Perception connects an agent to the physical world. We follow one modality — vision — from the physics of image formation (the pinhole camera, perspective projection, lenses, shading, color) through the early operations that turn a pixel array into edges, texture, and motion, and into recognition by appearance. The recurring problem is inversion: a camera collapses a 3-D world onto a 2-D grid, and an agent that wants to act must build the scene back up. Rebuilding the scene is the subject of the companion lesson.\n",{"title":1248,"path":1249,"lessonNumber":12,"topics":1250,"summary":1251},"Vision: Reconstructing the 3D World","\u002Fartificial-intelligence\u002Ffrontiers\u002Freconstructing-the-3d-world",[1239],"A camera collapses a three-dimensional world onto a flat grid; this lesson inverts that collapse. We build the camera projection matrix (intrinsics and extrinsics), triangulate a point from two views, then work through the toolbox of depth cues — motion parallax, binocular stereopsis, multiple views, texture, shading, and contour — that turn an ambiguous image back into a scene. We add structural recognition (pictorial-structure \"cardboard people\"), the task-driven use of vision in cars and robots, and the shift from hand-built pipelines to learned deep-vision networks.\n",{"title":1253,"path":1254,"lessonNumber":994,"topics":1255,"summary":1256},"Robotics","\u002Fartificial-intelligence\u002Ffrontiers\u002Frobotics",[1239],"A robot is an agent with a body: sensors that read the physical world and effectors that push back on it. This lesson grounds the abstract AI machinery in that body. We build up the hardware (range finders, proprioception, degrees of freedom), then cast perception as probabilistic filtering — the kinematic motion and sensor models, Monte Carlo localization, the extended Kalman filter, and simultaneous localization and mapping (SLAM). The companion lesson takes the estimated pose forward into planning and control.\n",{"title":1258,"path":1259,"lessonNumber":1000,"topics":1260,"summary":1261},"Robotics: Planning and Control","\u002Fartificial-intelligence\u002Ffrontiers\u002Frobot-planning-and-control",[1239],"A robot that knows where it is still has to decide how to move, and then make a slipping, sensing-imperfect body actually go there. This lesson takes the pose estimate forward: planning motion in configuration space with cell decomposition and sampling-based roadmaps (PRMs and RRTs), planning under uncertainty with most-likely-state and online replanning, closing the loop with P\u002FPD\u002FPID control and potential fields, and finally the software architectures — subsumption, three-layer, and pipeline — that assemble it all, plus the learning-based turn in modern robotics.\n",{"title":1263,"path":1264,"lessonNumber":1030,"topics":1265,"summary":1266},"Natural Language for AI Agents","\u002Fartificial-intelligence\u002Ffrontiers\u002Fnatural-language-in-ai",[1239],"Language is how agents acquire the knowledge already written down and how they communicate with the humans they serve. This lesson gives the classical AI account of language as a source of information: n-gram language models and the information-seeking tasks built on them — text classification, information retrieval (BM25, the inverted index, PageRank), and information extraction with finite-state templates and hidden Markov models. Throughout, we point to the dedicated NLP subject for the modern deep-learning treatment; the companion lesson takes up grammar, translation, and speech.\n",{"title":1268,"path":1269,"lessonNumber":1036,"topics":1270,"summary":1271},"Language for AI Agents: Grammar, Translation, and Speech","\u002Fartificial-intelligence\u002Ffrontiers\u002Fnlp-grammar-translation-and-speech",[1239],"N-gram models see only a local window; they cannot say why \"black dog\" is well-formed English and \"dog black\" is not, because that is a fact about structure. This lesson takes up structure: phrase-structure and probabilistic context-free grammars, syntactic analysis by chart parsing and CYK, augmented grammars and compositional semantics, then the two major statistical successes — machine translation and speech recognition — cast as noisy-channel problems. It closes with the bridge from n-grams to transformers and where the classical account sits relative to modern NLP.\n",{"title":1273,"path":1274,"lessonNumber":1042,"topics":1275,"summary":1276},"Philosophy, Ethics, and the Future of AI","\u002Fartificial-intelligence\u002Ffrontiers\u002Fphilosophy-and-future",[1239],"Two questions have shadowed the field since its founding: can machines act intelligently (weak AI), and can they really think (strong AI)? We work through Turing's objections and their rebuttals — the arguments from disability, mathematics, and informality — then the strong-AI debate: the mind-body problem, functionalism and the brain prosthesis, Searle's Chinese Room and the systems reply, and consciousness and qualia. The companion lesson turns from what AI can do to what it should, and closes the course.\n",{"title":1278,"path":1279,"lessonNumber":1048,"topics":1280,"summary":1281},"The Ethics and Future of AI","\u002Fartificial-intelligence\u002Ffrontiers\u002Fai-ethics-and-future",[1239],"Having asked whether machines can act intelligently and really think, we turn to whether we should build them at all. This lesson works through the six ethical risks — lost jobs, autonomous weapons, surveillance and privacy, biased decisions, the safety of superintelligence, and the erosion of accountability — then the value-alignment problem in the LLM era, and where the classical agent components could go next. It closes the course by tying search, logic, probability, and learning into a single picture of intelligence as rational agency.\n",1785117679093]