Skim Pages 29-61: Problems, Problem Spaces, and Search

  • There are some who believe the simple statement, "AI is search"
  • State space is sometimes explicit, like a matrix of board positions, and sometimes implicit, like a set of rules or productions
  • The analytical approach to problem solving is generally the same in every domain. In AI the usual procedure is
    1. define a state space
    2. identify initial states
    3. identify goal states
    4. specify operators that change states
  • Note, this is roughly the same procedure as any requirements analysis for any software project.
  • Note, define a state space means sub-problem decomposition, also something done in every software project. See How to Solve It by G. Polya
  • It's stated like this in AI because so often the problem area is akin to a board game
  • Control strategies break down into the three types of searches
    1. depth-first search: top to bottom, left to right, the most easily implemented (recursive) algorithm
    2. breadth-first search: left to right, top to bottom, visiting all the children before visiting a grandchild
    3. heuristic search, sometimes called "best first": where theres an evaluation function you can use to choose the next path
  • Key quote from the chapter (pg. 53). "These two problems, chess and newspaper story understanding, illustratte the difference between problems for which a lot of knowledge is important only to constrain the search for a solution and those for which a lot of knowledge is required even to be able to recognize a solution".

Skim Pages 63-98: Heuristic Search Techniques

  • The general messaage(s) are these:
    • very hard problems will tend to have very large search spaces.
    • heuristics (general rules that USUALLY apply), can be used to limit search
    • some sort of evaluation function is always necessary
    • key vocabulary: heuristics allow you to "prune the search tree"
  • generate-and-test: a brute-force depth first search in its simplest form
  • hill-climbing: a variation on generate and test that incorporates visualization (see the usual diagram)
    key vocabulary: the problem of local minima / maxima
  • backtracking is a simple universal strategy, that requires the algorithms to maintain state information.
  • simulated annealing: a variation on hill-climbing where random guesses are introduced (sometimes caled stochastic search)
  • best-first search: much the same as above, but where the evaluation function is much more reliable.
  • agenda-driven search: perhaps the most interesting topic in this chapter, as it produces answers for evaluation by re-ordering tasks. This is an oddity in this chapter
  • problem reduction: another term for "pruning"
  • constraint satisifaction: be aware AI uses a strange sense of "constraint" - the classic example is the seating chart problem.
  • means-ends analysis: not usually described in a chapter on heuristic search. Based on human behavior (as described in Polya and elsewhere)
    key vocabulary: sub-problem decomposition

Read: 105-129: Knowledge Representation Issues

  • the problem-solving power of search techniques is limited in part because of their generality
  • it is generally understood (in symbolic AI) that solving complex problems depends on knowledge and mechanisms to manipulate it
  • the challenge is known as the (knowledge) representation problem
  • the discussion on knowledge level and symbol level, and "representation mappings", is all about the relation between symbols (syntax) and meaning
  • one basic problem is translating informal natural language statements into a formal notation
    • dog(Spot) => Spot is a dog
    • All X: dog(x) -> hastail(x) =>
      All dogs have tails OR Every dog has a tail
    • note: this one fact, and one inference rule, is enough to produce a NEW fact => hastail(Spot)
  • the authors note this is akin to generalized computer programming: finding concrete implementation of abstract concepts
  • the authors do not note that the obverse of representation is interpretation - representing facts and relations is for the sole purpose of supporting inference.
    i.e. dog(Spot) is just ASCII symbols without an inference mechanism to provide meaning
  • the typical AI represention is composed of two types of thing: concepts (usually nouns) and relations
  • relations are sometimes represented as a slot-and-filler structure (also commonly, slots-with-roles-and-fillers), which are also called attribute-value-pairs
  • vocabulary: frame system is a set of structures linked by semantic relations
    a semantic network is a set of concepts linked by semantic relations
    the latter is an older specialization of the former, mostly used in early (associational) memory modeling systems
  • sadly, there is no generally agreed upon set of relations
  • the other key idea in knowledge representation is abstraction/inheritance (and the special relation: ISA, sometimes written AKO, and its inverse: instance-of)
  • by combining these in straight-forward ways, we can infer that Spot is warm-blooded without explicitly representing that fact.
  • procedural knowledge refers to programming that effects actions (like robot arms) or in if-then-else decision making. This is an older term not very useful any more.
  • Note: many of the issues in knowledge representation are similar to data structure issues
  • Note: representing time is difficult (hence, there is an entire branch of logic devoted to it)
  • Vocabulary: granularity, "what level of detail?" "what are the primitives?"

Skim: 131-169: Logic

  • one fundamental issue with predicate logic is everything is "truth valued"; which causes a difficult representational "fit" for a large class of problems
  • another issue is that theorem proving is both "generative" and undecidable, where
    • generative (also called forward reasoning) means starting with axioms and theorems (i.e. starting from first principles), and trying to generate a new proposition that matches the goal
    • unecidable means if the goal is a non-theorem, there's no guarantee the procedure will halt
  • note, however, that while the idea is conceptually generative, the algorithms usually generate proofs by chaining backward from the theorem to be proved to the axioms
  • resolution theorem proving is conceptually the same, but takes the approach of "contradicting the negation"
  • note that unification is one of the steps in resolution
  • one of the main reasons for the popularity of resolution, unification, and PROLOG, is that the first two are relatively easy to implement in the third
  • note, as the authors say, "people do not think in resolution".

Skim: 171-193: Rules

  • rule-based systems are often called "expert systems"
  • these are typically applied to diagnostic domains (eg. medicine) although the most commercially successful configured systems (R1 by DEC).
  • PROLOG is often used to implement rule-based systems
  • one essential control method is the order in which the rules are stored in the rule base
  • the conceptual algorithm is the same as with logic-based systems: begin with a goal statement (to be "proved") and look for (chains of) assertions that prove it
  • PROLOG provides a built-in search engine, but search control is fixed (depth-first with backtracking), and it is very difficult to apply domain knowledge to constrain search
  • a pure PROLOG system (using strictly Horn clauses) is decidable, and implements "negation as failure"
  • negation as failure implies a "closed world assumption" (that every useful fact is stored in the rule-base)
  • this assumption causes a difficult representational "fit" for a large class of problems
  • rule-based systems get more interesting when there is a fcility for "partial matching" (as with the regular expressions in ELIZA)
  • expert systems evolved rule sets that included "meta rules" (rules about rules) as a way to exert more control over problem-solving and run-times
  • historical note: expert systems were extremely fashionable (and fundable) in the mid-80s. This led to the formation of a mini-industry for "expert system shells" (systems for building exert systems) which in turn led to the famous de-bunking paper: "The expert system shell game".
  • summary: expert systems are known to be "brittle" - they are difficult to maintain and difficult to add onto - and they are known for "ungraceful" failures (not producing answers, or producing very bad answers).

Skim: 195-229: Uncertainty

  • non-monotonic reasoning (also called "defeasible")
  • the basic intuition views this as reasoning about "possible worlds" where some facts are not indisputable and new facts can change the state of the universe
  • you can think of it as a "set" of logic- or rule-based systems, where every uncertainty is enumerated in one or another of the possible worlds
  • then problem solving reduces to computing solutions in ALL the possible worlds to find the best one
  • this is why non-monotonic reasoning is criticized for its "combinatorial explosion".
  • special note: abductive reasoning is a new formalism that relaxes the usual rules of deductions;
    • eg. if A imlies B, and B is true, then abduction says we can assume A is true, even without direct evidence.
    • critics call this "reasoning from a faulty premise" but there is an abductive reasoning community out there.

Skim: 231-248: Statistics

  • statistical reasoning (sometimes called stochastic reasoning) divides into two general areas
  • probabilities associated with rules
    • where, for example, low grade fever and a runny nose indicate the common cold, but only about 80% of the time.
    • these systems depend on judgements of domain experts and reasonably standard set theory and logic.
  • fuzzy logic, where concepts or entities can have conditional membership in a set
    • fuzzy logic is intended to support reasoning on propositions that have "degrees of truth".
    • supporters claim this is a better model of reality
    • critics observe that decisions based on fuzzy logic always depend on threshhold values, which effectively reduces to truth valued logic.

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