B₁ ∪ B₂ ∪ … ∪ B_n ⸦ A₁ ∩ A₂ ∩ ... ∩ A_m

What is the antecedent and consequent?

Antecedent: right side (i.e., A_i ... A_m)

Consequent: left side (i.e., B₁ … B_n)

-Process of inferring a proposition from given propositions

-Allows inferred propositions to be computed from given propositions

Infer a proposition given the following propositions:

older(joanne, jake) ⸦ mother(joanne, jake)

wiser(joanne, jake) ⸦ older(joanne, jake)

• sorted(list) ⸦ ∀_j such that 1 ≤ j < n, list(j) ≤ list(j + 1)
• sort(old_list, new_list) ⸦ permute(old_list, new_list) ∩ sorted(new_list)

1. permute is a predicate returned true if its _____ parameter is a permutation of its _____ parameter
2. sort the items in _____ and put them into _____

Prolog

An atom or an integer

Symbolic value of Prolog, consists of either:

• a string of letters, digits, and underscores beginning with a lowercase letter
• a string of printable ASCII characters delimited by apostrophes

Prolog

any string of letters, digits, and underscores beginning with an uppercase letter

Prolog

• binding of a variable to a value
• Lasts as long as it takes to satisfy one complete goal

• Used for the hypotheses
• Headless Horn clauses.

female(shelley).

male(bill).

father(bill, jake).

• Used for the hypotheses
• Headed Horn clause

Prolog

May be single term OR conjunction

Prolog

Must be single term

• For theorem proving, theorem is in form of proposition that we want system to _____ or _____
• In Prolog, these propositions are called goals (statements) or _____; same format as _____ Horn clause
• _____ propositions are propositions with _____ also legal goals

father(X, mike)

System will then attempt, through _____, to find an instantiation of X that results in a true value

Prolog: Inferencing Process

If a goal is a compound proposition, each of the facts is a _____

_____-_____ resolution, _____ chaining

• Begin with facts and rules of database and attempt to find sequence that leads to goal
• Works well with a large set of possibly correct answers

_____-_____ resolution, _____ chaining

• Begin with goal and attempt to find sequence that leads to set of facts in database
• Works well with a small set of possibly correct answers

• With a goal with multiple subgoals, if fail to show truth of one of subgoals, reconsider previous subgoal to find an alternative solution
• Begin search where previous search left off
• Can take lots of time and space because may find all possible proofs to every subgoal

Tracing model of execution- 4 events:

• _____ (beginning of attempt to satisfy goal)
• _____ (when a goal has been satisfied)
• _____ (when backtrack occurs)
• _____ (when goal fails)

speed(ford, 100).

speed(chevy, 105).

speed(dodge, 95).

speed(volvo, 80).

time(ford, 20).

time(chevy, 21).

time(dodge, 24).

time(volvo, 24).

distance(X, Y) :- speed(X, Speed), time(X, Time), Y is Speed * Time.

Solve is query: distance(chevy, Chevy_Distance).

Prolog: List Structures

[apple, prune, grape, kumquat]

[]

[X | Y] /* head _____, tail _____; head: _____, tail: _____ */

[X | Y] = [a, b, c] /* x = _____; y = _____ */

What is the result of Family?

append([], List, List).

append([Head | List_1], List_2, [Head | List_3]) :- append(List_1, List_2, List_3).

append([bob, jo], [jake, darcie], Family).

Deficiencies of Prolog

• Resolution order control: In a pure logic programming environment, the order of attempted matches is _____ and all matches would be attempted _____
• The closed-world assumption: The only knowledge is what is in the _____
• The negation problem: Anything not stated in the database is assumed to be _____
• Essential limitations: It is easy to state a sort process in _____, but difficult to actually _____ - it doesn't know how to sort