Logic: TD as search, Datalog variables

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Logic TD as search, Datalog (variables)
Computer Science cpsc322, Lecture 23 (Textbook
Chpt 5.4, 6.1- 6.3) March, 7, 2008
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Lecture Overview

• Recap Top Down
• TopDown Proofs as search
• Datalog

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TD Example derivations

• a ? b ? c. a ? e ? f. b ? k ? f.
• c ? e. d ? k. e.
• f ? j ? e. f ? c. j ? c.

Query a (two ways)

yes ? a.
yes ? a.

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Top-down definite clause interpreter

• To solve the query ?q1 ? ? qk
• ac yes ? q1 ? ? qk
• repeat
• select atom qi from the body of ac
• choose clause C from KB with qi as head
• replace qi in the body of ac by the body of C
• until ac is an answer.

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Lecture Overview

• Recap Top Down
• TopDown Proofs as search
• Datalog

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TopDown Proofs as Searching

• The non-deterministic interpreter we just saw a
  selection strategy (to pick which atom to work
  on)
• Can be implemented as a search problem
• Each node represents .
• The neighbors of a node
• With qi as the selected atom
• The goal node is of the form?

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Search Graph
Prove ?? a ? d.

• a ? b ? c. a ? g.
• a ? h. b ? j.
• b ? k. d ? m.
• d ? p. f ? m.
• f ? p. g ? m.
• g ? f. k ? m. h ? m. p.

Heuristics?
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Recap Logics so far

• Propositional logic

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Lecture Overview

• Recap Top Down
• TopDown Proofs as search
• Datalog

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Representation and Reasoning in Complex domains

• In complex domains expressing knowledge with
  propositions can be quite limiting
• It is often natural to consider individuals and
  their properties

down(s1) up(s2) up(s3) ok(cb1) ok(cb2)
live(outside) live(w1)
down_s1. up_s2. up_s3. ok_cb1. ok_cb2.
live_outside, live_w1
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Individuals and Properties (aka Predicates /
Relations)

• Some key advantages
• Economy of symbols 10 individuals and 1 binary
  relation can express.
• Express knowledge that hold for set of
  individuals (by introducing variables)

live(W) lt- connected_to(W,W1) live(W1)
wire(W) wire(W1).

• Also by introducing variables, we can ask generic
  queries (i.e., containing variables)

? connected_to(W, w1)
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Datalog a relational rule language
It expands the syntax of PDCL.
Definition (variable) An variable is a symbol
starting with an upper case letter
Definition (constant) A constant is a symbol
starting with lower-case letter or a sequence of
digits.
Definition (predicate symbol) A predicate symbol
is a symbol starting with lower-case letter.
Definition (term) A term is either a variable or
a constant.
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Datalog Syntax (cont)
Definition (atom) An atomic symbol (atom) is a
of the form p or p(t1 . tn) where p is a
predicate symbol and ti are terms
Definition (definite clause) A definite clause is
an atomic symbol (a fact) or of the form
h ? b1 ? ? bm where h and the bi are
atomic symbol (Read this as h if b.'')
Definition (knowledge base) A knowledge base is a
set of definite clauses
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Datalog Semantics (only general idea)
In propositional definite clause logic an
interpretation is A model of a KB is

• In datalog an interpretation specifies
• What objects are in the world
• The correspondence between symbols in the KB and
  objects and relations in the world
• Constants
• Predicates
• A model of a KB is

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Datalog Top Down Proof
Extension of TD for PDCL. How do you deal with
variables? Example
in(alan, r123). part_of(r123,cs_building). in(X,Y)
lt- part_of(Z,Y) in(X,Z).
Query in(alan, cs_building).
yes lt- in(alan, cs_building).
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Datalog queries with variables
in(alan, r123). part_of(r123,cs_building). in(X,Y)
lt- part_of(Z,Y) in(X,Z).
Query in(alan, X1).
Yes(X1) lt- in(alan, X1).
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Midterm review
Average 67 Best 101, Worst 11

• Carefully examine your mistakes (and our
  feedback)
• If you still do not see the correct
  answer/solution go back to your notes, the slides
  and the textbook
• If you are still confused come to office hours
  with specific questions

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Very common misconceptions

• Breadth First is always optimal. This is the case
  only if..
• The 3queen problem has 9 states. They are 84
• The difference between a goal and a preference
• A goal function is a boolean condition. For each
  state it tells you whether it is a goal state or
  not.
• A preference function tells you for each state
  how desirable that state is (typically range
  between 0 and 1)

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Next class
Environment
Stochastic
Deterministic
Search
Single Action
Constraint Satisfaction (CSPs)
Decision
Logics
Search
Sequence of Actions
Constraint Satisfaction (CSPs)
Planning