Download ARTIFICIAL INTELLIGENCE

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CHAPTER 4
Reasoning and Inference
Techniques
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INTRODUCTION
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 From the previous chapter, once the
knowledge representation in the knowledge
base is completed, or is at least at a high
level of accuracy, it is ready to be used.
 A computer program is needed to access the
knowledge for making inferences.
 This program is an algorithm that controls a
reasoning process and is usually called the
inference engine or the control program.
 This program is also called rule interpreter.
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CATEGORIES OF REASONING
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Reasoning can be defined in different
ways, depending on whether it is used in
the context of idealist philosophy or logic
and argument
Within idealist philosophical contexts,
reasoning is "the mental process that
informs our imagination, perceptions,
thoughts, and feelings with whatever
intelligibility these might have.
Two major categories are : model-based
reasoning
(MBR)
and
case-based
reasoning (CBR).
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CASE-BASED REASONING (CBR)
CBR allows one to build a library of
cases, or experiences, which are
described according to a fixed set of
descriptors called the domain model. The
domain model has features (such as
"Smoke Colour") and values (such as
"black", "white", etc.). Later on, one can
call up relevant cases by specifying a set
of Feature-Values.
Cases will be sent to the user with a
similarity rating which tells him what
percentage of the case values correspond
to the values of the query.
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MODEL-BASED REASONING
(MBR)
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The Model-Based Reasoning (MBR) can
be viewed as the symbolic processing of
an explicit representation of the internal
workings of a system in order to predict,
simulate, and/or explain the resultant
behavior of the system from the
structure, causality, functional and
behavior of its components.
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MODEL-BASED REASONING
(MBR)
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Thus, the first step in MBR is building an
accurate representation (model) of the
system that you want to be able to reason
about.
Once there is a complete model and an
algorithm which correctly reproduces the
relationships and behavior of the system,
one can get complete, precise solutions
based on a set of inputs.
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INFERENCE TECHNIQUES
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Modus Ponens
In logic, modus ponens (Latin: mode that
affirms; often abbreviated MP) is a valid,
simple argument form
It is a very common form of reasoning, and
takes the following form:
If P, then Q.
P
Therefore, Q
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Modus Ponens
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In logical operator notation:
The modus ponens rule may also be written
as:
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INFERENCE TECHNIQUES
Resolution
In mathematical logic and automated
theorem proving, resolution is a rule of
inference leading to a refutation theoremproving technique for sentences in
propositional logic and first-order logic
The resolution rule in propositional logic is
a single valid inference rule producing, from
two clauses, a new clause implied by them
(a clause is a disjunction of literals, where a
literal is an atom or a negated atom)
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Resolution
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The resolution rule takes two clauses
containing complementary literals (i.e.
literals with the same atom, but opposing
signs), and produces a new clause with all
the literals of both except for the
complementary ones
Formally, whereas ai and bj are
complementary literals:
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Resolution
The clause produced by the resolution
rule is called the resolvent of the two input
clauses
When the two clauses contain more than
one pair of complementary literals, the
resolution
rule
can
be
applied
(independently) for each such pair
However, only the pair of literals that are
resolved upon can be removed: all other
pair of literals remain in the resolvent
clause
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A Resolution Technique
When coupled with a complete search
algorithm, the resolution rule yields a
sound and complete algorithm for
deciding
the
satisfiability
of
a
propositional formula, and, by extension,
the validity of a sentence under a set of
axioms
This resolution technique uses proof by
contradiction and is based on the fact that
any sentence in propositional logic can be
transformed into an equivalent sentence
in conjunctive normal form
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Resolution
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The steps are as follow:
– All sentences in the knowledge base
and the negation of the sentence to be
proved
(the
conjecture)
are
conjunctively connected
– The resulting sentence is transformed
into a conjunctive normal form (treated
as a set of clauses, S)
– The resolution rule is applied to all
possible pairs of clauses that contains
complementary literals
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Resolution
After each application of the resolution
rule, the resulting sentence is simplified
by removing repeated literals.
If the sentence contains complementary
literals, it is discarded (as a tautology)
If not, and if it is not yet present in the
clause set S, it is added to S, and is
considered
for
further
resolution
inferences
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Resolution
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If after applying a resolution rule the
empty clause is derived, the complete
formula is unsatisfiable (or contradictory),
and hence it can be concluded that the
initial conjecture follows from the axioms
If, on the other hand, the empty clause
cannot be derived, and the resolution rule
cannot be applied to derive any more new
clauses, the conjecture is not a theorem of
the original knowledge base
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CONTROL STRATEGIES
Forward-chaining inference is often called
data driven — in contrast to backwardchaining inference, which is referred to as
goal driven reasoning.
The top-down approach of forward
chaining is commonly used in expert
systems, such as CLIPS.
One of the advantages of forward-chaining
over backwards-chaining is that the
reception of new data can trigger new
inferences, which makes the engine better
suited to dynamic situations in which
conditions are likely to change.
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Control Strategies
Forward Chaining
Forward chaining is one of the two main
methods of reasoning when using inference
rules (in artificial intelligence)
Forward chaining starts with the available
data and uses inference rules to extract more
data (from an end user for example) until an
optimal goal is reached
An inference engine using forward chaining
searches the inference rules until it finds one
where the If clause is known to be true
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Backward Chaining
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One of the two main methods of reasoning when
using inference rules
Backward chaining starts with a list of goals (or a
hypothesis) and works backwards to see if there
are data available that will support any of these
goals
An inference engine using backward chaining
would search the inference rules until it finds one
which has a Then clause that matches a desired
goal
If the If clause of that inference rule is not known
to be true, then it is added to the list of goals (in
order for your goal to be confirmed you must also
provide data that confirms this new rule)
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Backward Chaining
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For example, suppose that the goal is to conclude
the color of my pet Fritz, given that he croaks and
eats flies, and that the rule base contains the
following two rules:
1. If Fritz croaks and eats flies - Then Fritz is a
frog
2. If Fritz is a frog - Then Fritz is green
This rule base would be searched and the second
rule would be selected, because its conclusion (the
Then clause) matches the goal (that Fritz is green).
It is not yet known that Fritz is a frog, so the If
statement is added to the goal list (in order for Fritz
to be green, he must be a frog
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Backward Chaining
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The rule base is again searched and this time the first
rule is selected, because its Then clause matches
the new goal that was just added to the list (whether
Fritz is a frog)
The If clause (Fritz croaks and eats flies) is known to
be true and therefore the goal that Fritz is a frog can
be concluded (Fritz croaks and eats flies, so must be
green; Fritz is green, so must be a frog)
Because the list of goals determines which rules are
selected and used, this method is called goal driven,
in contrast to data-driven forward-chaining inference
This bottom-up approach is often employed by expert
systems
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SEARCHING TECHNIQUES
Breadth First Techniques
In graph theory, breadth-first search (BFS)
is a graph search algorithm that begins at
the root node and explores all the
neighboring nodes.
Then for each of those nearest nodes, it
explores their unexplored neighbor nodes,
and so on, until it finds the goal.
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Depth First Search
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Depth-first search (DFS) is an algorithm
for traversing or searching a tree, tree
structure, or graph. Intuitively, one starts
at the root (selecting some node as the
root in the graph case) and explores as far
as possible along each branch before
backtracking
Formally, DFS is an uninformed search
that progresses by expanding the first
child node of the search tree that appears
and thus going deeper and deeper until a
goal node is found, or until it hits a node
that has no children
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Searching Techniques
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Then the search backtracks, returning to
the most recent node it hadn't finished
exploring
Space complexity of DFS is much lower
than BFS (breadth-first search)
It also lends itself much better to heuristic
methods of choosing a likely-looking
branch
Time complexity of both algorithms are
proportional to the number of vertices
plus the number of edges in the graphs
they traverse (O(|V| + |E|))
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Searching Techniques
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When searching large graphs that cannot
be fully contained in memory, DFS suffers
from non-termination when the length of a
path in the search tree is infinite
The simple solution of "remember which
nodes I have already seen" doesn't always
work because there can be insufficient
memory
This can be solved by maintaining an
increasing limit on the depth of the tree,
which is called iterative deepening depthfirst search
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Searching Techniques
A depth-first search starting at A, assuming that
the left edges in the shown graph are chosen
before right edges, and assuming the search
remembers previously-visited nodes and will not
repeat them (since this is a small graph), will visit
the nodes in the following order: A, B, D, F, E, C,
G
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Searching Techniques
Performing the same search without
remembering previously visited nodes
results in visiting nodes in the order A, B,
D, F, E, A, B, D, F, E, etc. forever, caught in
the A, B, D, F, E cycle and never reaching
C or G.
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Best First Search
Best-first search is a search algorithm
which optimizes breadth-first search by
expanding the most promising node
chosen according to some rule
Best-first search estimates the promise
of node n by a "heuristic evaluation
function f(n) which, in general, may
depend on the description of n, the
description of the goal, the information
gathered by the search up to that point,
and most important, on any extra
knowledge about the problem domain"
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