5. METHOD OF INFERENCES IFK15037, 3 credits
Tree
v A tree is a hierarchical data structure consisting of:
v Nodes – store information
v Branches – connect the nodes
v The top node is the root, occupying the highest hierarchy.
v The leaves are at the bottom, occupying the lowest hierarchy. v Every node, except the root, has exactly one parent.
v Every node may give rise to zero or more child nodes.
v A binary tree restricts the number of children per node to a maximum of two.
Graph
Ø Graphs are sometimes called a network or net.
Ø A graph can have zero or more links between nodes – there is no distinction between parent and child.
Ø Sometimes links have weights – weighted graph; or, arrows – directed graph.
Ø Simple graphs have no loops – links that come back onto the node itself.
Ø A circuit (cycle) is a path through the graph beginning and ending with the same node.
Ø Acyclic graphs have no cycles.
Making Decision
Trees / la,ces are useful for classifying
objects in a hierarchical nature.
Trees / la,ces are useful for making
decisions.
We refer to trees / la,ces as structures.
Binary Decision Tree
Every quesFon takes us down one level in the tree.
• All leaves will be answers.
• All internal nodes are quesFons.
• There will be a maximum of 2N answers for N quesFons.
A binary decision tree having
N
nodes:
Decision trees can be self learning.
State and Problem Spaces
A state space can be used to define an object’s behavior.
Different states refer to characterisFcs that define the status of the object.
A state space shows the transiFons an
State and Problem Spaces
A FSM is a diagram describing the finite number of
states of a machine.
At any one Fme, the machine is in one parFcular state.
The machine accepts input and progresses to the next
state.
Using FSM to Solve Problem
Characterizing
ill-structured problems – one having uncertainFes.
Well-formed
problems:
• Explicit problem, goal, and operaFons are known
• DeterminisFc – we are sure of the next state when an
State Diagram Example
AND-OR Tree and Goals
Ø 1990s, PROLOG was used for commercial applications in business and industry. Ø PROLOG uses backward
chaining to divide problems into smaller problems and then solves them.
Ø AND-OR trees also use backward chaining.
Ø AND-OR-NOT lattices use logic gates to describe
Types of Logic
§ Deduction – reasoning where conclusions must follow from premises
§ Induction – inference is from the specific case to the general
§ Intuition – no proven theory
§ Heuristics – rules of thumb based on experience
§ Generate and test – trial and error
§ Abduction – reasoning back from a true condition to the premises that may have caused the condition
§ Default – absence of specific knowledge
§ Autoepistemic – self-knowledge
§ Nonmonotonic – previous knowledge
DeducWve Logic
Argument – group of statements where the last is
jusFfied on the basis of the previous ones
DeducFve logic can determine the validity of an
argument.
Syllogism – has two premises and one conclusion
Syllogism vs Rules
Syllogism:
All basketball players are tall.
Jason is a basketball player.
Jason is tall
.
IF-THEN rule:
IF
All basketball players are tall and
Jason is a basketball player
Categorical Syllogism
Rule of Inference
Ø Venn diagrams are insufficient for complex arguments.
Ø Syllogisms address only a small portion of the possible logical statements.
1. If a class is empty, it is shaded.
2. Universal statements, A and E are always drawn before particular ones.
3. If a class has at least one member, mark it with an *. 4. If a statement does not specify in which of two adjacent
classes an object exists, place an * on the line between the classes.
5. If an area has been shaded, not * can be put in it.
Direct Reasoning- Modus Ponens
Rules of Inference
The Modus Meanings
LimitaWons of PreposiWonal Logic
If an argument is invalid, it should be interpreted as
such – that the conclusion is necessarily incorrect.
An argument may be invalid because it is poorly
concocted.
Shallow and Causal Reasoning
ExperienFal knowledge is based on experience.
In shallow reasoning, there is li`le/no causal chain of cause and effect from one rule to another.
Advantage of shallow reasoning is ease of programming.
Frames are used for causal / deep reasoning.
Chaining
Chain – a group of mulFple inferences that connect a
problem with its soluFon
A chain that is searched / traversed from a problem
to its soluFon is called a forward chain.
A chain traversed from a hypothesis back to the facts
that support the hypothesis is a backward chain.
Some CharacterisWc FC and BC
Analogy – relaFng old situaFons (as a guide) to new ones.
Generate-and-Test – generaFon of a likely soluFon then test to see if proposed meets all requirements.
AbducFon – Fallacy of the Converse
Metaknowledge
v
The Markov decision process (MDP) is a good
application to path planning.
v
In the real world, there is always uncertainty, and
pure logic is not a good guide when there is
uncertainty.
v
A MDP is more realistic in the cases where there is
REFERENCES
• Joseph C. Giarratano, Gary D. Riley, Expert Systems: Principles and
