5. METHOD OF INFERENCES IFK15037, 3 credits - 5. Methods of Inference

  IFK15037, 3 credits YUITA ARUM SARI, S.Kom, M.Kom yuita@ub.ac.id

OUTLINE

  Tree Graph

La,ce

  Forward & _{Backward Chaining} Logic, _{Syllogism, Modus Ponens} ^{Shallow and} _{Casual Reasoning} ^{Other Inference Method}

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. v  Degenerate trees have only a single pathway from root to its one leaf.

  Tree

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. Ø  Connected graphs have links to all the nodes. Ø  Digraphs are graphs with directed links. Ø  Lattice is a directed acyclic graph.

  Simple Graph

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.

  Decision trees are useful for represenFng and reasoning about knowledge.

  A binary decision tree having N nodes: Decision trees can be self learning.

  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 2 ^N answers for N quesFons.

  Decision trees can be translated into producFon rules.

  Decision Tree Example

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 object can make in going from one state to another.

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.

  FSMs are oYen used in compilers and validity checking programs.

Using FSM to Solve Problem

  Characterizing ill-

  Well-formed

  structured problems – one

  problems: having uncertainFes.

• Explicit problem, goal, and operaFons are known   DeterminisFc – we are sure of
• the next state when an operator is applied to a state.
>The problem space is bounded.
• The states are discrete.

  State Diagram Example State Diagram for a Soft Drink Vending Machine Accepting Quarters (Q) and Nickels (N)

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 problems.

Types of Logic

• – reasoning where conclusions must follow from premises
• – inference is from the specific case to the general

  §   Deduction

  §   Induction

• – no proven theory

  §   Intuition

• – rules of thumb based on experience

  §   Heuristics

• – trial and error

  §   Generate and test

• – reasoning back from a true condition to the premises that may have caused the condition

  §   Abduction

• – absence of specific knowledge

  §   Default

  §   Autoepistemic – self-knowledge §   Nonmonotonic – previous knowledge §   Analogy

• – inferring conclusions based on similarities with other situations

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 DeducFve argument – conclusions reached by following true premises must themselves be true

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 THEN Jason is tall.

  Categorical Syllogism

  Premises and conclusions are defined using categorical statements of the form:

  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.

  Ø Propositional logic offers another means of describing arguments.

  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. Proving the validity of syllogistic arguments using Venn Diagram

  Direct Reasoning- Modus Ponens

  Modus ponens is necessary because it shows a basic rule-based expert systems

  Rules of Inference _{Programming, Fourth Edi:on} Expert Systems: Principles and

  The Modus Meanings The condiFonal and its Variant

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.

  An argument may not be provable using proposiFonal logic, but may be provable using predicate logic.

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.

  Causal reasoning can be used to construct a model that behaves like the real system.

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.

  Problem with backward chaining is find a chain linking the evidence to the hypothesis.

  Causal Forward Chaining

  Some CharacterisWc FC and BC

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 Nonmonotonic Reasoning – theorems may not increase as the number of axioms increase.

  Types od Inference

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

partial or hidden information about the state and

parameters, and the need for planning.