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Reasoning & Conceptual Graphs

Ayaz Ahmed Shariff KAsst. Professor, Dept. Of CSE

Birla Institute of Technology International Centre

Ras Al Khaimah

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AD-HOC Methods

• Ad Hoc are methods deals with uncertainty are

methods which have no formal theoretical basis.

• Different ad-hoc procedures have been employed

successively in no. of AI systems, particularly Expert

Systems like MYCIN system.

• MYCIN System: Earliest Expert System (ES) to

diagnose meningitis & infectious blood diseases.

• MYCIN’s KB composed of “if.... Then rules” to

assess various forms of patient evidence.

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Contents

• Ad Hoc Methods

• Heuristic Reasoning Methods

• Frames

• Associative Networks

• Conceptual Graphs

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AD HOC Methods...

• Typical rule of MYCIN ES has form:

• This is a rule that would be used by Inference

mechanism to help to identify the organism

IF: The stain of the organism is gram +ve, and

The morphology of the organism is coccus, and

The growth conformation of the organism is chains

THEN: There us suggestive evidence (0.`7) that the identity of

the organism is Streptococcus

• The Ad Hoc method measures both belief & disbelief

to represent degrees of confirmation respectively

given hypothesis.

• Represented by MB (H,E), is measure of increased

belief in Hypothesis H due to Evidence E.

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Heuristic Reasoning Methods

• The Heuristic methods are based on use of procedures, rules

and other forms of encoded knowledge to achieve specified

goals under uncertainty.

• Using heuristics , one of the several alternative conclusions may

be chosen through the strength of positive v/s negative evidence

presented in form of justifications or endorsements.

• For ex: SOLOMON a prototype system developed by Paul

Cohen in 1985, endorsements in form of heuristics are used to

reason about uncertainties associated with client’s investment

portfolio.

• Thus belief is associated with the rule is a “Subjective

conditional probability”

– P(H | E1, E2, E3) ; H is hypothesis, E is evidence

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Heuristic Reasoning

Methods...• IF: Client income need is high & net worth is medium

to high; THEN: Risk-Tolerance level is medium.

• IF: Client tax bracket is high and risk-tolerance is low;

THEN: Tax-exempt mutual funds are indicated.

• IF: Client age is high & income needs are high &

retirement income is medium; THEN: Risk-Tolerance

is low.

• IF: Two +ve endorsements are medium or high and

one -ve endorsement is high; THEN: Favor positive

choice.

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Associative Networks (AN)

• Network representations provide means of structuring

& exhibiting the structure in knowledge. It provides

more natural way to map NLs and pictorial

representation of objects.

• Associative Networks introduced by Quillion in 1996

to model semantics of English words

• Associative Networks are

– Directed graphs with labelled nodes & arcs

– Ex: 7.2 p128

– Bird -> class of objects, tweety -> class, properties -> color

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Syntax & Semantics of AN

• No generally accepted syntax nor semantics for AN

• Designer dependent & vary from one to other

• Based on PL & FOPL with extensions

• Syntax for any given system is determined by object

& relation primitives chosen & by any special rules if

any to connect nodes

• Language of AN is formed from letters of alphabet

(upper case & lower case), relation symbols, set

membership, decimals, square & oval nodes,

directed arcs

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Associative Networks...

• “ISA” is predicate has been used to exhibit following

type of structures

• Generic – Generic Relationships (subset – superset,

Generalization – Specialization, AKO)

• Generic – Individual Relationships (set membership,

Abstraction)

• PREDICATE shows relations in form of arcs

• AKO Subset

• Member of Attributes

• ISA Instance of

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Semantics of Associative

Networks• If a class A of objects has some property P, and “a” is

a member of A, then we can infer that “a has property

P”

• Associative Networks can use in parallel inference

rules like modus ponens, chain rule & resolution

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Conceptual Graphs (CG)

• Conceptual Graphs (CG) may become de-facto

standard for Associative Networks (AN) in future

• CG may be regarded as primitive building block of

AN is a formalism of knowledge representation

• “CG is a graphical representation of a mental

perception which consists of basic or primitive

concepts & relationships that exist b/w the concepts”

• A single CG is equivalent to a graphical diagram of

natural language sentence where words are depicted

as concepts & relationships

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CG....

INSTRUMENT

SPOON

PERSON : joe FOOD: soupagent eat object

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CG...

• Concepts refers to entities, actions, properties or

events in the world.

• A concept can be Generic or Individual. Individual

concepts have type field followed by referent field

• Generic concepts have no referent field

• Concepts are enclosed in boxes and relations

between concepts in ovals.

• Direction of arrow depends to the order of the

arguments in the relation they occur

• Edges do not have labels

• Standard concepts: AGENT, INSTRUMENT,

OBJECT, PART etc

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Conversion from CG to FOPL

1. Assign unique variable names to every generic concepts.

Ex: EAT, SPOON will be given x & y

2. Labels like PERSON, FOOD converted into unary

predicates with some name

3. Standard Conceptual relations like AGENT, OBJECT,

INSTRUMENT are converted into predicates with many

attributes if required

4. Concept referents like joe, soup become FOPL constants

5. Generic concepts with no quantifier in the referent field

have an existential quantifier placed before the formula

for each variable

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Conversion from FOPL to CG

• Put FOPL formula into prenex normal form & convert

all logic connectives to negation & conjunction.

• Every occurrence of Universal quantification is

replaced by ~E~x

• Every variable x & every occurrence of existential

quantification is then replaced with most general type

concept denote as [T: *x]

• Implication in CG can be represented with negation &

conjuction

• Ex: P Q can be written as ~[P ~[Q]]

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Frame Structures

• Introduced by Marvin Minsky in 1975 as a data

structure to represent a mental model of situation like

“driving a car”, “attending meeting”, “eating in hotel”.

• Frames are general record like structures which

consists of slots & slot values. Slots can of any size

& type.

• Slots which have names & values (or) subfields are

called facets.

• Facets may have names & number of values

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Syntax: Frame Structures

(<frame name>)

(<slot 1> (<facet 1><value 1> ......... <value k1>)

(<facet 2><value 2> ......... <value k2>)

...

...

(<facet n><value n> ......... <value kn>)

...

...

(<slot 2> (<facet 1><value 1> ......... <value k1>)

...

...

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Example: Frame structures

(ford (AKO(VALUE car)

(COLOR (VALUE silver)

(GAS-MILEAGE (DEFAULT fget)

(RANGE (VALUED undefined)

....

....

Note: Gas-Mileage(fget function) to fetch default

value from another frame

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Thank You !!!

Reference: Artificial Intelligence & Expert Systems by Dav W Patterson