Excerpt) (aswp) Chap 5 logic & inference: Rules

ArticleDirectory

• 1. Monotonic rules
• 2. Nonmonotonic ruels
• 3. description logic
• 4. Horn logic
• 1. Ingredient of rules
• 2. Form of the rule
• 3. Fact
• 4. Logic Program
• 5. Goal
• 1. Monotonic rule system:
• 2. defeasible rule
• 3. priorites among rules
• 4. priciples to determine the priority
• 1 Terms
• 2 atomic Formulas
• 3 fact
• 4 Rule
• 5 Query
• 6 DTD for the XML
• 7 ruleml
• 1. Syntactic Difference in Nonmonotonic rules

Logic and inference: Rules

This chapter is not very familiar with many concepts. You need to review it recently.

5 logic and inference: rules5.1 introduction1. monotonic rules

If a conclusion can be drawn, it remains valid even if new
Knowledge becomes available.

The rule is not denied.

2. Nonmonotonic ruels3. description logic4. horn logic5.2 example of monotonic rules : Family
Relationships5.3 monotonic rules: syntax1. ingredient of rules

Variable

Constant

Predicate

Function symbol

2. Form of the rule

B1, B2 ,..., BN->

Head:

Premise: B1, B2 ,..., BN

Body: {b1, b2 ,..., BN}

3. Fact

A fact is a atomic formula.

4. Logic Program

A logic program P is a finite set of facts and rules.

5. Goal

A goal denotes a query g asked to a logic program. It has
The Form

B1,..., bn→

If n = 0 we have the empty goal

5.4 monotonic rules: Semantics

?Ground witness,

Parameterized witness

5.5 Nonmonotonic rules: motivation and syntax1. monotonic rule system:

Once the premises of a rule were proved, the rule cocould be
Applied and its head cocould be derived as a conclusion.

2. defeasible rule

Has the form: R: L1 ,..., LnBytes L

Where R isLabel,
{L1,..., ln}Body(Or premises ),
And lHeadOf the rule.

Defeasible Logic Program

Is a triple (F, R,>) consisting of a set F of facts,
Finite Set R of defeasible rules, and an acyclic binary relation> on R

 

3. priorites among rules4. priciples to determine the priority

(1) The source has more authority.

(2) recent one is favorable.

(3) specific one is preferred.

5.6 example of Nonmonotonic rules: brokered trade5.7 rule markup in XML: Monotonic rules1 terms

Terms are represented using XML tags <term>,
<Function>, <var>, and <const>.

2 atomic Formulas

For atomic formulas we use additionally the tag <atom>
And the tag <predicate>.

3 fact

A fact is just an atomic formula, enclosed by opening and
Closing <fact> tags.

4 Rule

A rule consist of a head and a body. A head is an atomic
Formula. The body is a (possibly empty) sequence of atomic formulas. We use new
Tags <rule>,

5 Query

Queries are represented as the bodies of rules, surrounded
By <query> tags.

6 DTD for the XML

See the book.

7 ruleml

Ruleml is an important standardization effort in the area
Rules in the context of the semantic web.

In XML the order of elements is important, whereas it is
Ignored in RDF. In ruleml, the position of which in an expression is
Irrelevant.

5.8 rule markup in XML: Nonmonotonic rules1. Syntactic Difference in Nonmonotonic rules

Ü 
There areNo
Function symbols; Therefore the term structure is flat.

Ü 
Negated
AtomsMay occur in the head and the body of a rule.

Ü 
Each rule hasLabel.

Ü 
Apart from rules and facts, a program also
ContainsPriority statements.

2. Use a <stronger> tag to represent priorities, and an ID label in
Rules to denote their name.5.9 Summary

•Horn logic is a subset
Predicate Logic that allows efficient reasoning. It forms a subset orthogonal
To description logics.

•Horn logic is the basis
Monotonic rules.

•Nonmonotonic rules are useful
In situations where the available information is incomplete. They are rules
That may be overridden by contrary eviden (other rules ).

•Priorities are used to resolve
Some conflicts between Nonmonotonic rules.

•The representation of rules in
XML-like versions is straightforward.

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