Logic and Inference: Rules
这一章有许多概念都不是太熟悉，近期需要复习一下。
5 Logic and Inference: Rules
5.1 Introduction
1. monotonic rules
If a conclusion can be drawn, it remains valid even if new knowledge becomes available.
规则不会被否定
2. nonmonotonic ruels
3. description logic
4. horn logic
5.2 Example of Monotonic Rules：Family Relationships
5.3 Monotonic Rules: Syntax
1. ingredient of rules
variable
constant
predicate
function symbol
2. form of the rule
B1,B2,…,Bn->A
head: A
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 Syntax
1. monotonic rule system:
Once the premises of a rule were proved, the rule could be applied and its head could be derived as a conclusion.
2. defeasible rule
has the form: r: L1,…,Ln ⇒ L
where r is the label, {L1, . . . , Ln} the body (or premises), and L the head of the rule.
defeasible logic program
Is a triple (F,R,>) consisting of a set F of facts, a finite set R of defeasible rules, and an acyclic binary relation > on R
3. priorites among rules
4. 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 Trade
5.7 Rule Markup in XML: Monotonic Rules
1 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>, <head>, and <body>.
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 of 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 Rules
1. Syntactic difference in nonmonotonic rules
ü There are no function symbols; therefore the term structure is flat.
ü Negated atoms may occur in the head and the body of a rule.
ü Each rule has a label.
ü Apart from rules and facts, a program also contains priority 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 of predicate logic that allows efficient reasoning. It forms a subset orthogonal to description logics.
• Horn logic is the basis of monotonic rules.
• Nonmonotonic rules are useful in situations where the available information is incomplete. They are rules that may be overridden by contrary evidence (other rules).
• Priorities are used to resolve some conflicts between nonmonotonic rules.
• The representation of rules in XML-like languages is straightforward.