5 Logic and Inference: Rules5.1 Introduction1. monotonic rulesIf a conclusion can be drawn, it remains valid even if new knowledge becomes available. 規(guī)則不會被否定 2. nonmonotonic ruels3. description logic4. horn logic5.2 Example of Monotonic Rules：Family Relationships5.3 Monotonic Rules: Syntax1. ingredient of rulesvariable constant predicate function symbol 2. form of the ruleB1,B2,…,Bn->A head: A premise: B1,B2,…,Bn body: {B1,B2,…,Bn} 3. factA fact is a atomic formula. 4. Logic ProgramA logic program P is a finite set of facts and rules. 5. GoalA 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 could be applied and its head could be derived as a conclusion. 2. defeasible rulehas 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 programIs 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 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 termsTerms are represented using XML tags <term>, <function>, <var>, and <const>. 2 atomic formulasFor atomic formulas we use additionally the tag <atom> and the tag <predicate>. 3 factA fact is just an atomic formula, enclosed by opening and closing <fact> tags. 4 ruleA 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 queryQueries are represented as the bodies of rules, surrounded by <query> tags. 6 DTD for the XMLsee the book. 7 RuleMLRuleML 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 Rules1. Syntactic difference in nonmonotonic rules<!--[if !supportLists]-->ü <!--[endif]-->There are no function symbols; therefore the term structure is flat. <!--[if !supportLists]-->ü <!--[endif]-->Negated atoms may occur in the head and the body of a rule. <!--[if !supportLists]-->ü <!--[endif]-->Each rule has a label. <!--[if !supportLists]-->ü <!--[endif]-->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. Suggested Reading |
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