专家系统谓词逻辑推理

21
Propositional Logic
Biconditional p q

states that p implies q and q implies p (p → q) ∧ (q → p) has the following meanings:
p if and only if q q if and only if p if p then q, and if q then p

In particular, it deals with the manipulation of logical variables, which represent propositions
P: A square has four equal sides Q: George Washington was the second president
The conditional does not mean exactly the same
as the IF-THEN in a procedural language or a rulebased expert system


IF-THEN means to execute the actions following the THEN if the conditions of the IF are true In logic, the conditional is defined by its truth table （真值表）:p → q is false only when p is true and q is false otherwise it is true.
Its meaning can be translated into natural
language in a number of ways

p implies q if p then q q is necessary for p
p
is sufficient for q q if p p only if q
Basic concept

It is a symbolic logic for manipulating propositions
Propositions means declarative sentences that
can be classified as true or false
“A square has four equal sides” “George Washington was the second president”


Logic is the study of rules of exact reasoning （精 确推理）– inferring conclusions from premises Automated reasoning – logic programming in the context of expert systems
2
Introduction
The core of ES
Programs= Algorithms + Data Structures Expert Systems= Inference + Knowledge
3
Introduction
Importance of knowledge representation and inference in ES
16
Propositional Logic
Four types of sentences
Propositional logic/propositional calculus/statement calculus/sentential calculus（演算）
17
Propositional Logic
4
Introduction
Importance of knowledge representation and inference in ES


Knowledge representation is key to the success of expert systems Knowledge representation affects the development, efficiency, speed, and maintenance of the system
Premise: Premise: Conclusion:
All cats are climbers. Garfield is a cat. Garfield is a climber.
11
Logic and Sets
Another form to represent knowledge--Venn diagrams（文氏 图） E.g.:

13
Logic and Sets
Some terms of sets



Universal set (universe) （论域）is the topic of discussion Subsets, proper subsets, intersection, union , and complement An empty set (null set) has no elements
10
Logic and Sets
Earliest form of logic is based on the syllogism （三段论） Syllogisms – have two premises that provide evidence to support a conclusion

Example:
Introduction Logic and Sets Propositional Logic First Order Predicate Logic Rules of Inference for Propositional Logic Logic Systems Resolution and Deduction Resolution and First-Order Predicate Logic Case
9
Logic and Sets

E.g.1: Premise: All X are Y Premise: Z is a X Conclusion: Z is a Y

E.g.2: Premise: All squeegs are moofs Premise: John is a squeeg Conclusion: John is a moof
5
Introduction
A number of knowledge-representation techniques have been devised:



Logic Rules Semantic nets Frames Scripts Conceptual graphs
6
Agenda

p q is true only when p and q are both true or when they are both false
22
Propositional Logic
Tautology（重言式） – a statement that is true for all possible cases



We need to be able to separate the actual meanings of words with the reasoning process itself We need to make inferences w/o relying on semantics We need to reach valid conclusions based on facts only
All men are mortal Socrates is a man Socrates is mortal
12
Logic and Sets
Set--view the Venn diagrams in math terms
A circle represents a set which is a collection of objects E.g. A = {1,3,5} B = { airplanes, balloons, blimps, jet } 1∈A, 2∉A
8
Logic and Sets
Basic concept of Logic

Formal logic
“formal” means that the logic is concerned with
the form of logical statements rather than their meaning In other words, formal logic is concerned with the syntax of statements, not their semantics The words may be nonsense, but the form is correct – this is a “valid argument ” This is extremely important in building expert systems because we have to separate knowledge from reasoning
18
Propositional Logic
Compound statements/propositions