Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
METHODS OF INFERENCE Hasan Zafari METHODS OF INFERENCE What is reasoning? Inferences with rules trees The inference tree Inference by Inheritance Inference with frames Reasoning with semantic networks Reasoning with logic KR LANGUAGES AND NATURAL LANGUAGE how is a knowledge representation language different from natural language e.g. English, Spanish, German, … natural languages are expressive, but have evolved to meet the needs of communication, rather than representation the meaning of a sentence depends on the sentence itself and on the context in which the sentence was spoken e.g. “Look!” sharing of knowledge is done without explicit representation of the knowledge itself and they are ambiguous (e.g. small dogs and cats) GOOD KNOWLEDGE REPRESENTATION LANGUAGES combines the best of natural and formal languages: expressive concise unambiguous independent of context formal what you say today will still be interpretable tomorrow the knowledge can be represented in a format that is suitable for computers effective there is an inference procedure which can act on it to make new sentences REASONING process of constructing new sentences from old ones proper reasoning ensures that the new sentences represent facts that actually follow from the facts that the old sentences represent this relationship is called entailment and can be expressed as KB |= alpha knowledge base KB entails the sentence alpha WHAT INFERENCE METHODS DO? an inference procedure can do one of two things: given a knowledge base KB, it can derive new sentences that are (supposedly) entailed by KB KB |-- ==> KB |= given a knowledge base KB and another sentence alpha, it can report whether or not alpha is entailed by KB KB ==> KB |= an inference procedure that generates only entailed sentences is called sound or truth-preserving the record of operation of a sound inference procedure is called a proof an inference procedure is complete if it can find a proof for any sentence that is entailed TREES: MAKING DECISIONS Trees / lattices are useful for classifying objects in a hierarchical nature. Trees We / lattices are useful for making decisions. refer to trees / lattices as structures. Decision trees are useful for representing and reasoning about knowledge. 7 DECISION TREE EXAMPLE 8 مثالی دیگر از درخت تصمیم گیری سایت جالب http://en.akinator.com/ 9 AND-OR TREES AND GOALS 1990s, PROLOG was used for commercial applications in business and industry. PROLOG uses backward chaining to divide problems into smaller problems and then solves them. AND-OR trees also use backward chaining. AND-OR-NOT lattices use logic gates to describe problems. 10 11 12 INHERITANCE Inheritance is one of the main kind of reasoning done in semantic nets The ISA (is a) relation is often used to link a class and its superclass. Some links (e.g. haspart) are inherited along ISA paths The semantics of a semantic net can be relatively informal or very formal Often defined at the implementation level Animal isa Bird hasPart isa Robin isa Rusty isa Red Wings INFERENCE BY INHERITANCE One of the main types of reasoning done in a semantic net is the inheritance of values (properties) along the subclass and instance links. Semantic networks differ in how they handle the case of inheriting multiple different values. All possible values are inherited, or Only the “lowest” value or values are inherited 14 15 MULTIPLE INHERITANCE A node can have any number of superclasses that contain it, enabling a node to inherit properties from multiple parent nodes and their ancestors in the network. It can cause conflicting inheritance. Nixon Diamond (two contradictory inferences from the same data) subclass pacifist Person non-pacifist Republican Quaker instance instance Nixon P ? !P subclass Q R N CONFLICT RESOLUTION double arrows signify deductive or strict (i.e., non-defeasible) inferences single arrows signify defeasible inferences, and strikethrough single arrows signify that the negation of the pointed formula is defeasibly implied Penguins are birds (no exceptions); Birds usually fly; and Penguins usually don't fly. conflict Penguin ⇒ Bird → flies Penguin → not-flies According to the Specificity Principle an inference with a more specific antecedent overrides a conflicting defeasible inference with a less specific antecedent. FRAMES Frames – semantic net with properties A frame represents an entity as a set of slots (attributes) and associated values A frame can represent a specific entry, or a general concept Frames are implicitly associated with one another because the value of a slot can be another frame 3 components of a frame •frame name •attributes (slots) •values (fillers: list of values, range, string, etc.) Book Frame Slot Filler •Title AI. A modern Approach •Author Russell & Norvig •Year 2003 FEATURES OF FRAME REPRESENTATION More natural support of values than semantic nets (each slots has constraints describing legal values that a slot can take) Can be easily implemented using object-oriented programming techniques Inheritance is easily controlled INHERITANCE Similar to Object-Oriented programming paradigm Hotel Chair Hotel Room •what room •where hotel •contains –hotel chair –hotel phone –hotel bed •what chair •height 20-40cm •legs 4 Hotel Phone •what phone •billing guest Hotel Bed •what •size •part bed king mattress Mattress •price 100$ استنتاج در فریم فریم از اجزای به هم وابسته ای تشکیل می شود بین اجزای فریم ارتباطات معناداری وجود دارد دانستن برخی اجزای فریم به استنباط دیگر اجزا کمک می کند مثال FrameNet :برای درک متن در مثال زیر دو جمله با ساختارها و افعال متفاوت بیان شده اند که به دلیل تعلق به یک فریم مشابه می توان یکی بودن معنای آنها را نتیجه گرفت 21 INFERENCE WITH FRAMES 22 Reasoning with semantic networks - Knowledge explicitly represented in a semantic network can be used to infer additional facts which are NOT explicitly represented (1) Inferences may rely on rules of common sense e.g., For all objects X, Y, and Z cup-1 if X is on Y is left of and Y is left of Z is on then X is left of Z in the example network teapot-1 saucer-1 is left of cup-1 is on saucer-1 and saucer-1 is left of teapot-1 it follows the above general rule, then: cup-1 is left of teapot-1 Inferences based on transitivity - Relationship is a is transitive if X is a Y and Y is a Z then X is a Z holds for all distinct objects X, Y and Z drinking vessel is a is a cup-1 is a cup - Relationship part of is transitive - Relationship supported by is transitive, allowing the inference shown by the dotted line in the following semantic network fragment table-1 supported by supported by cup-1 saucer-1 supported by - However, the relationship is on (i.e., resting directly on) is not transitive cup-1 is on saucer-1 and saucer-1 is on table-1 but cup-1 is not on table-1 - Relationships among people brother of is transitive but not father of Inference based on inheritance - A node inherits information from its related more general node - Add a general object node, other nodes inherit its properties - Eases the task of coding knowledge - Automatically infer information about related objects in hierarchy Example: attribute purpose is inherited a cup is a drinking vessel purpose of a drinking vessel is drinking drinking vessel it follows by inheritance that: purpose of a cup is drinking is a cup purpose purpose drinking Inferences based on transitivity and inheritance drinking vessel purpose drinking is a cup purpose is a cup-1 Two steps involved in the inference shown by the dotted line: Step 1. inference based on transitivity Step 2. inference based on inheritance Dealing with exceptions - Inheritance is a default mechanism and exceptions do occur Wings Air HAS Tweety Canary IS-A IS-A Bird BREATHE IS-A Animal TRAVEL IS-A Fly Penguin From the above semantic network, it can be inferred that: Canary is a animal, Tweety is a bird, Tweety is a animal, Penguin is a bird, Penguin is a animal, Penguin travel fly …... - If an attribute’s value is explicitly represented in a semantic net, it takes priority over the value that would otherwise by inherited Step 1. Account for exceptions on local basis Step 2. Link new node with information that over-ride the incorrectly inherited information Wings Air HAS Tweety IS-A Canary IS-A IS-A Penguin TRAVEL Walk Bird BREATHE IS-A TRAVEL Fly Animal SEMANTIC NET OPERATION User How do you travel? Bird Fly TRAVEL Fly How do you travel? How do you travel? How do you travel? Tweety User Fly Bird Canary Fly Fly TRAVEL Fly ADVANTAGES & DISADVANTAGES Advantages Explicit and succinct Reduced search time Inheritance Has correspondence with human memory Disadvantages No interpretation standards Invalid inferences Combinatorial explosion: if a relation is false many or all of the relations in the network must be examined. Rules of Inference Expert Systems: Principles and Programming, Fourth Edition 32 REASONING WITH LOGIC Truth Table Modus Ponens Expert Systems: Principles and Programming, Fourth Edition 34 Types of Logic • Deduction – reasoning where conclusions must follow from premises • Induction – inference is from the specific case to the general • Analogy – inferring conclusions based on similarities with other situations • Abduction – reasoning back from a true condition to the premises that may have caused the condition Expert Systems: Principles and Programming, Fourth Edition 35 Deductive Logic • Argument – group of statements where the last is justified on the basis of the previous ones • Deductive logic can determine the validity of an argument. • Syllogism – has two premises and one conclusion • Deductive argument – conclusions reached by following true premises must themselves be true Expert Systems: Principles and Programming, Fourth Edition 36 Syllogisms vs. Rules • Syllogism: – All basketball players are tall. – Jason is a basketball player. – Jason is tall. • IF-THEN rule: IF All basketball players are tall and Jason is a basketball player THEN Jason is tall. Expert Systems: Principles and Programming, Fourth Edition 37 Figure 3.21 Causal Forward Chaining Expert Systems: Principles and Programming, Fourth Edition 38 Comparing abduction, deduction, and induction A => B A --------B Deduction: major premise: minor premise: conclusion: All balls in the box are black These balls are from the box These balls are black Abduction: rule: observation: explanation: All balls in the box are black A => B B These balls are black These balls are from the box ------------Possibly A Induction: case: These balls are from the box Whenever observation: These balls are black A then B ------------hypothesized rule: All ball in the box are black Possibly A => B Deduction reasons from causes to effects Abduction reasons from effects to causes Induction reasons from specific cases to general rules 40