Methods of Inference 1 Session 5 Course: T0273 – EXPERT SYSTEMS Year: 2014

Learning Outcomes LO 2 : Describe the characteristics of Expert Systems After taking this course, students should be expected to explain and use the Method of inference. 3T Expert Systems

Lecture Outline Introduction Trees, Lattices, and Graphs State and Problem Spaces AND-OR Trees and Goals Deductive Logic and Syllogisms Rules of Inference Limitations of Propositional Logic First-Order Predicate Logic Logic Systems Summary Exercise 4T Expert Systems

Introduction It is important to separate the meaning of the words used in reasoning from the reasoning itself. Making inferences is the fundamental method by which expert systems solve problems. 5T Expert Systems

Trees, Lattices, and Graphs A tree is a hierarchical data structure consisting of nodes, which store information or knowledge and branches which connect the nodes. If a node has more than one parent, it is in a network. 6T Expert Systems

Trees, Lattices, and Graphs A simple graph has no links that come immediately back on the node itself. A circuit or cycle is a path through a graph that begins and ends on the same node. An acyclic graph has no cycles. A connected graph has links to all its nodes. A graph with directed links, called a digraph. A directed acyclic graph is a lattice. A tree with only a single path from the root to its one leaf is a degenerate tree. 7T Expert Systems

Trees, Lattices, and Graphs 8T Expert Systems

Trees, Lattices, and Graphs Another application of trees and lattices is making decisions; these are called decision trees or decision lattices and are very common for simple reasoning. A decision structure is both a knowledge representation scheme and a method of reasoning about its knowledge. 9T Expert Systems

State and Problem Spaces A useful method of describing the behavior of an object is to define a graph called the state space. A state is a collection of characteristics that can be used to define the status of state of an object. The state space is the set of spaces showing the transitions between states that the object can experience. A transition takes an object from one state to another. 10T Expert Systems

State and Problem Spaces As a simple example of state spaces, consider the purchase of a soft drink from a machine. As you put coins into the machine, it makes a transition from one state to another. State diagram for a soft drink vending machine accepting quarters (Q) and nickels (N) 11T Expert Systems

State and Problem Spaces This diagram is also called a finite state machine diagram because it describes the finite number of states of a machine. Finite state machines are often used in compilers and other programs to determine the validity of an input. State diagrams are also useful in describing solutions to problems. In these kinds of applications we can think of the state space as a problem space, where some states correspond to intermediate stages in problem solving and some states corresponding to answers. 12T Expert Systems

AND-OR Trees and Goals One type of tree or lattice that is useful in representing backward-chaining problems is AND-OR tree. 13T Expert Systems SELL THE CAR REPAIR THE CAR bad transmi ssion bad fuel pump trouble changing gears can’t go into reverse poor acceler ation engine stalls a lot AND EXCLUSIVE OR

Deductive Logic and Syllogisms Some methods of inference: Deduction Induction Intuition Heuristics Trial and error abduction 14T Expert Systems

Deductive reasoning Deductive reasoning, also deductive logic or logical deduction or, informally, "top-down" logic] is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. The law of syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another.syllogism P → Q Q → R Therefore, P → R. T Expert Systems15

The law of detachment also known as affirming the antecedent and Modus ponens is the first form of deductive reasoning. A single conditional statement is made, and a hypothesis (P) is stated. The conclusion (Q) is then deduced from the statement and the hypothesis. The most basic form is listed below: P → Q (conditional statement) P (hypothesis stated) Q (conclusion deduced) T Expert Systems16

The following is an example of an argument using the law of detachment in the form of an if-then statement: If an angle satisfies 90° < A < 180°, then A is an obtuse angle. A = 120°. A is an obtuse angle. T Expert Systems17

Inductive Reasoning Inductive Reasoning is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion % of biological life forms that we know of depend on liquid water to exist. 2. Therefore, if we discover a new biological life form it will probably depend on liquid water to exist. 1.All biological life forms that we know of depend on liquid water to exist. 2. All biological life probably depends on liquid water to exist. T Expert Systems18

Intuition Intuition (Mind), a phenomenon of the mind described as the ability to acquire knowledge without inference or the use of reason T Expert Systems19

Heuristic Heuristic method is any approach to problem solving, learning, or discovery that employs a practical methodology not guaranteed to be optimal or perfect 1.If the problem is abstract, try examining a concrete example. 2.Try solving a more general problem first (the "inventor's paradox": the more ambitious plan may have more chances of success).f T Expert Systems20

Trial and error Trial and error is a fundamental method of solving problems. It is characterized by repeated, varied attempts which are continued until success, or until the agent stops trying. T Expert Systems21

Abduction is a form of logical inference that goes from an observation to a hypothesis that accounts for the observation, ideally seeking to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not guarantee the conclusion. One can understand abductive reasoning as "inference to the best explanation" T Expert Systems22

Deductive Logic and Syllogisms One of the most often-used methods of drawing inferences in deductive logic, which has been used since ancient times to determine the validity of an argument. The premises are also called the antecedent and the conclusion is called the consequent. The classic syllogism is a special type called a categorical syllogism. 23T Expert Systems

Rules of Inference The following is an example of a very simple inference within the scope of propositional logic: Premise 1: If it's raining then it's cloudy. Premise 2: It's raining. Conclusion: It's cloudy. Premise 1: P→Q Premise 2: P Conclusion: Q 24T Expert Systems

Limitations of Propositional Logic There are no logical connectives in the premises or conclusions and so each premise and each conclusion must have a different logical variable. Propositional logic has no provision for quantifiers and so there is no way to represent the quantifier “all” in the first premise. 25T Expert Systems

First-Order Predicate Logic Syllogistic logic can be completely described by predicate logic. The four categorical statements and their representation and predicate logic are shown in the table below: 26T Expert Systems

Logic Systems A logic system is a collection of objects such as rules, axioms, statements, and so forth organized in a consistent manner. Goals of the logic system: –Specify the forms of arguments –Indicate the rules of inference that are valid One important function of a logic system is to determine the well-formed formulas (wffs) that are used in arguments. Only wffs can be used in logic arguments. 27T Expert Systems

Logic Systems For example, in syllogistic logic All S is P could be a wff, but: All All is S P Is S all are not wffs. Although the symbols of the alphabet are meaningless, the sequence of symbols that make up the wff is meaningful. 28T Expert Systems

Summary Making inferences is the fundamental method by which expert systems solve problems. A tree is a hierarchical data structure consisting of nodes. Another application of trees and lattices are called decision trees or decision lattices. A useful method of describing the behavior of an object is to define a graph called the state space. One type of tree or lattice that is useful in representing backward-chaining problems is AND-OR tree. There are some methods of inference. 29T Expert Systems

Exercise 1.Draw a state diagram for a well-structured travel problem having: –Three methods of payment: cash, check, or change –Traveler’s interests: sun, snow –Four possible destinations depending on the traveler’s interests and money –Three types of transportation Write IF-THEN rules to advise a traveler where to go depending on money and interests. Pick real destinations and find out the costs to get there from your location. 30T Expert Systems

Quiz 1.Gambar dan jelaskan secara terperinci komponen utama Sistem Pakar 2.Jelaskan berbagai tipe error (ambiguous, incomplte, incorrect dan measurement) 3.Berikan contoh penerapan fuzzy logic pada sistem pakar. 31T Expert Systems

Joseph Giarratano, Gary Riley Expert Systems: Principles and Programming Chapter 3. Thomson Course Technology. Australia. ISBN: Peter Jackson Introduction to Expert Systems. Addison-Wesley. Harlow, England. ISBN: References T Expert Systems32