Knowledge representation and reasoning Introduction Knowledge representation and

Knowledge representation and reasoning

Introduction • Knowledge representation and reasoning is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can utilize to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology about how humans solve problems and represent knowledge in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of reasoning, such as the application of rules or the relations of sets and subsets.

KNOWLEDGE REPRESENTATION FRAMEWORK • Problem solving requires large amount of knowledge and some mechanism for manipulating that knowledge. – Knowledge is a description of the world; it determines a system's competence by what it knows. – Representation is the way knowledge is encoded; it defines the system's performance in doing something.

SOME GENERAL REPRESENTATIONS 1. Logical Representations 2. Production Rules 3. Semantic Networks Conceptual graphs, frames 4. Description Logics

LOGIC Representation

Introduction • Logic is concerned with the truth of statements about the world. • Generally each statement is either TRUE or FALSE. • Logic includes : – Syntax : Specifies the symbols in the language about how they can be combined to form sentences. The facts about the world are represented as sentences in logic. – Semantic : Specifies how to assign a truth value to a sentence based on its meaning in the world. It Specifies what facts a sentence refers to. A fact is a claim about the world, and it may be TRUE or FALSE. – Inference Procedure : Specifies methods for computing new sentences from an existing sentences.

Types • Logics are of different types : – Propositional logic, – Predicate logic, – Temporal logic, – Modal logic, – Description logic – Propositional logic and Predicate logic are fundamental to all logic. – Propositional Logic is the study of statements and their connectivity. – Predicate Logic is the study of individuals and their properties.

PROPOSITIONAL LOGIC (PL) • A proposition is a statement, which in English would be a declarative sentence. Every proposition is either TRUE or FALSE. • Examples: – (a) The sky is blue. , – (b) Snow is cold. , – (c) 12 * 12=144

Properties • propositions are “sentences” , either true or false but not both. • a sentence is smallest unit in propositional logic. • if proposition is true, then truth value is "true". • if proposition is false, then truth value is "false". • The Truth Value of a proposition is True(denoted as T) if it is a true statement, and False(denoted as F) if it is a false statement.

For Example, 1. The sun rises in the East and sets in the West. 2. 1 + 1 = 2 3. 'b' is a vowel. All of the above sentences are propositions, where the first two are Valid(True) and the third one is Invalid(False).

Propositional Calculus • The area of logic which deals with propositions is called propositional calculus or propositional logic.

Symbols • 1. Negation – If Ƥ is a proposition , then the negation of is denoted by ¬ Ƥ, which when translated to simple English. • Example, The negation of “It is raining today”, is “It is not the case that is raining today” or simply “It is not raining today”.

Conjunction • Conjunction is a truth-functional connective which forms a proposition out of two simpler propositions, for example, P and Q. The conjunction of P and Q is written P ∧ Q, and expresses that each are true. We read P ∧ Q for "P and Q". For any two propositions, there are four possible assignments of truth values: • P is true and Q is true • P is true and Q is false • P is false and Q is true • P is false and Q is false •

Example • The conjunction of the propositions – “Today is Friday” and – “It is raining today”, is “Today is Friday and it is raining today”. This proposition is true only on rainy Fridays and is false on any other rainy day or on Fridays when it does not rain.

Disjunction • The disjunction of the propositions – – “Today is Friday” and – – “It is raining today”, – This proposition is true on any day that is a Friday or a rainy day(including rainy Fridays) and is false on any day other than Friday when it also does not rain.

Exclusive Or • The exclusive or of the propositions – – “Today is Friday” and – “It is raining today”, – is “Either today is Friday or it is raining today, but not both”. This proposition is true on any day that is a Friday or a rainy day(not including rainy Fridays) and is false on any day other than Friday when it does not rain or rainy Fridays.

Implication • The implication P→ Q is false iff P is true however Q is false. • In all other cases the implication is true. • In implication first proposition is called premise and the other is called conclusion

Biconditional (↔) • P ↔ Q is true iff P and Q have same values both are true or both are false. • If P and Q have different values, the biconditional is false.

Biconditional (↔) • Example, “It is raining today if and only if it is Friday today. ” is a proposition which is of the form. The above proposition is true if it is not Friday and it is not raining or if it is Friday and it is raining, and it is false when it is not Friday or it is not raining.