Chapter 4 - Knowledge Representation and Reasoning (1).pdf
- 1. Wolaita Sodo University School of Informatics Department of Computer Science Course title: Introduction to Artificial Intelligence
- 2. Chapter 4 Knowledge Representation and Reasoning (KRR)
- 3. Logical Agents • Humans know things and do reasoning, which are important for artificial agents. • Knowledge-based agents – agents that have an explicit representation of knowledge that can be reasoned with. • An intelligent agent needs knowledge about the real world for taking decisions and reasoning to act efficiently. • Knowledge-based agents are those agents who have the capability of maintaining an internal state of knowledge, reason over that knowledge, update their knowledge after observations and take action. • Understanding natural language requires concluding hidden states. • Flexibility for accepting new tasks.
- 4. Logic • Logic proves to be a vital tool to think about how computers store knowledge. • Logic is part of mathematics and can be used in various forms to reason about the correctness of computational representation and inference. What is logic in AI? • A formal language in which knowledge can be expressed. • In Artificial Intelligence, the representation of knowledge is done via logic. • Logical AI involves representing knowledge of an agent's world, its goals and the current situation by sentences in logic.
- 5. Cont… Types of Logic 1. Propositional Logic 2. Predicate Logic
- 6. Propositional logic • Propositional logic (PL) is the simplest form of logic where all the statements are made by propositions. • A proposition is a declarative statement which is either true or false. It is a technique of knowledge representation in logical and mathematical form. • Propositional logic may be viewed as a representation language which allows us to express and reason with statements that are either true or false. • Statements like these are called propositions and are usually denoted in propositional logic by uppercase letters. • Propositions can be combined using logical operators NOT, OR, AND, implies, if and only if, to create new propositions.
- 7. Syntax of propositional logic • The syntax of propositional logic defines the allowable sentences for the knowledge representation. There are two types of propositions: 1. Atomic Propositions 2. Compound propositions Atomic Proposition: are the simple propositions. It consists of a single proposition symbol. These are the sentences which must be either true or false. A proposition is a statement that can either be true (denoted T) or false (denoted F) (simple propositions such as P and Q are called atomic propositions or atoms for short). Example: a) 2+2 is 4, it is an atomic proposition as it is a true fact. b) "The Sun is cold" is also a proposition as it is a false fact. Compound proposition: are constructed by combining simpler or atomic propositions, using parenthesis and logical connectives. Example: a) "It is raining today, and street is wet." b) “Abera is a doctor, and his clinic is in Wolaita Sodo."
- 8. Logic connectives • Logical connectives are used to connect two simpler propositions or representing a sentence logically. • In the language of propositional logic, we have the following five connectives at our disposal: • negation: ￢ (not) • conjunction: ∧ (and) • disjunction: ∨ (or) • implication: → (if then) • bi-implication: ↔ (if and only if)
- 9. • We can create compound propositions with the help of logical connectives. There are mainly five connectives, which are given as follows:
- 10. Cont… Truth Table: • In propositional logic, we need to know the truth values of propositions in all possible scenarios. • We can combine all the possible combination with logical connectives, and the representation of these combinations in a tabular format is called Truth table. Following are the truth table for all logical connectives:
- 11. Exercise • Prepare the truth table for the following ❖I need coffee and I need food ❖I am not hungry ❖I need food or coffee or tea ❖I am hungry, I need food ❖I am hungry and I need food or coffee
- 12. Tautology, contradiction and contingent • A tautology➔ compound statement that is always true. • A contradiction ➔compound statement that is always false. • Contingent statement is one that is neither a tautology nor contradiction (may be some times true some times false). • Example: the truth table of P V ~P shows it is a tautology whereas P ^ ~P is a contradiction ➔Show that the truth table of PV~P is tautology and P ^ ~P is a contradiction
- 13. Inference in propositional Logic • In artificial intelligence, we need intelligent computers which can create new logic from old logic or by evidence, so generating the conclusions from evidence and facts is termed as Inference. • Inference is generating the conclusions from evidence and facts. • Inference rules are the templates for generating valid arguments. • In inference rules, the implication among all the connectives plays an important role.
- 14. Cont… Following are some terminologies related to inference rules: • Implication: It is one of the logical connectives which can be represented as P → Q. It is a Boolean expression. • Converse: The converse of implication, which means the right-hand side proposition goes to the left- hand side and vice-versa. It can be written as Q → P. • Contrapositive: The negation of converse is termed as contrapositive, and it can be represented as ¬ Q → ¬ P. • Inverse: The negation of implication is called inverse. It can be represented as ¬ P → ¬ Q. • Let’s prove using truth table: • Hence from the above truth table, we can prove that P → Q is equivalent to ¬ Q → ¬ P, and Q→ P is equivalent to ¬ P → ¬ Q.
- 15. First-order / Predicate logic • In propositional logic, atoms are the basic elements of formulas which are either true or false. • A limitation of propositional logic is the impossibility to express general statements concerning similar cases. • In case of propositional logic, we are not allowed to conclude the truth of some or ALL statements. • For example: • All the above statements are neither True nor False, thus they are not prepositions. • Predicates are the statements involving variables which are neither True nor False until or unless the values of variables are specified.
- 16. Cont…
- 17. Cont… • First-order / predicate logic is more expressive than propositional logic, and such general statements can be specified in its language. • Predicate logic is concerned with the internal structure of sentences due to prepositional logic has lack of data structure in programming and not sufficient for complex sentences. • Predicate logic in artificial intelligence, also known as first-order logic or first order predicate logic in AI, is a formal system used in logic and mathematics to represent and reason about complex relationships and structures. • It plays a crucial role in knowledge representation, which is a field within artificial intelligence and philosophy concerned with representing knowledge in a way that machines or humans can use for reasoning and problem-solving. • In particular it is concerned with the use of special words called quantifiers such as “all”, “some”, “no”.
- 18. Following are the basic elements of FOL syntax: For instance, in a chess-playing AI, predicates could define piece positions, functions might calculate possible moves, and quantifiers would help evaluate board states for strategic planning.
- 19. Knowledge Representation • Humans are best at understanding, reasoning, and interpreting knowledge. • Knowledge Representation is the systematic means of encoding knowledge obtained from different sources in an appropriate medium. • Knowledge representation plays a crucial role in artificial intelligence. • Knowledge Representation is a radical and new approach in AI that is changing the world. • Knowledge representation (KR) is the study of: – how knowledge and facts about the world can be represented, and – what kinds of reasoning can be done with that knowledge.
- 20. Cont… • Knowledge Representation and Reasoning (KRR) represents information from the real world for a computer to understand and then utilize this knowledge to solve complex real-life problems like communicating with human beings in natural language.
- 21. What to represent • Object: a thing or an entity in our world domain that can be identified/described. • Events: Events are the actions which occur in our world/happens at specific time. • Performance: It describe behavior which involves knowledge about how to do things/how well the task is accomplished. • Meta-knowledge: It is knowledge about what we know/knowledge about knowledge. • Facts: Facts are the truths about the real world and what we represent. ❖Knowledge: Knowledge is awareness or familiarity gained by experiences of facts, data, and situations.
- 22. Knowledge representation languages Goal: express the knowledge about the world in a computer tractable form. • Key aspects of knowledge representation languages: – Syntax: describes how sentences are formed in the language. – Semantics: describes the meaning of sentences, what is it the sentence refers to in the real world. – Computational aspect: describes how sentences and objects are manipulated in concordance with semantically conventions.
- 23. • Representational adequacy (suitability) - should allow to represent the knowledge we need. • Representational quality • computational cost of related inferences
- 24. Knowledge-based systems (KBS) • A knowledge-based system (KBS) is a form of artificial intelligence (AI) that aims to capture the knowledge of human experts to support decision-making. • Knowledge-based systems are computerized systems that emulate human reasoning. • Such systems are built with specific knowledge in certain domains of application, and operate in a way similar to that of a human expert. • The typical architecture of a knowledge-based system, which informs its problem- solving method, includes a knowledge base and an inference engine.
- 25. Cont… • The knowledge base contains a collection of information in a given field -- medical diagnosis, for example. • The inference engine deduces insights from the information housed in the knowledge base. • Knowledge-based systems also include an interface through which users query the system and interact with it. Examples of knowledge-based systems include expert systems, which are so called because of their reliance on human expertise.
- 26. • A knowledge-based system may vary with respect to its problem-solving method or approach. • Some systems encode expert knowledge as rules and are therefore referred to as rule-based systems. • Another approach, case-based reasoning, substitutes cases for rules. • Cases are essentially solutions to existing problems that a case-based system will attempt to apply previous solution to a new problem. Cont…
- 27. Knowledge based agents • An intelligent agent needs knowledge about the real world for taking decisions and reasoning to act efficiently. • Knowledge-based agents are those agents who have the capability of : • maintaining an internal state of knowledge • reason over that knowledge • update their knowledge after observations and take actions. • Knowledge-based agents are composed of two main parts: 1. Knowledge-base and 2. Inference system.
- 28. Cont… A knowledge-based agent must able to: • represent states/situations, actions, etc. • incorporate new percepts • update the internal representation of the world • realize the internal representation of the world • reason appropriate actions.
- 29. • The architecture of knowledge-based agent:
- 30. • The knowledge-based agent (KBA) take input from the environment by perceiving the environment. • The input is taken by the inference engine of the agent and which also communicate with KB to decide as per the knowledge store in KB. • The learning element of KBA regularly updates the KB by learning new knowledge. Cont…
- 31. Cont… Knowledge base: • A knowledge base is an organized collection of facts about the system's domain. • Knowledge-base is a central component of a knowledge-based agent. • Knowledge-base is required for updating knowledge for an agent to learn with experiences and take action as per the knowledge.
- 32. Inference system • Inference means deriving new sentences (decisions) from old. • Inference system allows us to add a new sentence to the knowledge base. • Inference system applies logical rules to the KB to realize new information. • Inference system generates new facts so that an agent can update the KB. • An inference system works mainly in two rules which are given as: ✓Forward chaining ✓Backward chaining
- 33. Reading Assignment Case study: Medical diagnosis