The document discusses different types of logical reasoning systems used in artificial intelligence, including knowledge-based agents, first-order logic, higher-order logic, goal-based agents, knowledge engineering, and description logics. It provides examples of objects, properties, relations, and functions that can be represented and reasoned about logically. It also compares different approaches to logical indexing and outlines the key components and inference tasks involved in description logics.

1. Logic in AI

2. A Knowledge Based Agent These are Agents That Reason Logically The central component of a knowledge-based agent is its knowledge base, a knowledge base is a set of representations of facts about the world.

3. Description of knowledge-based agent The knowledge level or epistemological level is the most abstract. If TELL and ASK work correctly, then most of the time we can work at the knowledge level and not worry about lower levels. The logical level is the level at which the knowledge is encoded into sentences. The implementation level is the level that runs on the agent architecture. By a complex set of pointers connecting machine addresses corresponding to the individual symbols

4. What are Inference in computers? Logics : consists of syntax, symantecs and proof theory. Propositional logic, symbols represent whole propositions (facts). Ontological commitments have to do with the nature of reality Temporal logic assumes that the world is ordered by a set of time points or intervals, and includes built-in mechanisms for reasoning about time. fuzzy logic can have degrees of belief in a sentence, and also allow degrees of truth:a fact need not be true or false in the world, but can be true to a certain degree.

5. First Order Logic First-order logic makes a stronger set of ontological commitments. The main one is that the world consists of objects, that is, things with individual identities and properties that distinguish them from other objects. Among these objects, various relations hold. Some. Of these relations are functions - relations in which there is only one "value" for a given "input."

6. Examples of objects, properties, relations, and functions: Objects: people, houses, numbers, theories, Ronald McDonald, colors, baseball games, wars, centuries . . .Relations: brother of, bigger than, inside, part of, has color, occurred after, owns . . .Properties: red, round, bogus, prime, multistoried...Functions: father of, best friend, third inning of, one more than ...

7. Higher-order logic Higher-order logic allows us to quantify over relations and functions as well as over objects. For example, in higher-order logic we, can say that two objects are equal if and only if all propertiesapplied to them are equivalent:Vx, y (x = y) & (Vp p(x) O p(y)) ........ (V stands "for every")

8. A Simple Reflex Agent The simplest possible kind of agent has rules directly connecting percepts to actions. These rules resemble reflexes or instincts. For example, if the agent sees a glitter, it should do a grab in order to pick up the gold.

9. Limitations of simple reflex agents Consider climb problem: A pure reflex agent cannot know for sure when to Climb, because neither having the goal nor being in the start is part of the percept; they are things the agent knows by forming a representation of the world. Reflex agents are also unable to avoid infinite loops

10. Goal based agent The presence of an explicit goal allows the agent to work out a sequence of actions that will achieve the goal. There are at least three ways to find such a sequence: Inference: It is not hard to write axioms that will allow us to ASK the KB for a sequence of actions that is guaranteed to achieve the goal safely. Search: We can use a best-first search procedure to find a path to the goal. Planning: This involves the use of special-purpose reasoning systems designed to reason about actions.

11. What is Knowledge engineering? The knowledge engineer must understand enough about the domain in question to represent the important objects and relationships, representation language, implementation of the inference procedure.

12. Knowledge engineering versus programming

13. Steps in development of a knowledge base 1) Decide what to talk about.2) Decide on a vocabulary of predicates, functions, and constants.3) Encode general knowledge about the domain.4) Encode a description of the specific problem instance.5) Pose queries to the inference procedure and get answers.

14. General Ontology Characteristics of general-purpose ontology : 1) A general-purpose ontology should be applicable in more or less any special-purposedomain (with the addition of domain-specific axioms). 2) In any sufficiently demanding domain, different areas of knowledge must be unified because reasoning and problem solving may involve several areas simultaneously.

15. Different Logical Reasoning Systems Four main categories of logic systems: Theorem provers and logic programming languages Production systems Frame systems and semantic networks Description logic systems

16. Table-based indexing The keys to the table will be predicate symbols, and the value stored under each key will have four components: A list of positive literals for that predicate symbol. A list of negative literals. A list of sentences in which the predicate is in the conclusion. A list of sentences in which the predicate is in the premise.

17. Tree-based indexing Tree-based indexing is one form of combined indexing, in that it essentially makes a combined key out of the sequence of predicate and argument symbols in the query. The cross-indexing strategy indexes entries in several places, and when faced with a query chooses the most promising place for retrieval.

18. Logic Programming Systems Logic programming tries to extend these advantages to all programming tasks. Any computation can be viewed as a process of making explicit the consequences of choosing a particular program for a particular machine and providing particular inputs Algorithm = Logic + Control

19. Description Logics The principal inference tasks are subsumption :: checking if one category is a subset of another based on their definitions and classification :: checking if an object belongs to a category.

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