Ai lecture 11(unit03)
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Knowledge Based Reasoning: Agents, Facets of Knowledge. Logic and Inferences: Formal Logic, Propositional and First Order Logic, Resolution in Propositional and First Order Logic, Deductive Retrieval, Backward Chaining, Second order Logic. Knowledge Representation: Conceptual Dependency, Frames, Semantic nets.
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1) Linear analysis involves grouping characters into tokens with collective meanings like identifiers and operators.
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2. Global optimizations that analyze control flow across basic blocks, such as common subexpression elimination.
3. Loop optimizations that improve performance of loops by removing invariant data and induction variables.
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The purpose of types:
To define what the program should do.
e.g. read an array of integers and return a double
To guarantee that the program is meaningful.
that it does not add a string to an integer
that variables are declared before they are used
To document the programmer's intentions.
better than comments, which are not checked by the compiler
To optimize the use of hardware.
reserve the minimal amount of memory, but not more
use the most appropriate machine instructions.
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1) The document discusses proof by resolution in first-order logic (FOL) with two examples.
2) The first example aims to prove that "Raja is angry" from the facts that "Rimi is hungry", "If Rimi is hungry she barks", and "If Rimi is barking then Raja is angry".
3) The second example aims to prove that "Someone is smiling" from the facts that "All people who are graduating are happy", "All happy people smile", and "Someone is graduating".
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An algorithm is a tool for solving any computational problem. It may be defined as a sequence of finite,
precise and unambiguous instructions which are applied either to perform a computation or to solve a
computational problem. These instructions are applied on some raw data called the input, and the
solution of the problem produced is called the output.
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The document discusses recursive functions and provides examples of recursive algorithms for calculating factorial, greatest common divisor (GCD), Fibonacci numbers, power functions, and solving the Towers of Hanoi problem. Recursive functions are functions that call themselves during their execution. They break down problems into subproblems of the same type until reaching a base case. This recursive breakdown allows problems to be solved in a top-down, step-by-step manner.
State Space Representation and Search
- A state space consists of nodes representing problem states and arcs representing moves between states. It can be represented as a tree or graph.
- To solve a problem using search, it must first be represented as a state space with an initial state, goal state(s), and legal operators defining state transitions.
- Different search algorithms like depth-first, breadth-first, A*, and best-first are then applied to traverse the state space to find a solution path from initial to goal state.
- Heuristic functions can be used to guide search by estimating state proximity to the goal, improving efficiency over uninformed searches.
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The document discusses inference rules for quantifiers in first-order logic. It describes the rules of universal instantiation and existential instantiation. Universal instantiation allows inferring sentences by substituting terms for variables, while existential instantiation replaces a variable with a new constant symbol. The document also introduces unification, which finds substitutions to make logical expressions identical. Generalized modus ponens is presented as a rule that lifts modus ponens to first-order logic by using unification to substitute variables.
Lexical analysis - Compiler Design
The document discusses lexical analysis in compilers. It describes how the lexical analyzer reads source code characters and divides them into tokens. Regular expressions are used to specify patterns for token recognition. The lexical analyzer generates a finite state automaton to recognize these patterns. Lexical analysis is the first phase of compilation that separates the input into tokens for the parser.
Frames
The document discusses different knowledge representation schemes used in artificial intelligence systems. It describes semantic networks, frames, propositional logic, first-order predicate logic, and rule-based systems. For each technique, it provides facts about how knowledge is represented and examples to illustrate their use. The goal of knowledge representation is to encode knowledge in a way that allows inferencing and learning of new knowledge from the facts stored in the knowledge base.
Principle source of optimazation
This produced by straight forward compiling algorithms made to run faster or less space or both. This improvement is achieved by program transformations that are traditionally called optimizations.compiler that apply-code improving transformation are called optimizing compilers.
Analysis of the source program
The document discusses the three phases of analysis in compiling a source program:
1) Linear analysis involves grouping characters into tokens with collective meanings like identifiers and operators.
2) Hierarchical analysis groups tokens into nested structures with collective meanings like expressions, represented by parse trees.
3) Semantic analysis checks that program components fit together meaningfully through type checking and ensuring operators have permitted operand types.
Code Optimization
This document discusses various techniques for optimizing computer code, including:
1. Local optimizations that improve performance within basic blocks, such as constant folding, propagation, and elimination of redundant computations.
2. Global optimizations that analyze control flow across basic blocks, such as common subexpression elimination.
3. Loop optimizations that improve performance of loops by removing invariant data and induction variables.
4. Machine-dependent optimizations like peephole optimizations that replace instructions with more efficient alternatives.
The goal of optimizations is to improve speed and efficiency while preserving program meaning and correctness. Optimizations can occur at multiple stages of development and compilation.
Type Checking(Compiler Design) #ShareThisIfYouLike
The purpose of types:
To define what the program should do.
e.g. read an array of integers and return a double
To guarantee that the program is meaningful.
that it does not add a string to an integer
that variables are declared before they are used
To document the programmer's intentions.
better than comments, which are not checked by the compiler
To optimize the use of hardware.
reserve the minimal amount of memory, but not more
use the most appropriate machine instructions.
Semantic nets in artificial intelligence
Semantic nets were originally proposed in the 1960s as a way to represent the meaning of English words using nodes, links, and link labels. Nodes represent concepts, objects, or situations, links express relationships between nodes, and link labels specify particular relations. Semantic nets can represent data through examples, perform intersection searches to find relationships between objects, partition networks to distinguish individual from general statements, and represent non-binary predicates. While semantic nets provide a visual way to organize knowledge, they can have issues with inheritance and placing facts appropriately.
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3) Propositional logic uses symbolic variables to represent propositions that can be either true or false. Compound propositions combine simpler propositions using logical connectives like "and" and "or". Truth tables define the values of logical connectives.
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Ai lecture 04(unit03)
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Ai lecture 03(unit03)
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Ai lecture 003(unit03)
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Ai lecture 01(unit03)
1. Knowledge based reasoning uses logic and facts stored in a knowledge base to draw conclusions. The knowledge base represents information about the world that an AI system can use to solve problems.
2. A knowledge based agent is an AI system that maintains an internal state of knowledge in its knowledge base, reasons over that knowledge using inference rules, updates its knowledge base after observing new information, and takes actions.
3. A knowledge based agent's architecture includes a knowledge base to store facts, an inference system to apply logical rules to deduce new information and update the knowledge base, and the ability to perceive information, reason over its knowledge, and perform actions.
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Ai lecture 11(unit03)
- 1. Topic To Be Covered: First Order Logic(Part-03) 1.Unification 2.Resolution In FOL Jagdamba Education Society's SND College of Engineering & Research Centre Department of Computer Engineering SUBJECT: Artificial Intelligence & Robotics Lecture No-1(UNIT-03) Logic & Reasoning Prof.Dhakane Vikas N
- 2. What is Unification Unification Unification is a process of making two different logical atomic expressions identical by finding a substitution. Unification depends on the substitution process. It takes two literals as input and makes them identical using substitution.
- 3. What is Unification Unification :Conditions for Unification: Following are some basic conditions for unification: 1. Predicate symbol must be same, atoms or expression with different predicate symbol can never be unified. 2. Number of Arguments in both expressions must be identical. 3. Unification will fail if there are two similar variables present in the same expression.
- 4. What is Unification Unification :Example E.g. Let's say there are two different expressions, P(x, y), and P(a, f(z)). In this example, we need to make both above statements identical to each other. For this, we will perform the substitution. P(x, y)......... (i) P(a, f(z))......... (ii) Substitute x with a, and y with f(z) in the first expression, and it will be represented as a/x and f(z)/y. With both the substitutions, the first expression will be identical to the second expression and the substitution set will be: [a/x, f(z)/y].
- 5. What is Unification Unification :Example We can resolve two clauses which are given below: [Animal (g(x) V Loves (f(x), x)] and [￢ Loves(a, b) V ￢Kills(a, b)] Where two complimentary literals are: Loves (f(x), x) and ￢ Loves (a, b) These literals can be unified with unifier : [a/f(x), and b/x] , and it
- 6. What is Unification(Unification :Algorithm)
- 7. Resolution in FOL Resolution in FOL Resolution is a theorem proving technique that proceeds by building refutation proofs, i.e., proofs by contradictions. It was invented by a Mathematician John Alan Robinson in the year 1965. Resolution is used, if there are various statements are given, and we need to prove a conclusion of those statements. Unification is a key concept in proofs by resolutions. Resolution is a single inference rule which can efficiently operate on the conjunctive normal form or clausal form.
- 8. Resolution in FOL Resolution in FOL Clause: Disjunction of literals (an atomic sentence) is called a clause. It is also known as a unit clause. Conjunctive Normal Form: A sentence represented as a conjunction of clauses is said to be conjunctive normal form or CNF. Example: We can resolve two clauses which are given below: [Animal (g(x) V Loves (f(x), x)] and [￢ Loves(a, b) V ￢Kills(a, b)] Where two complimentary literals are: Loves (f(x), x) and ￢ Loves (a, b) These literals can be unified with unifier θ= [a/f(x), and b/x] , and it will generate a resolvent clause: [Animal (g(x) V ￢ Kills(f(x), x)].
- 9. Resolution in FOL Resolution in FOL Steps for Resolution: 1. Conversion of facts into first-order logic. 2. Convert FOL statements into CNF 3. Negate the statement which needs to prove (proof by contradiction) 4. Draw resolution graph (unification). To better understand all the above steps, we will take an example in which we will apply resolution.
- 10. Resolution in FOL Resolution in FOL Steps for Resolution: Convert FOL statements into CNF