isbn 0-321-33025-0 chapter 16 logic programming languages

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  • Slide 1
  • ISBN 0-321-33025-0 Chapter 16 Logic Programming Languages
  • Slide 2
  • Copyright 2006 Addison-Wesley. All rights reserved.1-2 Programming Languages as Cars Assembler - A formula I race car. Very fast but difficult to drive and maintain. FORTRAN II - A Model T Ford. Once it was the king of the road. FORTRAN IV - A Model A Ford. FORTRAN 77 - a six-cylinder Ford Fairlane with manual transmission and no seat belts. COBOL - A deliver van It's bulky and ugly but it does the work. BASIC - A second-hand Rambler with a rebuilt engine and patched upholstery. Your dad bought it for you to learn to drive. You'll ditch it as soon as you can afford a new one. PL/I - A Cadillac convertible with automatic transmission, a two-tone paint job, white-wall tires, chrome exhaust pipes, and fuzzy dice hanging in the windshield. C - A black Firebird, the all macho car. Comes with optional seatbelt (lint) and optional fuzz buster (escape to assembler). ALGOL 60 - An Austin Mini. Boy that's a small car.
  • Slide 3
  • Copyright 2006 Addison-Wesley. All rights reserved.1-3 Programming Languages as Cars (contd) Pascal - A Volkswagen Beetle. It's small but sturdy. Was once popular with intellectual types. Modula II - A Volkswagen Rabbit with a trailer hitch. ALGOL 68 - An Aston Martin. An impressive car but not just anyone can drive it. LISP - An electric car. It's simple but slow. Seat belts are not available. PROLOG/LUCID - Prototype concept cars. Maple/MACSYMA - All-terrain vehicles. FORTH - A go-cart. LOGO - A kiddie's replica of a Rolls Royce. Comes with a real engine and a working horn. APL - A double-decker bus. It takes rows and columns of passengers to the same place all at the same time but it drives only in reverse and is instrumented in Greek. Ada - An army-green Mercedes-Benz staff car. Power steering, power brakes, and automatic transmission are standard. No other colors or options are available. If it's good enough for generals, it's good enough for you.
  • Slide 4
  • Copyright 2006 Addison-Wesley. All rights reserved.1-4 Chapter 16 Topics Introduction A Brief Introduction to Predicate Calculus Predicate Calculus and Proving Theorems An Overview of Logic Programming The Origins of Prolog The Basic Elements of Prolog Deficiencies of Prolog Applications of Logic Programming
  • Slide 5
  • Copyright 2006 Addison-Wesley. All rights reserved.1-5 Introduction Logic programming language or declarative programming language Express programs in a form of symbolic logic Use a logical inferencing process to produce results Declarative rather that procedural: Only specification of results are stated (not detailed procedures for producing them) (e.g., the requirements of a solution to a Sudoku problem)
  • Slide 6
  • Copyright 2006 Addison-Wesley. All rights reserved.1-6 Sudoku Puzzle
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  • Copyright 2006 Addison-Wesley. All rights reserved.1-7 Proposition A logical statement that may or may not be true Consists of objects and relationships of objects to each other (e.g., Mt. Whitney is taller than Mt. McKinley)
  • Slide 8
  • Copyright 2006 Addison-Wesley. All rights reserved.1-8 Symbolic Logic Logic which can be used for the basic needs of formal logic: Express propositions Express relationships between propositions Describe how new propositions can be inferred from other propositions Particular form of symbolic logic used for logic programming called predicate calculus
  • Slide 9
  • Copyright 2006 Addison-Wesley. All rights reserved.1-9 Object Representation Objects in propositions are represented by simple terms: either constants or variables Constant: a symbol that represents an object (e.g., john) Variable: a symbol that can represent different objects at different times (e.g., Person) Different from variables in imperative languages
  • Slide 10
  • Copyright 2006 Addison-Wesley. All rights reserved.1-10 Compound Terms Atomic propositions consist of compound terms Compound term: one element of a mathematical relation, written like a mathematical function Mathematical function is a mapping Can be written as a table
  • Slide 11
  • Copyright 2006 Addison-Wesley. All rights reserved.1-11 Parts of a Compound Term Compound term composed of two parts Functor: function symbol that names the relationship Ordered list of parameters (tuple) Examples: student(jon) like(seth, OSX) like(nick, windows) like(jim, linux)
  • Slide 12
  • Copyright 2006 Addison-Wesley. All rights reserved.1-12 Forms of a Proposition Propositions can be stated in two forms: Fact: proposition is assumed to be true Query: truth of proposition is to be determined Compound proposition: Have two or more atomic propositions Propositions are connected by operators
  • Slide 13
  • Copyright 2006 Addison-Wesley. All rights reserved.1-13 Logical Operators NameSymbolExampleMeaning negation anot a conjunction a ba and b disjunction a ba or b equivalence a ba is equivalent to b implication a b a b a implies b b implies a
  • Slide 14
  • Copyright 2006 Addison-Wesley. All rights reserved.1-14 Quantifiers NameExampleMeaning universal X.PFor all X, P is true existential X.PThere exists a value of X such that P is true
  • Slide 15
  • Copyright 2006 Addison-Wesley. All rights reserved.1-15 Clausal Form Too many ways to state the same thing Use a standard form for propositions Clausal form: B 1 B 2 B n A 1 A 2 A m means if all the As are true, then at least one B is true Antecedent: right side Consequent: left side (e.g., likes(bob,trout) likes(bob,fish) fish(trout) )
  • Slide 16
  • Copyright 2006 Addison-Wesley. All rights reserved.1-16 Predicate Calculus and Proving Theorems A use of propositions is to discover new theorems that can be inferred from known axioms and theorems Resolution: an inference principle that allows inferred propositions to be computed from given propositions
  • Slide 17
  • Copyright 2006 Addison-Wesley. All rights reserved.1-17 Resolution Example father(bob, jake) mother(bob, jake) parent(bob, jake) grandfather(bob, fred) father(bob, jake) father(jake, fred) Resolution says that mother(bob, jake) grandfather(bob, fred) parent(bob, jake) father(jake, fred) if:bob is the parent of jake implies that bob is either the father or mother of jake and:bob is the father of jake and jake is the father of fred implies that bob is the grandfather of fred then:if bob is the parent of jake and jake is the father of fred then: either bob is jakes mother or bob is freds grandfather
  • Slide 18
  • Copyright 2006 Addison-Wesley. All rights reserved.1-18 Resolution Problem sister(sue, joe) brother(sue, joe) sibling(sue, joe) aunt(sue, jack) sister(sue, joe) parent(joe, jack) Resolution says ?
  • Slide 19
  • Copyright 2006 Addison-Wesley. All rights reserved.1-19 Resolution Unification: finding values for variables in propositions that allows matching process to succeed Instantiation: assigning temporary values to variables to allow unification to succeed After instantiating a variable with a value, if matching fails, may need to backtrack and instantiate with a different value
  • Slide 20
  • Copyright 2006 Addison-Wesley. All rights reserved.1-20 Sudoku Puzzle
  • Slide 21
  • Copyright 2006 Addison-Wesley. All rights reserved.1-21 Proof by Contradiction Hypotheses: a set of pertinent propositions Goal: negation of theorem stated as a proposition Theorem is proved by finding an inconsistency
  • Slide 22
  • Copyright 2006 Addison-Wesley. All rights reserved.1-22 Theorem Proving Basis for logic programming When propositions used for resolution, only restricted form can be used Horn clause - can have only two forms Headed: single atomic proposition on left side (e.g., likes(bob,trout) likes(bob,fish) fish(trout) ) Headless: empty left side (used to state facts) (e.g., father(bob, jake) ) Most propositions can be stated as Horn clauses
  • Slide 23
  • Copyright 2006 Addison-Wesley. All rights reserved.1-23 Overview of Logic Programming Declarative semantics There is a simple way to determine the meaning of each statement Simpler than the semantics of imperative languages Programming is nonprocedural Programs do not state now a result is to be computed, but rather the form of the result
  • Slide 24
  • Copyright 2006 Addison-Wesley. All rights reserved.1-24 Example: Sorting a List Describe the characteristics of a sorted list, not the process of rearranging a list sort(old_list, new_list) permute (old_list, new_list) sorted (new_list) sorted (list) j such that 1 j < n, list(j) list (j+1)
  • Slide 25
  • Copyright 2006 Addison-Wesley. All rights reserved.1-25 The Origins of Prolog University of Aix-Marseille Natural language processing University of Edinburgh Automated theorem proving
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  • Copyright 2006 Addison-Wesley. All rights reserved.1-26 Terms Edinburgh Syntax Term: a constant, variable, or structure Constant: an atom or an integer Atom: symbolic value of Prolog Atom consists of either: a string of letters, digits, and underscores beginning with a lowercase letter a string of printable ASCII characters delimited by apostrophes
  • Slide 27
  • Copyright 2006 Addison-Wesley. All rights reserved.1-27 Terms: Variables and Structu

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