UT Dallas CS 4337 - #Sebesta pl10e ch16 logic prog (39 pages)

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#Sebesta pl10e ch16 logic prog



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#Sebesta pl10e ch16 logic prog

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Pages:
39
School:
University of Texas at Dallas
Course:
Cs 4337 - Organization of Programming Languages
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Chapter 16 Logic Programming Languages 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 Copyright 2012 Addison Wesley All rights reserved 1 2 Introduction Programs in logic languages are expressed 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 Copyright 2012 Addison Wesley All rights reserved 1 3 Proposition A logical statement that may or may not be true Consists of objects and relationships of objects to each other Copyright 2012 Addison Wesley All rights reserved 1 4 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 Copyright 2012 Addison Wesley All rights reserved 1 5 Object Representation Objects in propositions are represented by simple terms either constants or variables Constant a symbol that represents an object Variable a symbol that can represent different objects at different times Different from variables in imperative languages Copyright 2012 Addison Wesley All rights reserved 1 6 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 Copyright 2012 Addison Wesley All rights reserved 1 7 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 Copyright 2012 Addison Wesley All rights reserved 1 8 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 Copyright 2012 Addison Wesley All rights reserved 1 9 Logical Operators Name Symbol Example Meaning negation a not a conjunction a b a and b disjunction a b a or b equivalence a b a is equivalent to b implication a b a b a implies b b implies a Copyright 2012 Addison Wesley All rights reserved 1 10 Quantifiers Name Example Meaning universal X P For all X P is true existential X P There exists a value of X such that P is true Copyright 2012 Addison Wesley All rights reserved 1 11 Clausal Form Too many ways to state the same thing Use a standard form for propositions Clausal form B1 B2 Bn A1 A2 Am means if all the As are true then at least one B is true Antecedent right side Consequent left side Copyright 2012 Addison Wesley All rights reserved 1 12 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 Copyright 2012 Addison Wesley All rights reserved 1 13 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 Copyright 2012 Addison Wesley All rights reserved 1 14 Proof by Contradiction Hypotheses a set of pertinent propositions Goal negation of theorem stated as a proposition Theorem is proved by finding an inconsistency Copyright 2012 Addison Wesley All rights reserved 1 15 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 Headless empty left side used to state facts Most propositions can be stated as Horn clauses Copyright 2012 Addison Wesley All rights reserved 1 16 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 Copyright 2012 Addison Wesley All rights reserved 1 17 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 Copyright 2012 Addison Wesley All rights reserved 1 18 The Origins of Prolog University of Aix Marseille Calmerauer Roussel Natural language processing University of Edinburgh Kowalski Automated theorem proving Copyright 2012 Addison Wesley All rights reserved 1 19 Terms This book uses the Edinburgh syntax of Prolog 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 Copyright 2012 Addison Wesley All rights reserved 1 20 Terms Variables and Structures Variable any string of letters digits and underscores beginning with an uppercase letter Instantiation binding of a variable to a value Lasts only as long as it takes to satisfy one complete goal Structure represents atomic proposition functor parameter list Copyright 2012 Addison Wesley All rights reserved 1 21 Fact Statements Used for the hypotheses Headless Horn clauses female shelley male bill father bill jake Copyright 2012 Addison Wesley All rights reserved 1 22 Rule Statements Used for the hypotheses Headed Horn clause Right side antecedent if part May be single term or conjunction Left side consequent then part Must be single term Conjunction multiple terms separated by logical AND operations implied Copyright 2012 Addison Wesley All rights reserved 1 23 Example Rules ancestor mary shelley mother mary shelley Can use variables universal objects to generalize meaning parent X Y mother X Y parent X Y father X Y grandparent X Z parent X Y parent Y Z Copyright 2012


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