К содержимому
learnspaceYOUR NEXT CHAPTER
ПРОСТРАНСТВО ОБУЧЕНИЯ
ГлавнаяКаталог курсовМоё обучениеCoursera

Знания без границ

Учитесь у лучших университетов и компаний мира.

Открыть Coursera
Интеграция
Пространство университета
Моё пространствоСтраница курса
↵
ЯЛичный кабинетСтудент
© 2026 LearnSpaceКаждый день — возможность узнать больше.Помощь
Logic for Computer Science · LearnSpace
Назад в каталог
courseraПрограммирование

Logic for Computer Science

Курс от Birla Institute of Technology & Science, Pilani
Начальный≈ 29.6 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

Unlock the power of logical thinking and formal reasoning essential for success in computer science, data analysis, and software development with this dynamic course. Ideal for students, software engineers, data scientists, and IT professionals, this comprehensive program delves into logic foundations critical for advanced computing careers. Starting with fundamental proofs and proof systems, you’ll explore soundness, completeness, first-order propositional, and predicate logic. Dive into advanced topics like modeling, program verification, and temporal logic. Master Gentzen’s natural deduction, and understand the semantics and syntax of logical forms. Tackle the undecidability of logic and learn model checking using temporal logics (LTL, CTL, CTL*) to verify system properties, applying Floyd-Hoare logics to ensure program correctness. Our structured approach incorporates practical techniques to enhance memory and overcome procrastination, benefiting both academic learning and professional efficiency. Engaging case studies offer hands-on experience verifying algorithms, such as array searching and sorting, essential for real-world problem solving. Geared towards those aiming for roles in tech innovation, this course equips you with the analytical tools and logical proficiency to excel in computing, programming, and data-driven problem-solving. Elevate your career and expertise in the ever-evolving technology landscape.

Навыки, которые вы освоите

Computational LogicDeductive ReasoningVerification And ValidationLogical ReasoningTheoretical Computer ScienceSoftware DevelopmentProgramming PrinciplesMachine LearningAnalytical SkillsComputer ProgrammingAlgorithmsData AnalysisProcess Modeling

Программа курса

10 модулей · 303 учебных материалов

01Propositional Logic 23 материалов

Let's Get Started

Introducing LogicВидеоCourse OverviewЧтениеCourse Structure & Critical InformationЧтение

Introduction to Propositional Logic

Introduction to Propositional Logic Видео

Учитесь у экспертов

BITS Pilani Instructors Group

Преподаватель курса

Logic for Computer Science
В каталоге вашей программы

Инвестируйте в себя

Новые знания — в удобное для вас время.

Начать на Coursera

Обучение откроется на Coursera
в новой вкладке

Обучение на Coursera

≈ 29.6 ч

10 модулей

Язык: Английский

Часть программы вашего университета
Need for Formal Logics in Computer Science Видео
Practice Quiz: Need for Formal Logics in Computer Science Задание
Ambiguity of Natural Language: An ExampleВидео
Practice Quiz: Ambiguity of Natural Language: An ExampleЗадание
Propositional Logic: The Distinction Between Syntax and Semantics Видео
Practice Quiz: Propositional Logic: The Distinction Between Syntax and SemanticsЗадание
Declarative Sentences: An ExampleВидео
Practice Quiz: Declarative Sentences: An ExampleЗадание
Recommended Reading: Declarative SentencesЧтение

Well-Formedness (Syntax) of Propositional Logic

Introduction to Connectives in Propositional Logic and Their Informal MeaningsВидеоPractice Quiz: Introduction to Connectives in Propositional Logic and Their Informal MeaningsЗаданиеPropositional Logic Syntax ВидеоPractice Quiz: Propositional Logic Syntax ЗаданиеExamples of a Well-Formed FormulaВидеоPractice Quiz: Examples of a Well-Formed FormulaЗаданиеRecommended Reading: Well-Formedness (Syntax) of Propositional LogicЧтение

Summary

Summary: Propositional LogicВидеоPractical Propositional Logic: Bridging Theory and Real-World ApplicationsDIALOGUETest Yourself: Propositional LogicЗадание
02Natural Deduction in Propositional Logic27 материалов

Proof Theory

Natural Deduction in Propositional LogicВидеоProof Systems: NotationsВидеоPractice Quiz: Proof Systems: NotationsЗаданиеRecommended Reading: Proof TheoryЧтение

Proofs Using Natural Deduction

Natural Deduction: Conjunction RuleВидеоPractice Quiz: Natural Deduction: Conjunction RuleЗаданиеNatural Deduction: Conjunction Rules—An Elementary ExampleВидеоPractice Quiz: Natural Deduction: Conjunction Rules—An Elementary Example ЗаданиеNatural Deduction: Implication RuleВидеоPractice Quiz: Natural Deduction: Implication RuleЗаданиеNatural Deduction: Negation RulesВидеоPractice Quiz: Natural Deduction: Negation RulesЗаданиеNatural Deduction: Disjunction RulesВидеоPractice Quiz: Natural Deduction: Disjunction RulesЗаданиеRecommended Reading: Proofs Using Natural DeductionЧтение

Usage of Natural Deduction as Proof Technique

Example 1: Modus TollensВидеоPractice Quiz: Modus TollensЗаданиеExample 2: Proof by Contradiction ВидеоPractice Quiz: Example 2: Proof by Contradiction ЗаданиеExample 3: Law of Excluded MiddleВидеоPractice Quiz: Example 3: Law of Excluded MiddleЗадание

Summary

Summary: Natural Deduction in Propositional Logic ВидеоNatural Deduction cross DisciplinesDIALOGUETest Yourself: Natural Deduction in Propositional LogicЗадание
03Semantics, Soundness, and Completeness of Natural Deduction30 материалов

Semantics of Propositional Logic

Semantics, Soundness, and Completeness of Natural DeductionВидеоInterpretation of Propositional Logic FormulasВидеоPractice Quiz: Interpretation of Propositional Logic FormulasЗаданиеInterpretation of a Complex Formula: The Truth Table MethodВидеоPractice Quiz: Interpretation of a Complex Formula: The Truth Table MethodЗаданиеTautologies and Fallacies, Satisfiability, and ValidityВидеоPractice Quiz : Tautologies and Fallacies, Satisfiability, and ValidityЗаданиеSatisfiability Using Truth Table MethodВидеоPractice Quiz: Satisfiability Using Truth Table MethodЗаданиеSemantic Equivalence, and Adequate Set of Connectives ВидеоPractice Quiz: Semantic Equivalence, and Adequate Set of Connectives ЗаданиеRecommended Reading: Semantics of Propositional Logic Чтение

Normal Forms

Normal Forms: CNF and DNFВидеоPractice Quiz: Normal Forms: CNF and DNFЗаданиеSatisfiability and Validity: DualityВидеоPractice Quiz : Satisfiability and Validity: DualityЗаданиеSatisfiability Proof Using ResolutionВидеоPractice Quiz : Satisfiability Proof Using ResolutionЗадание

Soundness and Completeness of Natural Deduction

Development of Logical Theory: A Look Back at Natural DeductionВидеоPractice Quiz : Development of Logical Theory: A Look Back at Natural DeductionЗаданиеSoundness and Completeness of Natural DeductionВидеоPractice Quiz : Soundness and Completeness of Natural DeductionЗаданиеRecommended Reading: Soundness and Completeness of Natural Deduction  Чтение

Summary

Summary: Semantics, Soundness, and Completeness of Natural DeductionВидеоTest Yourself: Semantics, Soundness and Completeness of Natural DeductionЗадание
04Model Checking Techniques and Temporal Logics29 материалов

Introduction to Model Checking

Model Checking Techniques and Temporal LogicsВидеоApproaches to Computer VerificationВидеоPractice Quiz: Approaches to Computer VerificationЗаданиеModel CheckingВидеоPractice Quiz: Model CheckingЗаданиеTransition System: An ExampleВидеоPractice Quiz: Transition System: An ExampleЗаданиеEssential Reading: Introduction to Model Checking 1 ЧтениеFormal Definition: Transition SystemВидеоPractice Quiz: Formal Definition: Transition SystemЗаданиеPaths and Traces: An ExampleВидеоPractice Quiz: Paths and Traces: An ExampleЗаданиеEssential Reading: Introduction to Model Checking 2 ЧтениеInvariants, Safety, and Liveness PropertiesВидеоPractice Quiz: Invariants, Safety, and Liveness PropertiesЗаданиеExamples of LTI PropertiesВидеоPractice Quiz: Examples of LTI PropertiesЗаданиеRecommended Reading: Model CheckingЧтение

Temporal Logics

Revisiting: Model Checking StepsВидеоPractice Quiz: Revisiting: Model Checking StepsЗаданиеFamily of Temporal LogicsВидеоPractice Quiz: Family of Temporal LogicsЗаданиеLinear Temporal Logic: An Informal IntroductionВидеоPractice Quiz: Linear Temporal Logic: An Informal IntroductionЗадание

Summary

Summary: Model Checking Techniques and Temporal LogicsВидеоTest Yourself: Model Checking Techniques and Temporal LogicsЗадание
05LTL and CTL Temporal Logics, Algorithms for Model Checking31 материалов

Linear Temporal Logic

Model Checking ВидеоLTL SyntaxВидеоPractice Quiz: LTL SyntaxЗаданиеExamples: Encoding of Natural Language Sentence into LTLВидеоPractice Quiz: Examples: Encoding of Natural Language Sentence into LTLЗаданиеLTL SemanticsВидеоPractice Quiz: LTL SemanticsЗаданиеRecommended Reading: Linear-Time Temporal LogicЧтениеEquivalences of LTL FormulaВидеоPractice Quiz: Equivalences of LTL FormulaЗаданиеRelease and Weak Until OperatorsВидеоPractice Quiz: Release and Weak Until OperatorsЗаданиеRecommended Reading: Syntax of LTLЧтениеLTL Model Checking: Naive IdeaВидеоPractice Quiz: LTL Model Checking: Naive IdeaЗаданиеLTL Model Checking : Discussion on Properties Inexpressible in LTLВидеоPractice Quiz: LTL Model Checking: Discussion on Properties Inexpressible in LTLЗаданиеRecommended Reading: Syntax of LTL and LTL Model-Checking AlgorithmЧтение

Computational Tree Logic

Computational Tree Logic: The SyntaxВидеоPractice Quiz: Computational Tree Logic: The SyntaxЗаданиеExamples: Encoding of Natural Language Sentence into CTLВидеоPractice Quiz: Examples: Encoding of Natural Language Sentence into CTLЗаданиеRecommended Reading: Computational Tree LogicЧтениеComputational Tree Logic: The SemanticsВидео

Summary

Summary: Temporal Logics and Algorithms for Model CheckingВидеоLinear vs. Branching Time: Exploring LTL and CTL in System VerificationDIALOGUETest Yourself: LTL and CTL Temporal Logics; Algorithms for Model CheckingЗадание
06Predicate Logic49 материалов

Need for Predicate Logic and its Expressiveness

Predicate LogicВидеоNeed for Predicate Logic ВидеоPractice Quiz: Need for Predicate Logic ЗаданиеExpressiveness of Predicates: Variables and Quantifiers—Part IВидеоPractice Quiz: Expressiveness of Predicates: Variables and Quantifiers—Part IЗаданиеExpressiveness of Predicates: Variables and Quantifiers—Part IIВидеоPractice Quiz: Expressiveness of Predicates: Variables and Quantifiers—Part IIЗаданиеExpressiveness of Predicates: Arguments of PredicatesВидеоPractice Quiz: Expressiveness of Predicates: Arguments of PredicatesЗаданиеExpressiveness of Predicates: Function TermsВидеоPractice Quiz: Expressiveness of Predicates: Function TermsЗаданиеExpressiveness of Predicates: Non-deterministic RelationsВидеоPractice Quiz: Expressiveness of Predicates: Non-deterministic RelationsЗаданиеRecommended Reading: Need for Predicate Logic and its Expressiveness Чтение

Expressing using Predicate Logic

Expressing Using Predicates: Conventions and Examples 1ВидеоPractice Quiz: Expressing Using Predicates: Conventions and Examples 1ЗаданиеExpressing Using Predicates: Conventions and Examples 2ВидеоPractice Quiz: Expressing Using Predicates: Conventions and Examples 2ЗаданиеExpressing Using Predicates: Examples 3ВидеоPractice Quiz: Expressing Using Predicates: Examples 3Задание

Proofs and Proof Rules

Universal Quantifier Elimination with ExamplesВидеоPractice Quiz: Universal Quantifier Elimination with ExamplesЗаданиеExistential Quantifier Introduction with ExamplesВидеоPractice Quiz: Existential Quantifier Introduction with ExamplesЗаданиеRecommended Reading: Universal Quantifier Elimination and Existential Quantifier IntroductionЧтениеSubstitution and BindingВидео

Summary

Summary: Predicate LogicВидеоTest Yourself: Predicate LogicЗадание
07Natural Deduction in Predicate Logic25 материалов

Proof Rules for Natural Deduction in Predicate Logic

Natural Deduction in Predicate LogicВидеоProof Rules for Natural Deduction in Propositional Logic: RevisionВидеоPractice Quiz: Proof Rules for Natural Deduction in Propositional Logic: RevisionЗаданиеUniversal Quantifier Elimination and Existential Quantifier Introduction: ExamplesВидеоPractice Quiz: Universal Quantifier Elimination and Existential Quantifier Introduction: ExamplesЗаданиеUniversal Quantifier Introduction with ExampleВидеоPractice Quiz: Universal Quantifier Introduction with ExampleЗаданиеExistential Quantifier Elimination with ExampleВидеоPractice Quiz: Existential Quantifier Elimination with ExampleЗаданиеUniversal Quantifier Introduction vs. Existential Quantifier EliminationВидеоPractice Quiz: Universal Quantifier Introduction vs. Existential Quantifier EliminationЗаданиеRecommended Reading: Proof Rules for Natural Deduction in Predicate Logic Чтение

Natural Deduction in Predicate Logic: Examples 1-4

ND in Predicate Logic: Example 1ВидеоND in Predicate Logic: Example 2ВидеоND in Predicate Logic: Example 3ВидеоND in Predicate Logic: Example 4ВидеоND in Predicate Logic: Example 5ВидеоPractice Problems 1: A List of Problems for ND ProofsЧтение

Natural Deduction in Predicate Logic: Examples 6-10

ND in Predicate Logic: Example 6ВидеоND in Predicate Logic: Example 7ВидеоND in Predicate Logic: Example 8ВидеоND in Predicate Logic: Example 9ВидеоND in Predicate Logic: Example 10ВидеоPractice Problems 2: A List of Problems for ND ProofsЧтение

Summary

Summary: Natural Deduction in Predicate LogicВидео
08Semantics, Soundness, Completeness, and Undecidability of Predicate Logic43 материалов

Semantics of Predicate Logic: Part I

Module Introduction: Semantics, Soundness, Completeness, and Undecidability of Predicate LogicВидеоSemantics in Predicate Logic: Introduction—Part IВидеоPractice Quiz: Semantics in Predicate Logic: Introduction—Part IЗаданиеSemantics in Predicate Logic: Introduction—Part IIВидеоPractice Quiz: Semantics in Predicate Logic: Introduction—Part IIЗаданиеSemantics: Models and Interpretations—Part 1ВидеоPractice Quiz: Semantics: Models and Interpretations—Part 1ЗаданиеSemantics: Models and Interpretations—Part 2ВидеоPractice Quiz: Semantics: Models and Interpretations—Part 2ЗаданиеSemantics: Models and Interpretations—Part 3ВидеоPractice Quiz: Semantics: Models and Interpretations—Part 3ЗаданиеSemantics: Models and Interpretations—Part 4ВидеоPractice Quiz: Semantics: Models and Interpretations—Part 4ЗаданиеSemantics: Models and Interpretations—Part 5ВидеоPractice Quiz: Semantics: Models and Interpretations—Part 5ЗаданиеRecommended Reading 1: Semantics of Predicate Logic: Part I Чтение

Semantics of Predicate Logic: Part II

Semantics: Interpretation Involving VariablesВидеоPractice Quiz: Semantics: Interpretation Involving VariablesЗаданиеSemantics: Interpretation Using Environments or Look-Up TablesВидеоPractice Quiz: Semantics: Interpretation Using Environments or Look-Up TablesЗаданиеModel Checks Relation with ExamplesВидеоPractice Quiz: Model Checks Relation with ExamplesЗадание

Satisfiability, Validity, and Undecidability of Predicate Logic

Satisfiability and Validity in Predicate LogicВидеоPractice Quiz: Satisfiability and Validity in Predicate LogicЗаданиеSatisfiability and Validity: Example 1ВидеоPractice Quiz: Satisfiability and Validity: Example 1ЗаданиеSatisfiability and Validity: Example 2ВидеоPractice Quiz: Satisfiability and Validity: Example 2Задание

Summary

Summary: Semantics, Soundness, Completeness, and Undecidability of Predicate LogicВидеоTest Yourself: Natural Deduction, Semantics and Model Interpretations in Predicate LogicЗадание
09Program Verification31 материалов

Formal Verification: Introduction and Partial Correctness

Module Introduction: Program VerificationВидеоFormal Verification: MotivationВидеоPractice Quiz: Formal Verification: MotivationЗаданиеFloyd-Hoare Logic: Introduction, and Partial vs. Total CorrectnessВидеоPractice Quiz: Floyd-Hoare Logic: Introduction, and Partial vs. Total CorrectnessЗаданиеFloyd-Hoare Logic: Correctness of Assignment StatementsВидеоPractice Quiz: Floyd-Hoare Logic: Correctness of Assignment StatementsЗаданиеFloyd-Hoare Logic: Correctness of SequencingВидеоPractice Quiz: Floyd-Hoare Logic: Correctness of SequencingЗаданиеFloyd-Hoare Logic: PragmaticsВидеоPractice Quiz: Floyd-Hoare Logic: PragmaticsЗаданиеRecommended Reading: Floyd-Hoare Logic for Assignment and Sequencing ЧтениеFloyd-Hoare Logic: Correctness of ConditionalsВидеоPractice Quiz: Floyd-Hoare Logic: Correctness of ConditionalsЗаданиеFloyd-Hoare Logic: Meta-Rule and ExamplesВидеоPractice Quiz: Floyd-Hoare Logic: Meta-Rule and ExamplesЗаданиеRecommended Reading: Floyd-Hoare Logic for Conditionals and Meta-Rule Чтение

Formal Verification: Total Correctness

Termination Arguments for Total CorrectnessВидеоPractice Quiz: Termination Arguments for Total CorrectnessЗаданиеTermination Arguments Examples 1ВидеоTermination Arguments Examples 2ВидеоPractice Problems 1: A List of Practice Questions on Program Termination ЧтениеProgram Variables vs. Logical VariablesВидео

Summary

Summary: Program VerificationВидео
10Program Verification Case Studies15 материалов

Formal Verification: Case Studies

Module Introduction: Program Verification: Case StudiesВидео Computing Power of two numbers: Partial CorrectnessВидеоComputing Power of two numbers: Proof of TerminationВидеоFinding an Element in an Unsorted ArrayВидеоFinding an Element in an Unsorted Array: Total CorrectnessВидеоPractice Problems 1Чтение

Correctness of Selection Sort

Selection Sort: IntuitionВидеоSelection Sort: C ProgramВидеоSelection Sort: Correctness of findMinIndex()ВидеоSelection Sort: Correctness of sort()ВидеоPractice Problems 2Чтение

Summary

Summary: Program Verification Case StudiesВидеоTest Yourself: Program VerificationЗадание

Course Wrap-up

Course Wrap-upВидеоCongratulations & Next StepsЧтение
Example 4: Natural Deduction Proof of a Logical IdentityВидео
Practice Quiz: Example 4: Natural Deduction Proof of a Logical IdentityЗадание
Recommended Reading: Usage of Natural Deduction as Proof TechniqueЧтение
Davis Putnam Algorithm: An IntroductionВидео
Practice Quiz : Davis Putnam Algorithm: An IntroductionЗадание
Davis Putnam Algorithm: A Running ExampleВидео
Practice Quiz : Davis Putnam Algorithm: A Running ExampleЗадание
Recommended Reading: Normal Forms Чтение
Computation Tree Logic: An Informal IntroductionВидео
Practice Quiz: Computation Tree Logic: An Informal IntroductionЗадание
Recommended Reading: Temporal Logics Чтение
Practice Quiz: Computational Tree Logic: The SemanticsЗадание
Model Checking Algorithm for CTL: Naive IdeaВидео
Practice Quiz: Model Checking Algorithm for CTL: Naive IdeaЗадание
Recommended Reading: Computational Tree Logic Чтение
Expressing Using Predicates: Examples 4Видео
Practice Quiz: Expressing Using Predicates: Examples 4Задание
Expressing Using Predicates: Example 5Видео
Practice Quiz Expressing Using Predicates: Example 5Задание
Expressing Using Predicates: Examples 6Видео
Practice Quiz Expressing Using Predicates: Examples 6Задание
Expressing Inductive Rules Using Predicate LogicВидео
Practice Quiz: Expressing Inductive Rules Using Predicate LogicЗадание
Syntax of Predicate LogicВидео
Practice Quiz: Syntax of Predicate LogicЗадание
Predicate Logic: Conventions UsedВидео
Practice Quiz: Predicate Logic: Conventions UsedЗадание
Recommended Reading: Expressing using Predicate Logic  Чтение
Practice Quiz: Substitution and BindingЗадание
Bound vs. Free VariablesВидео
Practice Quiz: Bound vs. Free VariablesЗадание
Substitution RevisitedВидео
Practice Quiz: Substitution RevisitedЗадание
Substitution and RenamingВидео
Practice Quiz: Substitution and RenamingЗадание
Recommended Reading: Substitution and Binding Чтение
Semantic EntailmentВидео
Practice Quiz: Semantic EntailmentЗадание
Recommended Reading: Semantics of Predicate Logic: Part II Чтение
Satisfiability and Validity: Example 3Видео
Practice Quiz: Satisfiability and Validity: Example 3Задание
Satisfiability and Validity: Example 4Видео
Practice Quiz: Satisfiability and Validity: Example 4Задание
Practice Problems: Checking Satisfiability and Validity in Predicate LogicЧтение
Undecidability, Soundness, and Completeness of Predicate LogicВидео
Practice Quiz: Undecidability, Soundness, and Completeness of Predicate LogicЗадание
Limitations of First-Order Logic and a Glimpse of Second-Order LogicВидео
Practice Quiz: Limitations of First-Order Logic and a Glimpse of Second-Order LogicЗадание
Recommended Reading: Undecidability of Validity, Soundness & Completeness, and Limitations of First-Order Logic Чтение
Practice Quiz: Program Variables vs. Logical VariablesЗадание
Verifying Correctness of Loops: Loop Invariants with ExamplesВидео
Practice Quiz: Verifying Correctness of Loops: Loop Invariants with ExamplesЗадание
Loop Invariants: Example 1Видео
Loop Invariants: Example 2Видео
Practice Problems 2: A List of Practice Questions on Loop InvariantsЧтение
Recommended Reading: Total Correctness and Loop InvariantsЧтение