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Course

Computer - Logic for Computer Science

Indian Institute of Technology Delhi

This course provides a deep dive into the principles of logic that are foundational for computer science. Understanding logic is crucial for developing algorithms and reasoning about program behavior. The curriculum encompasses:

  • Propositional Logic: Syntax, semantics, and tautologies.
  • Proof Theory: Including Hilbert-style systems and soundness.
  • Predicate Logic: Structures, quantification, and models.
  • Verification: Techniques for ensuring program correctness.

Students will engage with various logical systems and their applications while exploring both theoretical and practical aspects. By the end of this course, learners will have a robust understanding of how logic underpins computer science and its applications in programming and systems verification.

Course Lectures
  • Mod-01 Lec-01 Introduction
    Mod-01 Lec-01 Introduction
    Prof. S. Arun Kumar
    Play

    This module serves as an introduction to the course, outlining its objectives and significance in the realm of computer science. Students will learn how logic is used in various computational problems and its impact on algorithm design.

  • Mod-01 Lec-02 Propositional Logic Syntax
    Mod-01 Lec-02 Propositional Logic Syntax
    Prof. S. Arun Kumar
    Play

    This module covers the syntax of propositional logic. Students will learn about logical connectives, well-formed formulas, and the structure of logical expressions. Understanding syntax is crucial for formulating logical statements correctly.

  • Mod-01 Lec-03 Semantics of Propositional Logic
    Mod-01 Lec-03 Semantics of Propositional Logic
    Prof. S. Arun Kumar
    Play

    The focus of this module is to understand the semantics of propositional logic. Students will explore truth values, models, and the relationship between syntax and semantics, enabling them to evaluate logical statements effectively.

  • Mod-01 Lec-04 Logical and Algebraic Concepts
    Mod-01 Lec-04 Logical and Algebraic Concepts
    Prof. S. Arun Kumar
    Play

    This module introduces students to logical and algebraic concepts that intertwine with propositional logic. Key topics include Boolean algebra, simplification of logical expressions, and the applications of these concepts in computer science.

  • Mod-01 Lec-05 Identities and Normal forms
    Mod-01 Lec-05 Identities and Normal forms
    Prof. S. Arun Kumar
    Play

    This module delves into identities and normal forms in propositional logic. Students will learn about key logical identities, as well as how to convert logical expressions into conjunctive and disjunctive normal forms.

  • Mod-01 Lec-06 Tautology Checking
    Mod-01 Lec-06 Tautology Checking
    Prof. S. Arun Kumar
    Play

    This module focuses on tautology checking, teaching students how to determine if a logical statement is a tautology. Various methods and algorithms will be discussed to facilitate this understanding.

  • Mod-01 Lec-07 Propositional Unsatisfiability
    Mod-01 Lec-07 Propositional Unsatisfiability
    Prof. S. Arun Kumar
    Play

    In this module, students will explore propositional unsatisfiability. They will learn the criteria that make a propositional formula unsatisfiable and how to apply these concepts in logical reasoning.

  • Mod-01 Lec-08 Analytic Tableaux
    Mod-01 Lec-08 Analytic Tableaux
    Prof. S. Arun Kumar
    Play

    This module introduces analytic tableaux as a method for evaluating logical expressions. Students will learn how to construct tableaux and use them to assess the validity of logical statements.

  • Mod-01 Lec-09 Consistency and Completeness
    Mod-01 Lec-09 Consistency and Completeness
    Prof. S. Arun Kumar
    Play

    Students will learn about consistency and completeness in logical systems in this module. Key concepts such as consistent sets of formulas and the implications of completeness will be explored.

  • Mod-01 Lec-10 The Completeness Theorem
    Mod-01 Lec-10 The Completeness Theorem
    Prof. S. Arun Kumar
    Play

    This module covers the Completeness Theorem, detailing its significance in logic. Students will understand the relationship between syntactic provability and semantic truth.

  • Mod-01 Lec-11 Maximally Consistent Sets
    Mod-01 Lec-11 Maximally Consistent Sets
    Prof. S. Arun Kumar
    Play

    This module introduces maximally consistent sets. Students will explore the concept of consistency in logical systems and how maximally consistent sets can be used in proofs.

  • Mod-01 Lec-12 Formal Theories
    Mod-01 Lec-12 Formal Theories
    Prof. S. Arun Kumar
    Play

    Students will learn about formal theories in this module. The focus will be on the structure of formal theories and their applications in proving logical statements.

  • Mod-01 Lec-13 Proof Theory : Hilbert-style
    Mod-01 Lec-13 Proof Theory : Hilbert-style
    Prof. S. Arun Kumar
    Play

    This module delves into Hilbert-style proof theory. Students will analyze the components of Hilbert systems and their application in formal proofs.

  • Mod-01 Lec-14 Derived Rules
    Mod-01 Lec-14 Derived Rules
    Prof. S. Arun Kumar
    Play

    In this module, students will study derived rules in logical systems. They will learn how these rules are formulated and their significance in deriving conclusions from premises.

  • Mod-01 Lec-15 The Hilbert System : Soundness
    Mod-01 Lec-15 The Hilbert System : Soundness
    Prof. S. Arun Kumar
    Play

    This module covers the soundness of the Hilbert system. Students will understand the concept of soundness and how it applies to derivations in logical systems.

  • Mod-01 Lec-16 The Hilbert System :Completeness
    Mod-01 Lec-16 The Hilbert System :Completeness
    Prof. S. Arun Kumar
    Play

    Students will explore completeness in the Hilbert system in this module. The relationship between syntactical and semantical completeness will be examined, providing a deeper understanding of logical systems.

  • Mod-01 Lec-17 Introduction to Predicate Logic
    Mod-01 Lec-17 Introduction to Predicate Logic
    Prof. S. Arun Kumar
    Play

    This module introduces predicate logic, focusing on its syntax and semantics. Students will learn how predicate logic extends propositional logic, allowing for more expressive representations of statements.

  • Mod-01 Lec-18 The Semantic of Predicate Logic
    Mod-01 Lec-18 The Semantic of Predicate Logic
    Prof. S. Arun Kumar
    Play

    In this module, students will study the semantics of predicate logic. Key topics include interpretation, models, and truth values, which are essential for grasping the meaning behind logical statements.

  • Mod-01 Lec-19 Subsitutions
    Mod-01 Lec-19 Subsitutions
    Prof. S. Arun Kumar
    Play

    This module covers substitutions in predicate logic. Students will learn how substitutions affect the validity of logical statements and how they can be used in logical proofs.

  • Mod-01 Lec-20 Models
    Mod-01 Lec-20 Models
    Prof. S. Arun Kumar
    Play

    Students will learn about models in predicate logic in this module. The focus will be on how models provide meanings to logical expressions and their role in validating logical statements.

  • Mod-01 Lec-21 Structures and Substructures
    Mod-01 Lec-21 Structures and Substructures
    Prof. S. Arun Kumar
    Play

    This module discusses structures and substructures in predicate logic. Students will understand the importance of these concepts in analyzing logical systems and their properties.

  • Mod-01 Lec-22 First - Order Theories
    Mod-01 Lec-22 First - Order Theories
    Prof. S. Arun Kumar
    Play

    In this module, students will study first-order theories. They will explore the axioms and rules that define these theories and their applications in logical reasoning.

  • Mod-01 Lec-23 Predicate Logic: Proof Theory (Contd..)
    Mod-01 Lec-23 Predicate Logic: Proof Theory (Contd..)
    Prof. S. Arun Kumar
    Play

    This module continues the exploration of predicate logic with a focus on proof theory. Students will learn techniques for proving the validity of logical statements within predicate logic.

  • Mod-01 Lec-24 Existential Quantification
    Mod-01 Lec-24 Existential Quantification
    Prof. S. Arun Kumar
    Play

    Students will learn about existential quantification in this module. The focus will be on how existential quantifiers are used in logical statements and their implications for truth values.

  • Mod-01 Lec-25 Normal Forms
    Mod-01 Lec-25 Normal Forms
    Prof. S. Arun Kumar
    Play

    This module discusses normal forms in predicate logic, including the conversion of logical statements into normal forms. Students will learn the significance of normal forms in computational logic.

  • Mod-01 Lec-26 Skalemization
    Mod-01 Lec-26 Skalemization
    Prof. S. Arun Kumar
    Play

    In this module, students will learn about skolemization, a process used in predicate logic to eliminate existential quantifiers. The focus will be on how this affects logical expressions and their validity.

  • Mod-01 Lec-27 Substitutions and Instantiations
    Mod-01 Lec-27 Substitutions and Instantiations
    Prof. S. Arun Kumar
    Play

    This module covers substitutions and instantiations in predicate logic. Students will understand how these concepts are used to manipulate logical statements and their role in proofs.

  • Mod-01 Lec-28 Unification
    Mod-01 Lec-28 Unification
    Prof. S. Arun Kumar
    Play

    This module introduces unification in predicate logic. Students will learn the process of unifying terms and its applications in logical reasoning and proof construction.

  • Mod-01 Lec-29 Resolution in FOL
    Mod-01 Lec-29 Resolution in FOL
    Prof. S. Arun Kumar
    Play

    This module focuses on resolution in first-order logic (FOL). Students will learn the resolution method as a proof technique and how to apply it to various logical problems.

  • Mod-01 Lec-30 More on Resolution in FOL
    Mod-01 Lec-30 More on Resolution in FOL
    Prof. S. Arun Kumar
    Play

    In this module, students will further explore resolution in FOL. They will learn advanced techniques and strategies for employing resolution in complex logical scenarios.

  • Mod-01 Lec-31 Resolution : Soundness and Completeness
    Mod-01 Lec-31 Resolution : Soundness and Completeness
    Prof. S. Arun Kumar
    Play

    This module covers soundness and completeness of the resolution method in first-order logic. Students will understand how these properties ensure the reliability of resolution as a proof technique.

  • Mod-01 Lec-32 Resolution and Tableaux
    Mod-01 Lec-32 Resolution and Tableaux
    Prof. S. Arun Kumar
    Play

    Students will study the relationship between resolution and tableaux methods in this module. They will learn how both techniques complement each other in proving logical statements.

  • Mod-01 Lec-33 Completeness of Tableaux Method
    Mod-01 Lec-33 Completeness of Tableaux Method
    Prof. S. Arun Kumar
    Play

    This module discusses the completeness of the tableaux method. Students will learn how to establish completeness and its implications for logical reasoning and proof construction.

  • Mod-01 Lec-34 Completeness of the Hilbert System
    Mod-01 Lec-34 Completeness of the Hilbert System
    Prof. S. Arun Kumar
    Play

    This module covers the completeness of the Hilbert system. Students will explore how completeness is established and its importance in logical systems.

  • Mod-01 Lec-35 First -Order Theories
    Mod-01 Lec-35 First -Order Theories
    Prof. S. Arun Kumar
    Play

    In this module, students will revisit first-order theories, focusing on their applications in logical reasoning and how they can be used to derive conclusions from premises.

  • Mod-01 Lec-36 Towards Logic Programming
    Mod-01 Lec-36 Towards Logic Programming
    Prof. S. Arun Kumar
    Play

    This module introduces students to logic programming. They will learn how logic is applied in programming languages and the role of logical inference in algorithm development.

  • Mod-01 Lec-37 Verification of Imperative Programs
    Mod-01 Lec-37 Verification of Imperative Programs
    Prof. S. Arun Kumar
    Play

    This module discusses the verification of imperative programs. Students will learn techniques to ensure that imperative programs behave as intended and meet specified requirements.

  • Mod-01 Lec-38 Verification of WHILE Programs
    Mod-01 Lec-38 Verification of WHILE Programs
    Prof. S. Arun Kumar
    Play

    In this final module, students will focus on the verification of WHILE programs. The emphasis will be on developing formal methods to ensure correctness in loop constructs.

  • Mod-01 Lec-39 References
    Mod-01 Lec-39 References
    Prof. S. Arun Kumar
    Play

    This module provides references for further reading and exploration in the field of logic and computer science. Students will find resources to deepen their understanding and knowledge.

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