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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
This module covers the Completeness Theorem, detailing its significance in logic. Students will understand the relationship between syntactic provability and semantic truth.
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.
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.
This module delves into Hilbert-style proof theory. Students will analyze the components of Hilbert systems and their application in formal proofs.
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.
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.
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.
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.
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.
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.
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.
This module discusses structures and substructures in predicate logic. Students will understand the importance of these concepts in analyzing logical systems and their properties.
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.
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.
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.
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.
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.
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.
This module introduces unification in predicate logic. Students will learn the process of unifying terms and its applications in logical reasoning and proof construction.
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.
In this module, students will further explore resolution in FOL. They will learn advanced techniques and strategies for employing resolution in complex logical scenarios.
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.
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.
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.
This module covers the completeness of the Hilbert system. Students will explore how completeness is established and its importance in logical systems.
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.
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.
This module discusses the verification of imperative programs. Students will learn techniques to ensure that imperative programs behave as intended and meet specified requirements.
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.
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.