Lectures related to Case Analysis Rule and Propositional Resolution

Automating First-Order Logic Proofs Using Resolution

Covers first-order logic syntax, semantics, Skolemization, resolution, and normal form transformations.

Covers the interpretation of propositional logic and inference rules for implication, conjunction, and double negation.

Explores completeness in propositional logic, resolution on clauses, conjunctive form, unit resolution, SAT solvers, and proof generation.

Soundness and Completeness of a Propositional Proof System

Explores the importance of soundness and completeness in a propositional proof system.

Formal Proofs: Checking Invariants and Bounded Model Checking

Explores formal proofs, satisfiability problems, and inductive invariants using SAT queries in sequential circuits.

Finite Systems Expressed with Formulas

Explores encoding finite systems with boolean functions, propositional logic, inductive invariants, and formal proof systems.

Hoare Logic: Foundations and Applications

Covers Hoare Logic, its foundations, applications, and significance in program verification.

Coq: Introduction

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Automating First-Order Logic Proofs Using Resolution

Covers first-order logic syntax, semantics, and resolution for proving properties.

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Theorem Proving and Vampire

Explores theorem proving in first-order logic and the saturation-based approach, highlighting the Vampire theorem prover.

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Theory of Computation: Decidability and Complexity

Delves into the theory of computation, covering decidability, complexity, P vs. NP, and reductions.

Proofs and Computations: A Journey Through Mathematical Theory

Explores historical mathematical proofs, decision problems, deductive systems, probabilistic and quantum proofs, and interactive proof systems.

Sequent Calculus: Basics and Applications

Covers the basics and applications of Sequent Calculus in Logic and Proof Theory, including Cut Elimination and practical proof analysis.

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What is a Formal Proof?

Covers the concept of formal proof systems, their structure, and soundness.

Predicate Logic: Quantifiers, CNF, DNF

Covers Predicate Logic, focusing on Quantifiers, CNF, and DNF.

Proofs: Logic, Mathematics & Algorithms

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.