Computer Supported Modeling and Reasoning (Lecture)

This lecture is about using logic for system (e.g., program or chip) development and analysis. The system behavior and desired system properties can both be formalized using logic, for the purpose of verifying the properties using computer support. The lecture is intended for anyone interested in artificial intelligence (KI), logic, hardware and software verification. The lecture is roughly structured in four parts. In part 1, we shall introduce various logic systems including propositional logic, first-order logic, and (naive) set theory. We shall see how proofs in these systems can be conducted both using paper and pencil and using the interactive theorem prover Isabelle. In part 2, we shall attempt to understand what happens behind the scenes: we shall study meta-logic, which is the general theory allowing us to implement all kinds of logic systems using a single tool. In part 3, we shall see how an important part of mathematics and programming languages can be modeled in this framework, including concepts such as arithmetic, data-types, and recursion. Part 4 will be a case study coming from functional or imperative programming or from the area of specification languages.