Recap: Why learn about logic?

In this activity, you have learned how to construct and fill in truth tables. Truth tables are a simple way of examining a propositional statement. You have learned about how you can model logic puzzles as propositions and propositional formula, using truth tables to help solve the puzzles.

We hope you are enjoying learning about propositional logic! You may, however, be asking yourself why we are doing all this, and where is it leading?

Let’s just set out why it matters and which areas of computer science rely on an understanding about logic:

Logic is a fundamental concept in computer science, and it has numerous applications in various fields of computer science. Some of the major applications of logic in computer science are as follows:

1. Programming: Logic is used in programming languages to define the rules and constraints that the program must follow. Programmers use logical statements and operators to perform various operations and decisions in the program.
2. Artificial Intelligence: Logic plays a crucial role in Artificial Intelligence (AI). Logical systems such as propositional logic, first-order logic, and modal logic are used in AI to represent and reason about knowledge and uncertainty.
3. Formal Verification: Formal verification is a process of mathematically proving the correctness of a system or software. Logic is used in formal verification to describe the system’s behaviour and to ensure that the system meets its specifications.
4. Database Systems: Database systems use logic to specify and manipulate the relationships between data entities. Logic-based query languages such as SQL and Prolog are used to search and retrieve data from databases.
5. Circuit Design: Logic gates such as AND, OR, and NOT gates are used to design digital circuits that perform logical operations. These circuits form the backbone of modern computers and electronic devices.
6. Theorem Proving: Logic-based theorem proving systems are used to automatically prove theorems and mathematical statements. These systems can help to verify the correctness of software and hardware designs.
7. Compiler Design: Logic is used in compiler design to analyse and optimise code. Compiler optimisation techniques use logical reasoning to improve the performance and efficiency of the compiled code.

Logic plays a critical role in many other areas of computer science, including algorithms, graph theory, automata theory and many more.

So although this may all be new to you, you can see how and why it might be useful to understand propositional logic. There’s a whole world of exciting applications out there!