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# 2 The Language of Logic

There are two main aspects of mathematical logic that are important for computer science1.

1. Logic provides a precise language for formulating statements (Aussagen) and denoting objects (Gegenstände). Since computer science deals with highly abstract entities with complicated properties, it is important to have such a precise language in which critical issues can be expressed without ambiguity. The role of natural language in scientific work is to communicate basic ideas and intuitions; the role of logic is to resolve ambiguities and to clarify details.
2. Logic provides an intellectual framework for correct reasoning (Schlußfolgern, Schließen) and arguing (Argumentieren). These activities can be ultimately reduced to a finite number of rules that are formulated so precisely that their correct application can be checked automatically. Computer programs are probably the most complex human artifacts; to reason about their properties is a central task of computer science.

A precise language and sound reasoning belong to the most valuable intellectual tools of a computer scientist or engineer. Only if she masters these tools thoroughly, she can utilize her creative potential in an effective and goal-directed way. Please note that it is not the heavy use of symbolism that characterizes precise expression and clear arguments. A computer scientist should be able to recognize and to present the underlying logical concepts on various language levels and in various notations. She can then flexibly adapt form and preciseness of her statements to the demands of a particular situation while preserving the essential contents. We therefore strive to demonstrate these concepts in various styles, from natural language ("every Ferrari is red") to purely symbolic (forall x: F(x) => R(x)).

• 2.1 Preliminaries
• 2.2 Propositional Logic
• 2.3 Predicate Logic
• 2.4 Example

• Author: Wolfgang Schreiner
Last Modification: October 4, 1999