Logic is concerned with propositions and proofs. A proposition is an abstract mathematical object corresponding to a declarative sentence. We speak of the sense of a proposition, i.e. the thought expressed by it, and of its truth value.
Logic deals with the truth value of propositions independently of subject matter. The raw data of logic are representations of the abstract notion of a proposition. The truth of a proposition depends on its meaning or its sense. Access to truth is via evidence, particularly in the form of proof.
The notion of proof is used also as the basis for meaning; to understand a proposition is to know how to prove it - although one may not know whether a proof can be found. These are the basic concepts of logic and the course presents precise versions of these concepts and the relationships among them.
Computer scientists have shown how to implement the computational core of logics as a programming language and reasoning system combined into one language. Such mathematical systems form a rich class of programming logics which have proven useful in computer science. Conversely, advances in computer science have created a new field of mathematics called Formalized Mathematics. This course will demonstrate these connections between computer science and logic.