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Lecture 1: Propositional Logic
? Associated reading: Rosen, Section 1.1
? Homework: Section 1.1, problems 1-23 odd, 37-42
Ingredients of logic:
? used for expressing rules and rationality within a system; i.e. modeling a system
? rules tend to be expressed using logical formulae which may be viewed in two funda-
mental ways:
- semantics: refers to the meaning behind a string of symbols
- syntax: refers to the structure of a string of symbols and the rules which govern
the creation of strings of symbols
? rationality within a system tends to depend upon a set of axioms and rules of inference
Some different types of logics that are of importance to computer science
? Propositional/Boolean logic: the design of combinatorial electronic circuits; pro-
gram control
? Predicate logic: formal specification, prolog programming language
? Higher-order logic: formal verification of hardware
? Sequential/temporal logic: design of computer memory; program concurrency
? Intensional logic: natural language ...

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