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LPL 3.1-3.3 lecture

# LPL 3.1-3.3 lecture - Negation Conjunction Disjunction In...

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Negation, Conjunction, Disjunction In FOL, atomic sentences have a limited expressive power. Consider the following set of statements: Claire is not taller than Max. Max is at home and Claire fed Scruffy. Either Claire is a student or Max is a student. In order to form more complex statements in FOL, such as those above, we need to combine atomic sentences with connectives . The first connectives we will consider are called Boolean connectives and they correspond to the English expressions it is not the case that , and , and or . The Boolean connectives, along with several others we will discuss later, are “truth- functional” connectives. The reason for this is that the truth value of a complex sentence using Boolean connectives is determined by the truth values of the simple sentences involved. Perhaps the best way to illustrate this is to construct a truth table for each connective, showing that the overall truth value of Boolean statements depends on the atomic sentences of which each Boolean statement is composed. For each new connective we introduce into our system, its truth-functional definition will be given by way of a truth table. Negation: ¬ Our first connective ( ¬ ) will be used to express negation. In English we might use the expressions not , is not the case that , non- , or un- to express such negation. In FOL, all of these English-language ways of expressing negation can be handled by the ¬ symbol.

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LPL 3.1-3.3 lecture - Negation Conjunction Disjunction In...

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