Propositional calculus

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Propositional calculus (also called propositional logic, sentential calculus, sentential logic, or sometimes zeroth-order logic) is the branch of mathematical logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components.

Description

Logical connectives are found in natural languages. In English for example, some examples are "and" (conjunction), "or" (disjunction), "not” (negation) and "if" (but only when used to denote material conditional).

The following is an example of a very simple inference within the scope of propositional logic:

  • Premise 1: If it's raining then it's cloudy.
  • Premise 2: It's raining.
  • Conclusion: It's cloudy.

Both premises and the conclusion are propositions. The premises are taken for granted and then with the application of modus ponens (an inference rule) the conclusion follows.

See also

Higher logical levels

Related topics

External links