Propositional calculus
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
- Boolean algebra (logic)
- Boolean algebra (structure)
- Boolean algebra topics
- Boolean domain
- Boolean function
- Boolean-valued function
- Categorical logic
- Combinational logic
- Combinatory logic
- Conceptual graph
- Disjunctive syllogism
- Entitative graph
- Equational logic
- Existential graph
- Frege's propositional calculus
- Implicational propositional calculus
- Intuitionistic propositional calculus
- Jean Buridan
- Laws of Form
- Logical graph
- Logical NOR
- Logical value
- Mathematical logic
- Operation
- Paul of Venice
- Peirce's law
- Peter of Spain
- Propositional formula
- Symmetric difference
- Truth function
- Truth table
- Walter Burley
- William of Sherwood
External links
- Propositional calculus @ Wikipedia
