propositional calculus
propositional calculus A system of symbolic logic, designed to study propositions. A proposition is a statement that is true or false. There are many alternative but equivalent definitions of propositional calculus, one of the more useful for the computer scientist being given below.
The only terms of the propositional calculus are the two symbols T and F (standing for true and false) together with variables for logical propositions, which are denoted by small letters p,q,r,…; these symbols are basic and indivisible and are thus called atomic formulas.
The propositional calculus is based on the study of wellformed formulas, or wff for short. New wff of the form (~A), (A ∨ B), (A ∧ B), (A ⊃ B), (A ≡ B), (IF A THEN B ELSE C)
are formed from given wff A, B, and C using logical connectives; respectively they are called negation, disjunction, conjunction, implication, equivalence, and conditional. If 〈atf〉 denotes the class of atomic formulas, then the class of wff, 〈wff〉, can be described in BNF notation (see Fig. 1).
Proofs and theorems within the propositional calculus are conducted in a formal and rigorous manner: certain basic axioms are assumed and certain rules of inference are followed. In particular these rules must deal with the various connectives.
The rules of inference are stated using a form such as α β
The rule should be interpreted to mean that on the assumption that α is true, it can be deduced that β is then true. Logicians often use the notation α⊦β. In writing the rules it is convenient to employ a notation such as Γ, A ⇒ B
Γ is some set of wff whose truth has been established; A and B are some other wff highlighted for the purposes of the rule; ⇒ denotes implication (to avoid confusion with the symbol ⊃). For example, the rules for the introduction and elimination respectively of the ∧ connective are shown in Fig. 2.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"propositional calculus." A Dictionary of Computing. . Encyclopedia.com. 21 Aug. 2018 <http://www.encyclopedia.com>.
"propositional calculus." A Dictionary of Computing. . Encyclopedia.com. (August 21, 2018). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/propositionalcalculus
"propositional calculus." A Dictionary of Computing. . Retrieved August 21, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/propositionalcalculus
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.