Cirquent calculus

Cirquent calculus is a <a href="/facts/Proof_calculus/oXTtCnhC">proof calculus</a> that manipulates <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graph</a>-style constructs termed cirquents, as opposed to the traditional <a href="/facts/Tree_(graph_theory)/TCWk4Joy">tree</a>-style objects such as <a href="/facts/Formula_(logic)/YpTVlzuj">formulas</a> or <a href="/facts/Sequent/7YoB2hYb">sequents</a>. Cirquents come in a variety of forms, but they all share one main characteristic feature, making them different from the more traditional objects of syntactic manipulation. This feature is the ability to explicitly account for possible sharing of subcomponents between different components. For instance, it is possible to write an expression where two subexpressions F and E, while neither one is a subexpression of the other, still have a common occurrence of a subexpression G (as opposed to having two different occurrences of G, one in F and one in E).

Cirquent calculus open-in-new

Cirquent calculus