Name
Title | ||
|---|---|---|
Propositional logic with short-circuit evaluation: a non-commutative and a commutative variant. |
Abstract | ||
|---|---|---|
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely used in programming, with sequential conjunction and disjunction as primitive connectives. study the question which logical laws axiomatize evaluation under the following assumptions: compound statements are evaluated from left to right, each atom (propositional variable) evaluates to either true or false, and atomic evaluations can cause a side effect. The answer to this question depends on the kind of atomic side effects that can occur and leads to different short-circuit logics. The basic case is FSCL (free logic), which characterizes the setting in which each atomic evaluation can cause a side effect. We recall some main results and then relate FSCL to MSCL (memorizing logic), where in the evaluation of a compound statement, the first evaluation result of each atom is memorized. MSCL can be seen as a sequential variant of propositional logic: atomic evaluations cannot cause a side effect and the sequential connectives are not commutative. Then we relate MSCL to SSCL (static logic), the variant of propositional logic that prescribes evaluation with commutative sequential connectives. present evaluation trees as an intuitive semantics for evaluation, and simple equational axiomatizations for the logics mentioned that use negation and the sequential connectives only. |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Logic in Computer Science | Discrete mathematics,Negation,Commutative property,Algebra,Short-circuit evaluation,Propositional calculus,If and only if,Propositional variable,Mathematics,Semantics |
DocType | Volume | Citations |
Journal | abs/1810.02142 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jan A. Bergstra | 1 | 1946 | 240.42 |
| Alban Ponse | 2 | 404 | 38.05 |
| D. J. C. Staudt | 3 | 1 | 1.07 |