Name
Abstract | ||
|---|---|---|
Short-circuit evaluation denotes the semantics of propositional connectives
in which the second argument is only evaluated if the first argument does not
suffice to determine the value of the expression. In programming, short-circuit
evaluation is widely used.
A short-circuit logic is a variant of propositional logic (PL) that can be
defined by short-circuit evaluation and implies the set of consequences defined
by a module SCL. The module SCL is defined using Hoare's conditional, a ternary
connective comparable to if-then-else, and implies all identities that follow
from four basic axioms for the conditional and can be expressed in PL (e.g.,
axioms for associativity of conjunction and double negation shift.) In the
absence of side-effects, short-circuit evaluation characterizes PL. However,
short-circuit logic admits the possibility to model side-effects. We use
sequential conjunction as a primitive connective because it immediately relates
to short-circuit evaluation. Sequential conjunction gives rise to many
different short-circuit logics. The first extreme case is FSCL (free
short-circuit logic), which characterizes the setting in which evaluation of
each atom (propositional variable) can yield a side-effect. The other extreme
case is MSCL (memorizing short-circuit logic), the strongest (most identifying)
variant we distinguish below PL. In MSCL, only static side-effects can be
modelled, while sequential conjunction is non-commutative. We provide sets of
equations for FSCL and MSCL, and for MSCL we have a completeness result.
Extending MSCL with one simple axiom yields SSCL (static short-circuit logic,
or sequential PL), for which we also provide a completeness result. We briefly
discuss two variants in between FSCL and MSCL, among which a logic that admits
the contraction of atoms and of their negations. |
Year | Venue | Keywords |
|---|---|---|
2010 | Journal of Neurology, Neurosurgery, and Psychiatry | short-circuit evaluation,sequential connective,conditional composition,side effect.,non-commutative conjunction,re- active valuation,side effect,propositional logic |
Field | DocType | Volume |
Intuitionistic logic,Discrete mathematics,Autoepistemic logic,Zeroth-order logic,Propositional calculus,Algorithm,Many-valued logic,Well-formed formula,Propositional variable,Mathematics,Intermediate logic | Journal | abs/1010.3 |
Citations | PageRank | References |
3 | 0.59 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jan A. Bergstra | 1 | 1445 | 140.42 |
| Alban Ponse | 2 | 404 | 38.05 |
| d j c staudt | 3 | 3 | 0.59 |