Abstract
In many knowledge representation formalisms, a
constructive semantics is defined based on sequential applications of rules or of a semantic operator.
These constructions often share the property that
rule applications must be delayed until it is safe to
do so: until it is known that the condition that triggers the rule will remain to hold. This intuition occurs for instance in the well-founded semantics of
logic programs and in autoepistemic logic. In this
paper, we formally define the safety criterion algebraically. We study properties of so-called safe
inductions and apply our theory to logic programming and autoepistemic logic. For the latter, we
show that safe inductions manage to capture the intended meaning of a class of theories on which all
classical constructive semantics fail