Safe Inductions: An Algebraic Study

Safe Inductions: An Algebraic Study

Bart Bogaerts, Joost Vennekens, Marc Denecker

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
Main track. Pages 859-865. https://doi.org/10.24963/ijcai.2017/119

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.
Keywords:
Knowledge Representation, Reasoning, and Logic: Non-monotonic Reasoning
Knowledge Representation, Reasoning, and Logic: Logics for Knowledge Representation