This intuition occurs for instance in the well-founded semantics of logic programs and in autoepistemic logic.
This abstract machine, called the SLG-WAM, uses tabling to efficiently compute the well-founded semantics of non-ground normal logic programs in a goal-directed way.
In recent years, various formalizations of nonmonotonic reasoning and different semantics for normal and disjunctive logic programs have been proposed, including autoepistemic logic, circumscription, CWA, GCWA, ECWA, epistemic specifications, stable, well-founded, stationary and static semantics of normal and disjunctive logic programs.
For understanding of approaches to logic programming built on well-founded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.
For Henkin's second style of language, at least in Hintikka's notation (see the entry on independence friendly logic), the syntax is well-founded, but the displacement of the quantifier scopes means that the usual quantifier clauses in the definition of satisfaction no longer work.
In this paper we define a general fixed-point semantics for preference logic programs based on an embedding into the well-founded semantics, and discuss its features and relation to previous preference logic semantics.
XSB: A system for efficiently computing well-founded semantics, by Prasad Rao, et al. Online justification for tabled logic programs, by Giridhar Pemmasani, et al. MulVAL: A logic-based network security analyzer, by Xinming Ou, Sudhakar Govindavajhala, and Andrew Appel.
Knorr et al. (2011) [9] formulated a three-valued formalism for the logic of Minimal Knowledge and Negation as Failure (MKNF), and proposed a well-founded semantics for hybrid MKNF knowledge bases.
In this paper we propose a well-founded semantics for nondisjunctive hybrid MKNF knowledge bases that promises to provide better efficiency of reasoning, and that is compatible with both the OWL-based semantics and the traditional Well-Founded Semantics for logic programs.
Her fear is well-founded.
