Implementing Belnap-logical conflation and implication operators in answer set programming

Two types of negation are allowed in answer set programming (ASP), default negation and classical negation. When using two-valued logic as its basis, the presence of classical negation in ASP can lead to gluts (both true and false) and gaps (neither true nor false), which are handled in unintuitive ways. Belnap’s four-valued logic, with gluts and gaps as truth values, is a more intuitive basis for ASP. This thesis examines the intuition behind Belnap logic, showing that the conflation operator, which has no obvious intuitive meaning, is central to the representation of default negation in Belnap logic. There is no single correct implication operator in Belnap logic that can be used in ASP rules, so we examine a number of different implication operators in Belnap logic, before presenting a new implication operator that generalizes them and showing how this implication operator can be implemented in ASP without changing its specifications.