Partial logics with two kinds of negation as a foundation for knowledge-based reasoning (Q2715521)

Partial logic is considered in the paper as a natural candidate for modeling knowledge-based reasoning. This kind of reasoning has to be able to deal with inexact predicates and with knowledge bases containing contradictory information. Two notions of falsity (implicit by default and explicit) and, correspondingly, two kinds of negation are distinguished. NEWLINENEWLINENEWLINEThe model theory of partial logic assigns a positive and a negative extension to each predicate. The class of all interpretations is 4-valued (true, false, unknown, contradictory). Important (sub)classes of coherent (3-valued), total and 2-valued interpretations are defined. NEWLINENEWLINENEWLINEThe satisfaction relation \(\models\) is defined by a dichotomous induction on the complexity of formulas \(F\) and \(\sim F\), where \(\sim\) is the strong negation (verification and falsification are independent truth-value assignments in partial logic). NEWLINENEWLINENEWLINEProof theory is presented in terms of sequent calculi. Four sequential systems are defined (correspondingly to the 2-valued, total, coherent, and 4-valued interpretations). If the absence of exact predicates is assumed, the systems are complete w.r.t. the corresponding model-theoretic consequence relations. NEWLINENEWLINENEWLINESeveral versions of nonmonotonic reasoning based on partial logic are studied in the paper. It is shown that the fundamental semantic notions of minimal, paraminimal and stable models in partial logics can be used to define the semantics of knowledge bases including relational and deductive databases, and extended logic programs.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00012].