On the relation between vector annotated logic programs and defeasible theories

Abstract

Abstract. In this paper, we propose an annotated logic program called a VALPSN (Vector Annotated Logic Program with Strong Negation) to deal with defeasible reasoning. We propose a translation from Billington's defeasible theory into VALPSN and clarify the relation between them based on the translation.

Introduction to Annotated Logics

“…Later, as a generalization of the framework, Nakamatsu [125] proposed vector annotated logic program with strong negation (VALPSN) and their extensions.…”

Application of paraconsistent annotated logic program bf-EVALPSN to intelligent control

“…It has already passed over two decades since paraconsistent annotated logic and its logic programming have been developed [3], [4]. Based on the original annotated logic program we have developed four kinds of paraconsistent annotated logic program, ALPSN (Annotated Logic Program with Strong Negation) that can deal with some non-monotonic reasonings such as default reasoning [5], VALPSN (Vector ALPSN) that can deal with defeasible and plausible reasonings [6], EVALPSN (Extended VALPSN) that can deal with defeasible deontic and plausible reasonings [7], [17], and bf(before-after)-EVALPSN that can deal with before-after relation between processes(time intervals) recently [16], [18]. Those annotated logic programs have been applied to various kinds of intelligent control and safety verification, railway interlocking safety verification [9], air traffic safety verification [8], traffic signal control [10], discrete event control [11], robot action control [15], pipeline valve control [14], real-time process order control [13], and so on.…”

The paraconsistent process order control method

“…Furthermore, we have developed the paraconsistent annotated logic program to deal with inconsistency and some kinds of non-monotonic reasoning in a framework of annotated logic programming by using ontological (strong) negation and the stable model semantics [6], which is called annotated logic program with strong negation (ALPSN for short). Later, to deal with defeasible reasoning [14], we proposed a new version of ALPSN called vector annotated logic program with strong negation (VALPSN for short) and applied it to resolving conflicts [7]. Furthermore, we have extended VALPSN to deal with deontic notions (obligation, forbiddance, etc.)…”