Reasoning With Background Knowledge–a Three‐level Theory

Abstract

We address the problem of reasoning in cases when knowledge bases containing background knowledge are understood not as sets of formulas (rules and facts) but as collections of partially ordered theories. In our system, the usual, two‐part logical structures, consisting of a metalevel and an object level, are augmented by a third level–a referential level. The referential level is a partially ordered collection of theories; it encodes background knowledge. As usual, current situations are described on the object level, and the metalevel is a place for rules that can eliminate some of the models permitted by the object level and the referential level. As a logic of reasoning the system generalizes the standard model of a rational agent: deducing actions and deriving new information about the world from a logical theory–its knowledge base. It is a natural logical system in which priorities on the possible readings of predicates, not special rules of inference, are the main source of nonmonotonicity. We introduce a theory forming operator PT(x) to exploit the priorities, and we investigate its basic logical properties. Then we show how such a system can be augmented by metarules. Although this paper concentrates on basic logical properties of the new theory, this formalism has already been applied to model a number of natural language phenomena such as the notion of text coherence, Gricean maxims, vagueness, and a few others. The paper also briefly compares it with the model of background knowledge of CYC, as proposed by Lenat and Guha.

A Sheaf Model of Contradictions and Disagreements. Preliminary Report and Discussion

“…Then, the insights of the cited works could help us choose most appropriate local sections, if global sections do not exist. This could be done, for example, using real valued measures proposed in Grant and Hunter [2016] or preferences on partially ordered theories, as in Zadrozny [1994], or some combinations of the two. Another difference and the limitation of our work is that we do not explicitly deal with quantified formulas.…”

NL understanding with a grammar of constructions

“…The organization of knowledge: The issue of the organization of knowledge has been discussed at h:ngth in [8] and [9] and the formal model tleveh)pe, d tiler(: ix applicabh; in the present context. At this t)oint, however, this tbrmal model has only been implenmntcd very crudely.…”