Vivid logic. Knowledge-based reasoning with two kinds of negation
type: Item
instance of: scholarly article
title: Vivid logic. Knowledge-based reasoning with two kinds of negation
zbMATH Open document ID: 0806.68105
DOI: 10.1007/3-540-57604-5
author: Gerd Wagner
published in: Lecture Notes in Computer Science
publication date: 1994-02-17T00:00:00Z
review text: The book aims at defining a cognitively adequate and computationally feasible model for commonsense reasoning. It proposes a concept of `vivid' knowledge representation and reasoning system (VKRS), extending computational systems like databases and logic programs. VKRSs are characterized by the presence of two kinds of negation, that respectively model default-implicit falsity and constructive-explicit falsity. Rather than developing yet another KRS, the author identifies some minimal requirements any VKRS must satisfy. The idea of vividness as a design principle for KRSs has originally been proposed by Levesque. Levesque defines vivid knowledge as complete knowledge about entities and relationships of interest in the world, that can be decomposed into atomic knowledge. He identifies existential, universal, disjunctive, and negated sentences as sources of incompleteness, and, consequently, he allows in a vivid knowledge base (VKB) only ground atoms. He requires VKBs to be consistent and complete, satisfying the domain closure axiom, the closed-world assumption and the usual equality axioms. In the book, such a notion of VKB is refined by (i) allowing the universe of discourse to dynamically change (no domain closure axiom), (ii) adding a notion of strong negation \(\sim\) to codify explicit negative information, thus making positive and negative statements perfectly symmetric, (iii) restricting the closed-world assumption to predicates which are totally represented in the knowledge base, and (iv) tolerating inconsistency. Accordingly, a VKRS has to satisfy the properties of restricted reflexivity, constructivity, and non-explosiveness. The first property restricts reflexivity to consistent formulas. The second property constrains the inference relation to satisfy the conditions of constructible truth (a disjunction can only by true if one of its disjuncts is) and constructible falsity (a conjunction can only be false if one of its conjuncts is). The first condition …
Mathematics Subject Classification ID: 68T35
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T30
Mathematics Subject Classification ID: 68-02
zbMATH DE Number: 514413
zbMATH Keywords: vivid logic
zbMATH Keywords: `vivid' knowledge representation and reasoning system
zbMATH Keywords: restricted reflexivity
zbMATH Keywords: constructivity
zbMATH Keywords: non-explosiveness
zbMATH Keywords: knowledge- based systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/3-540-57604-5
OpenAlex ID: W4231068940
description: scientific article; zbMATH DE number 514413