Nonmonotonic logic and temporal projection
type: Item
instance of: scholarly article
title: Nonmonotonic logic and temporal projection
zbMATH Open document ID: 0654.68107
DOI: 10.1016/0004-3702(87)90043-9
author: Steve Hanks
author: Drew McDermott
published in: Artificial Intelligence
publication date: 1987-01-01T00:00:00Z
review text: The reviewed article is a revised version of the paper that won the AI Journal Best Paper Award at AAAI-86. It addresses the following ``temporal projection problem'' (p. 385\({}^{17-20}):\) ``[...] given an initial description of the world [...], the occurrence of some events, and some notion of causality [...], what facts are true once all the events have occurred?'' The authors investigate an instance of this problem. They express the notions involved in the problem using a three-sorted, first-order language with constants, unary function `result', and two predicate symbols: binary t and ternary ab. The constants denote `events', `descriptors' of the world, and `situations' (instances of the world). Function \(result:\quad events\times situations\to situations\) denotes the effect of occurrence of an event. Predicate t (truth) denotes the satisfaction relation between `descriptors' and `situations'. Predicate ab (abnormality) characterizes all triples \(<descriptor\), event, \(situation>\) for which `event' applied to `situation' causes `descriptor' ``to stop being true'' (p. 387 4) in the resulting situation. For example, result(LOAD,s) denotes the situation immediately after occurrence of event LOAD in situation s, t(LOADED,s) is true for exactly those s's which are LOADED, and ab(ALIVE,\(SHOOT,s)\) is true for exactly those s's which are ALIVE and whose \(result(SHOOT,s)\) are not. The authors provide arguments for their thesis that the following axiomatization (p. 387) (1) \(t(ALIVE,S_ 0)\) (2) \(\forall s.t(LOADED\), result(LOADED,s)) (3) \(\forall s.t(LOADED,s)\supset ab(ALIVE,SHOOT,s)\wedge t(DEAD\), result(SHOOT,s)) (4) \(\forall f\), e, s.t(f,s\(\wedge \neg ab(f,e,s)\supset t(f\), result(e,s)) does not entail all intuitively true properties of the situation \[ S_ 3=result(SHOOT,\quad result(WAIT,\quad result(LOAD,S_ 0)))\quad, \] under assumption of minimality of (the semantics of) ab. E.g., they claim (p. 390\({}^{12,13})\) that in a certain minimal mod…
Mathematics Subject Classification ID: 68T99
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 4068337
zbMATH Keywords: default reasoning
zbMATH Keywords: minimal model semantics
zbMATH Keywords: non-monotonic logics
zbMATH Keywords: predicate circumscription
zbMATH Keywords: default logic
zbMATH Keywords: partial correctness problem
Wikidata QID: Q29997854
MaRDI profile type: Publication
full work available at URL: 0004-3702(87)90043-9
OpenAlex ID: W2036900631
cites work: The mathematics of non-monotonic reasoning
cites work: Formalizing nonmonotonic reasoning systems
cites work: Q5750390
cites work: Circumscription - a form of non-monotonic reasoning
cites work: Q5633670
cites work: Nonmonotonic Logic II
cites work: Non-monotonic logic. I
cites work: Completeness results for circumscription
cites work: A logic for default reasoning
description: scientific article; zbMATH DE number 4068337