Exploiting lattices in a theory of space and time
Computers & Mathematics with ApplicationsPublished 1 March 1992
David Randell, Anthony G. Cohn
Citations48
SJR quartileQ1
SJR score0.95
SNIP1.31
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
An axiomatic theory expressed in a first order predicate logic formalism that modifies and extends Bowman Clarke's calculus of individuals and various classification hierarchies are singled out and expressed as lattice structures.
Abstract
We outline an axiomatic theory expressed in a first order predicate logic formalism. The theory modifies and extends Bowman Clarke's calculus of individuals. The theory is primarily concerned with a topological description of space and time. From this theory various classification hierarchies are singled out and expressed as lattice structures. The nodes of these lattices correspond to concepts expressed in the theory as monadic predicates, but also concepts expressed using higher arity predicates. We concentrate upon that part of the theory that is used to describe space. The logical structure and interrelationship of these different lattice structures are discussed. Some attention is given to how, by singling out such structures, the theory may be effectively implemented within a resolution-based automated reasoning setting.
Keywords
Computer Science
Communications of the ACMMaintaining knowledge about temporal intervals
7,550 Citations1983James F. Allen
An interval-based temporal logic is introduced, together with a computationally effective reasoning algorithm based on constraint propagation, which is notable in offering a delicate balance between space and time.
Artificial IntelligenceTowards a general theory of action and time
2,562 Citations1984James F. Allen
A formalism for reasoning about actions that is based on a temporal logic allows a much wider range of actions to be described than with previous approaches such as the situation calculus and a framework for planning in a dynamic world with external events and multiple agents is suggested.
Greenwood Publishing Group Inc. eBooksFormal Theories of the Commonsense World
760 Citations1985Jerry R. Hobbs, Robert C. Moore
Journal of Symbolic LogicThe calculus of individuals and its uses
552 Citations1940Henry S. Leonard, Nelson Goodman
An unfortunate dependence of logical formulation upon the discovery and adoption of a special physical theory, or the presumption that such a suitable theory could in every case be discovered in the course of time, indicates serious deficiencies in the ordinary logistic.
Notre Dame Journal of Formal LogicA calculus of individuals based on ``connection''.
394 Citations1981Bowman L. Clarke
Calcul des individus, dans la ligne de la mereologie de Lesniewski et de ses developpements philosophiques chez Whitehead et Goodman, comprend trois parties: une partie mereologique (systematisation des predicats mereologiques), partie quasi booleenne (introduction des operateurs booleens and de l'individu universel).
Journal of Automated ReasoningAutomated deduction by theory resolution
280 Citations1985M.E. Stickel
Theory resolution constitutes a set of complete procedures for incorporating theories into a resolution theorem-proving program, thereby making it unnecessary to resolve directly upon axioms of the theory, and is a generalization of numerous previously known resolution refinements.
International Joint Conference on Artificial IntelligenceA common-sense theory of time
260 Citations1985James F. Allen, Patrick J. Hayes
This paper proposes an axiomatic a theory of time in terms of intervals and the single relation MEET and shows that this axiomatization subsumes Allen's interval-based theory.
ACM Transactions on Programming Languages and SystemsEfficient implementation of lattice operations
199 Citations1989Hassan Aı̈t-Kaci, Robert S. Boyer +2 more
A general technique for the efficient implementation of lattice operations such as greatest lower bound, least upper bound, and relative complementation based on an encoding method, which takes into account idiosyncrasies of the topology of the poset being encoded that are quite likely to occur in practice.
Computational IntelligenceMoments and points in an interval‐based temporal logic
166 Citations1989James F. Allen, Patrick J. Hayes
This paper presents a concise, formal axiomatization of “interval‐based” time as described by Allen and then explores the relationship between interval‐based and point‐based temporal theories in detail.
Modelling topological and metrical properties in physical processes
141 Citations1989David Randell, Anthony G. Cohn
The power of the formalism is illustrated by modelling the process of phagocytosis of theamoeba, together with an outline of how many pro-perties of physical entities and relations can be modelled within a unitary framework.
MIT Press eBooksRecent advances in qualitative physics
136 Citations1993Boi Faltings, Peter Strauß
This paper presents a meta-modelling study of qualitative-numeric simulation with Q3, a compiler from physical models into qualitative differential equations and an architecture for real-time qualitative reasoning about a large system using dimensional analysis.
Journal of Automated ReasoningA more expressive formulation of many sorted logic
112 Citations1987AnthonyG. Cohn
The many sorting logic described here has several unusual features which not only increase expressiveness but also can reduce the search space even more than a conventional many sorted logic.
NatureThe Axiomatic Method in Biology
91 Citations1938J. B. S. Haldane
This book proposes to deduce known biological generalizations, and to discover new ones by pure deduction from as small a number as possible of axioms and undefined terms, and uses a special set of symbols, including many taken from Whitehead and Russell and 125 new ones.
Artificial Intelligence ReviewTaxonomic reasoning with many-sorted logics
58 Citations1989Anthony G. Cohn
This paper provides an introduction to many-sorted logics and motivates their use for representation and reasoning, and discusses some many-Sorted logic programming languages and some implementation issues.
Artificial Intelligence in EngineeringA logical framework for commonsense predictions of solid object behaviour
36 Citations1988Ernest Davis
A first-order logic in which one can state simple physical problems and derive their solution deductively, without recourse to solving differential equations is presented, substantially more expressive and powerful than any previous AI representational system in this domain.
AI MagazineThoughts and afterthoughts on the 1988 Workshop on Principles of Hybrid Reasoning
32 Citations1991Alan M. Frisch, Anthony G. Cohn
The 1988 Workshop on Principles of Hybrid Reasoning, a one-day AAAI-sponsored workshop, was held in St. Paul, Minnesota on August 21, 1988 and some of the afterthoughts based upon prolonged discussion of the issues that arose during the workshop are presented.
Warwick Research Archive Portal (University of Warwick)Analysing the familiar: Reasoning about space and time in the everyday world
14 Citations1992David Randell
This thesis describes a first order axiomatic theory that can be used to encode much topological and metrical information that arises in the authors' everyday dealings with the physical world.
Boston studies in the philosophy of scienceOf Time and the Null Individual
10 Citations1966Richard M. Martin