THE TEMPORAL LOGIC OF TWO DIMENSIONAL MINKOWSKI SPACETIME IS DECIDABLE.
We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, x can access y if an electromagnetic or (slower than light) mechanical signal could be sent from x to y. We use Prior's tense language of F and P representing causal accessi...
| Published in: | Journal of Symbolic Logic Vol. 83; no. 3; pp. 829 - 868 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Published: |
Cambridge University Press
Sep2018
|
| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=132546291&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 132546291 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Sep2018 vid: 83 iid: 3 pid: 15979 pub: Cambridge University Press artinfo: ui: 132546291 10.1017/jsl.2017.79 ppf: 829 ppct: 39 formats: tig: atl: THE TEMPORAL LOGIC OF TWO DIMENSIONAL MINKOWSKI SPACETIME IS DECIDABLE. aug: au: HIRSCH, ROBIN REYNOLDS, MARK affil: DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY COLLEGE LONDON LONDON, UK SCHOOL OF COMPUTER SCIENCE AND SOFTWARE ENGINEERING THE UNIVERSITY OF WESTERN AUSTRALIA PERTH, AUSTRALIA su: Minkowski space Minkowski geometry Electromagnetism Decidability (Mathematical logic) Real numbers sug: subj: Minkowski space Minkowski geometry Electromagnetism Decidability (Mathematical logic) Real numbers keyword: 03B44 83A05 decidability interval logic Minkowski spacetime temporal logic ab: We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, x can access y if an electromagnetic or (slower than light) mechanical signal could be sent from x to y. We use Prior's tense language of F and P representing causal accessibility and its converse relation. We consider two versions, one where the accessibility relation is reflexive and one where it is irreflexive. In either case it has been an open problem, for decades, whether the logic is decidable or axiomatisable. We make a small step forward by proving, in each case, that the set of valid formulas over two-dimensional Minkowski spacetime is decidable and that the complexity of each problem is PSPACE-complete. A consequence is that the temporal logic of intervals with real endpoints under either the containment relation or the strict containment relation is PSPACE-complete, the same is true if the interval accessibility relation is "each endpoint is not earlier", or its irreflexive restriction. We provide a temporal formula that distinguishes between three-dimensional and two-dimensional Minkowski spacetime and another temporal formula that distinguishes the two-dimensional case where the underlying field is the real numbers from the case where instead we use the rational numbers. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2018 holdings: @attributes: islocal: N |
|---|