Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency: School/Workshop, Noordwijkerhout, The Netherlands May 30 – June 3, 1988

721 Pages·1989·14.203 MB·English

by  Johan van Benthem (auth.), J. W. de Bakker, W. -P. de Roever, G. Rozenberg (eds.)

Lecture Notes ni
Computer Science
Edited yb .G Goos and .J Hartmanis
354
II I
J.W. de Bakker W.-R de Roever
G. Rozenberg ).sdE(
Linear Time, Branching Time
and Partial Order ni Logics
dna Models rof Concurrency
School/Workshop, Noordwijkerhout, ehT sdnalrehteN
yaM 30- June ,3 8891
I II I
Springer-Verlag
nilreB Heidelberg London NewYork Paris oykoT
Editorial Board
D. Barstow W. Brauer .P Brinch Hansen D. Gries D. Luckham
C. Moler A. Pnueli G. Seegm~ller .J Stoer N. Wirth
Editors
.1. .W de Bakker
Centre for Mathematics and Computer Science
Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
W.-P. de Roever
Departmento f Computing Science
Eindhoven University of Technology
P.O. Box 513, 5600 MB Eindhoven, The Netherlands
G. Rozenberg
Institute of Applied Mathematics and Computer Science
University of Leiden
P.O. Box 9512, 2300 RA Leiden, The Netherlands
CR Subject Classification (1987): B.1, C.1-2, D.4, El, F.3-4
ISBN 3-540-51080-X Springer-Verlag Berlin HeidelbergN ew York
ISBN 0-387-51080-X Springer-Verlag New York Berlin Heidelberg
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ECAFERP
Modelling the behaviour of concurrent dna distributed systems sah nworg
into eno of the most challenging dna vigorous research areas within
theoretical computer science. ehT last edaced sah seen the ecnegreme of three
independent sehcaorppa to this problem, emos of them capturing differences
neewteb systems that others ignore. ehT first eno sledom a system yb
describing its execution runs, the dnoces eno yb analysing the execution
trees, dna the third eno sledom a system yb describing the (in)dependencies
dna choices neewteb the various events that yam occur. Paradigmatic for these
sehcaorppa era semantic sniamod with linear or branching elements, linear time
dna branching time temporal logic, dna net theory. Although it smees that the
erom features a captures system the better, if eno wants emos erusaem of
abstractness dna parsimony, emos of such features yam eb too detailed for a
given level of description.
This reviews volume these intrinsically different sehcaorppa dna
evaluates their relative .segatnavda It is desab no the pohskroW/loohcS" nO
Linear Time, Branching Time dna Partial Order in Logics dna Models for
Concurrency" organized yb the editors dna held in the period yaM 03 - June 3,
8891 at Noordwijkerhout, ehT Netherlands. ehT pohskroW/loohcS saw na activity
of the project XER - hcraeseR dna Education in Concurrent smetsyS sponsored yb
the Netherlands IFN (Nationale Faciliteit Informatica) .emmargorP ehT meeting
saw organized under auspices of the SCTAE dna saw furthermore supported yb the
Centre for Mathematics dna retupmoC Science, the University of Leiden, dna the
nevohdniE University of Technology.
ehT material presented in this volume sah been prepared yb the lecturers
(and their coauthors) after the meeting took place - in this yaw the srepap
reflect also the vivid discussions that took place during the meeting. eW era
proud that ew dah such na excellent group of lecturers dna such na eager dna
enthusiastic group of participants. eW era very grateful to both groups for
gnikam the meeting both scientifically interesting dna socially very pleasant,
dna to the margorP eettimmoC consisting of .M ,yssenneH E.-R. Olderog,
.A Pnueli, J. Sifakis, dna P.S. Thiagarajan for their help in preparing the
scientific margorp of the meeting.
eW gratefully egdelwonkca the financial support from the Netherlands
National Facility for Informatics (NFI).
ehT Centre for Mathematics dna retupmoC Science saw responsible for the
~echnical organization of the meeting. ehT University of Leiden dna the
nevohdniE University of cooperated have Technology in the organization no a
rebmun of vital points. sA directors of the pohskroW/loohcS ew want to extend
our special thanks to .sM Loes ,rekamesraaK-lemsaV .sM Marja Hegt, dna
.rM Frans Snijders for organizational assistance dnoyeb the call of duty.
VI
eW epoh that in the future tnempoleved of the theory of concurrent
smetsys this emulov yam help in bringing at least partial order into the
gnihcnarb structure that this tnempoleved undoubtedly will .evah
January, 9891 ehT Editors,
.W.J ed rekkaB
.P.W ed reveoR
.G grebnezoR
EHT XER TCEJORP
ehT XER - hcraeseR dna Education in Concurrent Systems-project
investigates syntactic, semantic dna proof-theoretic aspects of concurrency.
In addition, its objectives era the education of gnuoy researchers ,dna in
general, the dissemination of scientific results relating to these .semeht
XER is a collaborative effort of the Leiden University oG( ,)grebnezoR
the Centre for scitamehtaM dna retupmoC Science in madretsmA (J.W. ed Bakker),
dna the nevohdniE University of ygolonhceT .P.W( ed Roever), representing the
areas syntax, semantics dna proof theory, respectively. ehT project is
detroppus yb the Netherlands National Facility for Informatics (NFI); its
detcepxe duration is four years starting 'in 1988. In the years ,8891-4891 the
emas groups together dekrow in the Netherlands National ycnerrucnoC Project
,)CPL( supported yb the Netherlands noitadnuoF for the tnemecnavdA of eruP
hcraeseR .)OWZ(
ehT research activities of the XER project will include, erom
specifically,
(i) Three subprojects devoted to the :semeht
- syntax of concurrent :smetsys a graph oriented krowemarf for
structures dna sessecorp
- process theory dna the semantics of parallel logic gnimmargorp
segaugnal
high-level specification dna refinement of real-time distributed
.smetsys
(ii) Collaboration with visiting professors dna post-doctoral researchers, in
particular focused no the research semeht denoitnem .evoba In 9891/8891
these visitors include dr. E.-R. Olderog (Kiel), prof. P.S. Thiagarajan
(Madras), dr. .S hsemaR (Indian Institute of Technology).
(iii) spohskroW dna Schools. ehT pohskroW/loohcS no Linear Time, gnihcnarB
emiT dna Partial Ordeirn Logics dna sledoM for ycnerrucnoC saw the
first in a series of hcus events. roF ,9891 ew plan a pohskrow no
"Stepwise tnemenifeR of Distributed :smetsyS Models, ,smsilamroF
Correctness". In ,0991 ew shall organize a meeting no "Actor ,smetsys
object-oriented segaugnal dna massive parallelism" (tentative title).
ehT educational activities of XER include regular "concurrency days". A
ycnerrucnoc yad yam consist of tutorial introductions to selected topics, dna
of presentations of research results to a non-specialist audience. Often,
experts from daorba era invited to contribute to these days. In addition,
visiting professors era deksa to present lecture series concerning recent
stnempoleved in their fields of specialization. Clearly, the spohskroW/loohcS
lV
evah sa well na important educational function, providing their participants
with na intensive introduction to wen areas.
Finally, ew mention another aspect of the XER project. eW shall continue
the regular contacts with other naeporuE projects in eht area of Ycnerrucnoc
built pu during the CPL years. In particular, this applies to the hcnerF
3 -Cooperation, C ,noitacinummoC -ycnerrucnoC program, to the British retupmoC
Society - lamroF Aspects of retupmoC Science group, dna to groups within the
Gesellschaft fQr kitamehtaM dnu Datenverarbeitung )DMG( in .nnoB
sA denoitnem already, XER continues the CPL cooperation. emoS highlights
of the CPL years are:
(i) the organization of the CPL/TIRPSE decnavdA loohcS no Current sdnerT in
ycnerrucnoC (1985, proceedings deraeppa sa Lecture Notes in retupmoC
Science, Vol. 224, Springer, ;)6891
(ii) Ph.D. research no the topics vector synchronized ,smetsys dataflow
,scitnames dna real-time temporal logic;
(iii) fruitful interaction with TIRPSE projects 514 (Parallel Architectures
dna segaugnaL for AIP: a VLSI-directed )hcaorppa dna 739 (Descartes,
gniggubeD dna Specification of ADA Real-Time deddebmE Systems). CPL
contributed to the local organization of TIRPSE 514 conference ELRAP -
Parallel Architectures dna segaugnaL eporuE (1987, sgnideecorP deraeppa
sa Lecture Notes in retupmoC Vol. Science 258, 259, Springer);
(iv) eht setting-up of the international segnahcxe referred to .evoba
eW would like to conclude this brief presentation of the future (past) of
the XER )CPL( project yb inviting everyone ohw is interested in erom
information concerning XER (possibility of visits, plans for ,spohskrow other
forms of ,segnahcxe etc.) to write to eno of the project leaders.
.W.J ed rekkaB
.P.W ed reveoR
.G grebnezoR
STNETNOC
ECAFERP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
EHT XER TCEJORP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII
SLAIROTUT
J. van Benthem
Time, logic and computation . . . . . . . . . . . . . . . . . . . . . . . . 1
J.A. Bergstra, J.W. Klop
Process theory based no bisimulation semantics . . . . . . . . . . . . . . . 05
E.A. ,nosremE J. Srinivasan
Branching time temporal logic . . . . . . . . . . . . . . . . . . . . . . . 321
.M yssenneH
371
Observing processes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.Z ,annaM .A Pnueli
102
ehT anchored version of the temporal framework . . . . . . . . . . . . . . .
.A Mazurkiewicz
582
Basic notions of trace theory . . . . . . . . . . . . . . . . . . . . . . .
.G Winskel
463
nA introduction to event structures . . . . . . . . . . . . . . . . . . . .
LACINHCET SNOITUBIRTNOC
.A Bouajjani, .S Graf, J. Sifakis
A logic for the description of behaviours dna properties of
concurrent systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893
.G Boudol, I. Castellani
Permutation of transitions: nA event structure semantics for
SCC dna SCCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
.M.E Clarke, I.A. Draghicescu
Expressibility results for linear-time dna branching-time logics ...... 824
VIII
.P ,onageD .R eD Nicola, .U Montanari
Partial orderings descriptions dna observations of nondeterministic
834
concurrent processes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.H namfiaG
Modeling concurrency yb partial orders dna nonlinear transition
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764
.S Katz, .D Peled
nA efficient verification dohtem for parallel dna distributed
984
smargorp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.K Lodaya, .R ,majunamaR P.S. Thiagarajan
A logic for distributed transition systems . . . . . . . . . . . . . . . . . 805
.M Nielsen, .U Engberg, K.S. Larsen
Fully abstract models for a process language with refinement . . . . . . . . 325
E.-R. Olderog
Strong bisimilarity no nets: a wen concept for comparing net
semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945
.A Rabinovich, B.A. Trakhtenbrot
Nets of processes dna data flow . . . . . . . . . . . . . . . . . . . . . . 475
.W Reisig
sdrawoT a temporal logic of causality dna choice in distributed
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
.M.MoJ.J Rutten
Correctness dna full abstraction of metric semantics for concurrency .... 826
.C Stirling
laropmeT logics for SCC . . . . . . . . . . . . . . . . . . . . . . . . . . 066
.W.M Shields
Behavioural Presentations . . . . . . . . . . . . . . . . . . . . . . . . . 376
.W samohT
noitatupmoC tree logic dna regular w-languages . . . . . . . . . . . . . . . 096
TIME, LOGIC AND COMPUTATION
Johan van Benthem
Faculty of Mathematics and Computer Science
University of Amsterdam
Roetersstraat 15, 1018 WB Amsterdam, Holland
ABSTRACT. This paper startsw ith a survey of temporal logic in its original guise, pointing at its
connections with philosophy and linguistics. More specifically, a technical exposition is provided of the
basic 'tense-logical' system, baseodn points or 'moments' of time, with the research program in model
theory and proof theory which has grown around it. After that, a more recent stream of 'period' and 'event'
based approaches to time is discussed, again with some of the new logical themes engendered by it. Finally,
a review isg iven of some recent computational research in temporal logic. Here, a clear continuity of logical
concerns emerges between philosophy, linguistics and computer science. But, the latter adds severnaelw
themes and perspectives which might well give it a significant impact on the earlier standard enterprise.
Keywords. Completeness, computational semantics, correspondence, event structure, first-order
definability, period structure, point structure, temporal operator, tense logic.
CONTENTS
1 Introduction
2 Points
2.1 Basic Framework
2.2 Axiomatics
2.3 Model Theory
2.4 Further Developments
3 Periods and Events
3,1 Basic Period Ontology
3.2 Temporal Logic
3.3 Relating Points and Periods
3.4 Extending to Events
4 Perspectives from Computer Science
4.1 Application with Innovation
4.2 Semantic Parallels
4.3 Reinterpreting Logic
1. Introduction
The formal properties of Time have attracted the attention of philosophers and mathematicians ever
since Antiquity (cf. the anthology Smart 1964). Moreover, abstract temporal structure finds its reflection in
our linguistic habits of temporal reasoning, and hence logicians have entered this field too, creating a
discipline of 'temporal logic' (Reichenbach 1947, Prior 1957, Prior 1967). But in fact, time is a
phenomenon cutting across many academic boundaries: from physics (cf. Reichenbach 1957) to
psychology (cf. Michon & Jackson 1985). [A reference spanning virtually this whole spectrum is Whitrow
1980.] Within this wider area, temporal logic finds itself in particularly close contact with philosophy,
linguistics (cf. Dowty 1979) and increasingly also with computer science. For, these disciplines share an
interest in creating exact systems of temporal representation, coming with calculfio r reasoning about change
or persistence over time.
The purpose of this paper is twofold. On the one hand, a discursive survey will be given of temporal
logic as it has developed in this century - while on the other, there is a review of recent contacts with
computer science; whose variety, after a mere decade of research, is already impressive. No complete
coverage has been attempted, however, in either respect. For furtherd etails on temporal logic, there is an
array of informative texts, such as Gabbay 1976, van Benthem 1983, Burgess 1984 and Goldblatt 1987a.
Moreover, the present volume itself may be viewed as an anthology of computational research into temporal
logic. Therefore, we shall feel free to choose our own path through the area, with an emphasis on general
research lines, and an occasional new question or observation.
2. Points
2.1 Basic Framework
2.1.1 An instructive, and much-studied 'minimal' system of temporal logic was developed by Arthur
Prior in the fifties and sixties. This so-called 'tense logic' has propositional operators P forpast and F for
future. The original motivation for concentrating on these was two-sided. Philosophically, these are the
basic operators which assign changing temporal 'perspective' to events. I.e., they express the dynamic 'A-
series' of McTaggart 1908, who contrasted this with the static 'B-series' of an immutable order of events.
In Prior's system, B-series models provide the semantics for A-series languages, as we shall see, But also,
linguistically, the operators P, F correspond to the most basic 'tenses' of natural language:
q : Mary cries (present)
Pq : Mary cried (past)
Fq : Mary will cry (future).
Further iterations then reflect compound tenses:
PPq : Mary had cried (pastp erfect)
FPq : Mary will have cried (future perfect),
etcetera. The analogy is by nom eans without its problems: but it has had undeniable heuristic virtues.