BSISO18629-13:2006 INTERNATIONAL ISO STANDARD 18629-13 Firstedition 2006-08-15 Industrial automation systems andintegrationProcess specification language Part 13: Duration and ordering theories Systemes d'automatisation industrielleet integration-Langagede specificationdeprocedé- Partie13:Theories de classement et de duree Referencenumber IS018629-13:2006(E) ISO @IS02006 BSIS018629-13:2006 IS018629-13:2006(E) COPYRIGHTPROTECTEDDOCUMENT IS0 2006,Published in Switzerland All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying,or posting on the internet or an intranet, without prior writtenpermission.PermissioncanberequestedfromeitherIsoattheaddressbeloworIso'smemberbodyinthecountryof therequester. ISO copyrightoffice Ch.deBlandonnet8.CP401 CH-1214Vernier,Geneva, Switzerland Tel.+41227490111 Fax+4122749 0947 [email protected] www.iso.org i iS02006-Allrightsreserved BSIS018629-13:2006 IS018629-13:2006 Contents Page Foreword v Introduction. .vi 1 Scope. .1 2 Normativereferences .1 3 Terms,definitions,andabbreviations .1 3.1 Terms and definitions. .1 3.2 Abbreviations.. .5 4 GeneralinformationonIs018629 .5 5 OrganizationofthispartofIs018629 6 6 Subactivityoccurrence ordering coreTheory 6 6.1 PrimitiveRelationsof the Subactivityoccurrenceorderingtheory 6 6.2 DefinedRelationsoftheSubactivityoccurrenceorderingtheory 6 6.3 Relationshiptoother sets ofaxioms 6 6.4 InformalSemanticsoftheSubactivityoccurrenceorderingtheory .7 6.4.1 Soo .7 6.4.2 soo_precedes 7 6.4.3 soomap 7 6.5 Definitions in the Subactivity occurrence ordering theory 7 6.5.1 Definition1 (related toroot_soo) 7 6.5.2 Definition 2 (related to leaf_soo) 7 6.5.3 Definition 3 (related to next_soo) 8 6.6 AxiomsoftheSubactivityoccurrenceorderingtheory 8 6.6.1 Axiom1 8 6.6.2 Axiom 2 .8 6.6.3 Axiom 3 8 6.6.4 Axiom4 8 6.6.5 Axiom5 .8 6.6.6 Axiom6 8 6.6.7 Axiom 7. .9 6.6.8 Axiom 8. 9 7 Durationtheory 9 7.1 PrimitiverelationsintheDurationtheory 9 7.2 PrimitiveFunctionsand Constants. 9 7.3 Defined Relations of the Duration theory 9 7.4 Relationshiptoother setsofaxioms 9 7.5 Informal SemanticsoftheDurationtheory 10 7.5.1 timeduration. 10 7.5.2 lesser. 10 7.5.3 duration 10 7.5.4 time_add. 10 7.5.5 add. 10 7.5.6 mult 11 7.5.7 zero. 11 7.5.8 one. 11 7.5.9 max+ 11 7.5.10 max- 11 7.6 Definitions of Duration theory 11 7.6.1 Definition1 11 7.7 AxiomsfortheDuration theory 11 7.7.1 Axiom1 11 7.7.2 Axiom 2 12 7.7.3 Axiom3 12 IS02006-All rightsreserved ili BSIS018629-13:2006 IS018629-13:2006 7.7.4 Axiom4 .12 7.7.5 Axiom5 12 7.7.6 Axiom6 12 7.7.7 Axiom7 .12 7.7.8 Axiom 8. .12 7.7.9 Axiom 9 .12 7.7.10 Axiom 10. .13 7.7.11 Axiom 11. .13 7.7.12 Axiom12. 13 7.7.13 Axiom 13. 13 7.7.14 Axiom 14. .13 7.7.15 Axiom15 13 7.7.16 Axiom 16. .13 7.7.17 Axiom17 13 7.7.18 Axiom18 ..14 7.7.19 Axiom19 14 7.7.20 Axiom20 .14 7.7.21 Axiom 21 14 7.7.22 Axiom22 .14 8 Occurrencetreeautomorphisms. .14 8.1 PrimitiveRelationsintheOccurrencetreeautomorphismtheory .15 8.2 Defined Relations in the Occurrencetree automorphismtheory .15 8.3 Relationshiptoothersets ofaxioms. .15 8.4 Informal semanticsoftheOccurrencetreeautomorphismtheory 15 8.4.1 ubiquitous. .15 8.4.2 end_iso .15 8.4.3 legal_map ..16 8.4.4 tree_map. .16 8.5 DefinitionsintheOccurrencetreeautomorphismtheory .16 8.5.1 Definition1 .16 8.5.2 Definition 2 16 8.5.3 Definition3 .16 8.6 AxiomsfortheOccurrencetreeautomorphismtheory .17 8.6.1 Axiom 1 .17 8.6.2 Axiom 2 .17 8.6.3 Axiom 3 .17 9 Activityenvelopetheory .17 9.1 PrimitiveRelations in the Activity envelopetheory 17 9.2 Defined relation in Activity envelope theory ..18 9.3 Relationshiptoother sets of axioms .18 9.4 Informal semantics of theActivityenvelope theory .18 9.4.1 envelope .18 9.4.2 umbra .18 9.5 Definitionsinactivityenveloptheory .18 9.6 AxiomsoftheActivityenvelopetheory 18 9.6.1 Axiom1 19 9.6.2 Axiom 2 .19 9.6.3 Axiom 3. .19 9.6.4 Axiom 4. .19 9.6.5 Axiom5 19 9.6.6 Axiom