Table Of ContentOutstanding Contributions to Logic 1
Robert Trypuz Editor
Krister Segerberg
on Logic of Actions
Outstanding Contributions to Logic
Volume 1
Editor-in-Chief
Sven Ove Hansson, Royal Institute of Technology
Editorial board
Marcus Kracht, Universität Bielefeld
Lawrence Moss, Indiana University
Sonja Smets, Universiteit van Amsterdam
Heinrich Wansing, Ruhr-Universität Bochum
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Robert Trypuz
Editor
Krister Segerberg on
Logic of Actions
123
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RobertTrypuz
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ISSN 2211-2758 ISSN 2211-2766 (electronic)
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Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Part I
Krister Segerberg’s Philosophy of Action. . . . . . . . . . . . . . . . . . . . . . 3
Richmond H. Thomason
The Concept of a Routine in Segerberg’s Philosophy of Action. . . . . . 25
Dag Elgesem
On the Reconciliation of Logics of Agency and Logics
of Event Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Jan Broersen
Three Traditions in the Logic of Action: Bringing Them Together . . . 61
Andreas Herzig, Tiago de Lima, Emiliano Lorini and Nicolas Troquard
Deontic Logics Based on Boolean Algebra . . . . . . . . . . . . . . . . . . . . . 85
Pablo F. Castro and Piotr Kulicki
Dynamic Deontic Logic, Segerberg-Style . . . . . . . . . . . . . . . . . . . . . . 119
John-Jules Ch. Meyer
Part II
Contraction, Revision, Expansion: Representing Belief
Change Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Sven Ove Hansson
Segerberg on the Paradoxes of Introspective Belief Change . . . . . . . . 153
Sebastian Enqvist and Erik J. Olsson
v
vi Contents
Equivalent Beliefs in Dynamic Doxastic Logic . . . . . . . . . . . . . . . . . . 179
Robert Goldblatt
On Revocable and Irrevocable Belief Revision . . . . . . . . . . . . . . . . . . 209
Hans van Ditmarsch
Actions, Belief Update, and DDL. . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Jérôme Lang
DDL as an ‘‘Internalization’’ of Dynamic Belief Revision . . . . . . . . . . 253
Alexandru Baltag, Virginie Fiutek and Sonja Smets
Two Logical Faces of Belief Revision. . . . . . . . . . . . . . . . . . . . . . . . . 281
Johan van Benthem
Appendix A: Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Appendix B: Some Metaphilosophical Remarks . . . . . . . . . . . . . . . . . 319
Appendix C: Bibliography of Krister Segerberg. . . . . . . . . . . . . . . . . 323
Introduction
Theconceptsofactionandagencybelongtothecategoryofthoseconceptswhich
arenoteasytodealwith.Avastamountofliterature onthe philosophyofaction,
thelogicofactionandagencyandbroadlyunderstoodAIprovesthesewordstobe
true.Thedifficultyoneencounterswhenanalysingtheconceptsinquestionliesin
their complex nature manifestedby their strong relationship with mentalattitudes
(such as beliefs, desires and intentions), practical reasoning (consisting of delib-
eration, means-end reasoning and decision process), plans and routines, will,
agent’s abilities, time (a well-known problem of temporal extension of actions),
responsibility and causality binding mental attitudes with bodily motions and
action’sresults.ThusstartingfromAristotle,throughAnselmofCanterburytothe
newopeninginthephilosophyofactioninitiatedbyElizabethAnscombe,wecan
countmanywaysofexplaininganddefiningwhatactionandagencyare(almostas
many as there are philosophers who have been writing about them). It also has to
be emphasised that many issues concerning the notions of action and agency
studied previouslyinphilosophy,inparticularthosebeinginthescope ofinterest
of philosophical logic, have recently found their creative continuation (in some
cases got even their second life) in computer science, especially in AI, planning
and knowledge representation. Situation Calculus, Dynamic Logic, a family of
BDIlogicsortheinsightgivenbygametheory:Alternating-timeTemporalLogic
andCoalitionLogicarejustafewexamplesofartefactscreatedtosolveproblems
in computer science. Notwithstanding the fact that the aforementioned theories
havebeendevelopedinthescopeofcomputerscience,itisobvioustodaythatthey
point out problems relevant also to philosophy (frame problem being just one of
many examples).
While talking about actions, it is useful from the very beginning to distinguish
between real actions and doxastic (or epistemic) actions. Real actions are actions
having some manifestation in the environment external to the agent. We may
metaphorically call such actions ‘‘tangible’’. Doxastic or epistemic actions are
actions changing agents’ beliefs and knowledge about the environment as well as
about other beliefs. We may also call the actions in question ‘‘intangible’’, since
they do not have physical presence in the environment.
Krister Segerberg is a philosopher who for more than 30 years has been ana-
lysing intricacies of real and doxastic actions by means offormal tools—mostly
modal (dynamic)logic anditssemantics.He hashadsuch asignificant impact on
vii
viii Introduction
modallogicthat‘‘ItishardtoroamforlonginmodallogicwithoutfindingKrister
Segerberg’s traces’’, as Johan van Benthem noted in [Van-Benthem-Ch, p. 18].
Krister Segerberg himself admits in [24]: ‘‘I am a supporter offormal methods in
philosophy.ThisisnottosaythatIbelievethatallphilosophymustbemadewith
theirhelp.[...]Myownviewisthatformalmethodsareimportantforsomeparts
of philosophy and indispensable for a few.’’
KristerSegerbergwasalwaysopentoinsightsandproblemscomingbothfrom
philosophy and computer science. Working on the border between the fields, he
built many logical systems and conceptual frameworks, which resolved many
issues in the theory of action and agency, contributing both to philosophy and
computer science. A characteristic feature of his works is their outstanding
philosophical depth connected with perfect logical skills.
For the sake of presentation, the volume is divided into two parts. In the first
part there are papers devoted to the real actions. In this part there are also papers
takingintoaccounttheworksofKristerSegerbergondeonticlogicwhichhebuilt
uponatheoryofrealactions.Thesecondpartofthevolumecontainsthepaperson
the doxastic actions. Remaining part of this introduction briefly sketches the
content of the two parts. It is also intended to be a sort of roadmap to Krister
Segerberg’s works on actions and an incentive for many, in particular young,
researcherstocontinuefurtherexploration.InfactitwasKristerSegerberg’swish
toinvite youngresearcherstocontribute tothisvolume.Thusmanychapters, and
thisintroductionaswell,havebeenwrittenbyyoungauthorsorareco-authoredby
young researchers. Richmond Thomason’s chapter in the first part of the volume
and Sven Ove Hansson’s chapter in the second part of it can be seen as a much
more mature and experienced continuation of this introduction.
Real Actions
Variety ofapproaches towards actionscan bedivided intotwomain streams. The
first stream prefers to refer to actions directly and to study them as events of
certain kind. In the second stream actions are out of the picture—instead of
referring to actions, one studies how the states of affairs (or events) are brought
aboutbyagents,orhowtheagentsareresponsibleforthestatesofaffairs.Itshould
bealsomentionedthatquiterecentlytherehavebeenattemptstocombinethetwo
approaches together by creating formal languages enabling at the same time to
refer to actions and express agent’s responsibility.
Actions as events. In the first approach towards actions actions are events.
‘‘There is no action without a corresponding event’’—writes Krister Segerberg in
[71, p. 303]. In most of the works on the philosophy of action, ‘‘action’’ is syn-
onymouswith‘‘intentionalaction’’,meaninganactiondonewithintention[4,45]
ordoneforareason[13,6],whichissupposedtodifferentiateitfromunintentional
behaviour or reflex. Some philosophers researching actions, e.g., Donald David-
son,claimedthatactionsareeventsandindeed‘‘nothingisaddedtotheeventitself
Introduction ix
that makes it into an action’’ [14]. What distinguishes events which are actions
from those which are not, is the fact that the former are caused by some pro-
attitudes.However,asDavidsonputs it,‘‘thisisan addition tothedescription we
giveoftheevent,nottotheeventitself’’[14].Thereforeitisclearthatdespitethe
fact that mental attitudes are necessary for the presence of an action, they are not
‘‘part’’ofit.TheotherpointofviewisrepresentedforinstancebyJohnSearle.In
[46]hestatedthat‘‘thewholeactionconsistsoftwocomponents—theintention-in-
action and the bodily movement’’. In case of a premeditated action, an action is
additionally preceded by practical reasoning.
Similar definition of action we find in [57, p. 161], where Krister Segerberg
states ‘‘To understand action both are needed, agent and world, intention and
change’’. The concept of change for Krister Segerberg, much like for George
Henrik von Wright [99], is a transition between two states: prior and posterior
ones. Theory of change, developed in von Wright’s theory offacts, was formally
clarifiedandcomparedtoclassificationofverbs1byKristerSegerbergin[64,65].
According to Krister Segerberg, intention is directed towards change (an event)
[54,57].Theintentionwhichtriggersanactionmustbeoperational,i.e.,thereisa
routine[58]whichanagentcanrundirectlyinordertofulfilhisintention.‘‘Todo
something is to run a routine. To be able to do something is to have a routine
available. To deliberate is to search for a routine.’’ [58, p. 188]. The process of
searching for a routine Krister Segerberg calls ‘‘deliberation walk’’, which is in
practice aprocessofspecificationofthestartingintentioninordertofindtheone
whichisoperational.Bydeliberationwalkanagentendsupwiththeintentionset
consisting of the intentions linked or ordered in specific way, the last one being
operational. In order to find out with which intention an action was carried out,
Krister Segerberg introduces the infimum property which states that the last
intention in the set is the one with which the agent’s action is carried out. In [50]
he states that an action triggered on the basis of operational intention cannot
usually guaranteeinwhich posterior stateanagent willend up.Krister Segerberg
seestheroleofintentionasafunctionwhichrestrictsallpossibleoutcomesofthe
action to those which are intended. That concept of intention as a function was a
source of inspiration for the authors of chapter [Herzig-Ch].
Theideaofactionsaseventsfound itsformalrepresentationinmanyworksof
Krister Segerberg.2 In [50, 51, 54, 55, 57] one can find non-dynamic logics of
action.Thepapers[50,54,57]containaninterestingstudyoftheconceptofaction
andintention,whereanactionisinterpretedasanintention-outcomepair.Moreon
this subject one can find in chapter [Elgasem-Ch] of this volume, in Sect. 4,
Segerberg’s formal characterisation of intentional actions.
Another logic with actions, where action complement was interestingly ana-
lysed (by referring to the interior operation in topology), has been introduced in
1 Cf.[96].
2 Please see [63, 80, 88] for the outline of the logic of action and agency from Krister
Segerberg’sperspective.
x Introduction
[55].In[34,p.1203]wefindastudyofsuchoperatorsas:‘‘aisabouttodoe’’,‘‘a
has just finished doing e’’, ‘‘because of a’s action, e is just about to be realized’’
and ‘‘because of a’s action, e has just been realized’’.
OtherformalsystemsofKristerSegerbergrefertopropositionaldynamiclogic
(PDL) created by Vaughan R. Pratt for describing and analysing computer pro-
grams (cf. [42, 43]). PDL was brought to the philosophical ground by Krister
Segerberg. In 1980 he wrote about PDL: ‘‘This paper is perhaps the first one to
present it to a philosophical audience’’ [49, p. 276].
Richmond Thomason describes Krister Segerberg’s approach in chapter
[Thomason-Ch, p.2] in the following words:
KristerSegerberg’sapproachtoactiondiffersfromcontemporaryworkinthephilosophy
of action in seeking to begin with logical foundations. And it differs from much con-
temporaryworkinphilosophicallogicbydrawingondynamiclogicasasourceofideas.
Thecomputationalturnmakesalotofsense,foratleasttworeasons.First,aswenoted,
traditional philosophical logic doesn’t seem to provide tools that are well adapted to
modelling action. Theoretical computer science represents a relatively recent branch of
logic,inspiredbyanewapplicationarea,andwecanlooktoitforinnovationsthatmaybe
of philosophical value. Second, computer programs are instructions, and so are directed
towardsaction;ratherthanbeingtrueorfalse,acomputerprogramisexecuted.Alogical
theoryofprogramscouldwellservetoprovideconceptualrigouraswellasnewinsights
tothephilosophyofaction.
Krister Segerberg also provided an intuitive and extensive way of under-
standingprogramesasactionsbyreferringtotheconceptofroutine[58].Wehave
already quoted his motto, ‘‘To do something is to run a routine. To be able to do
somethingistohavearoutineavailable.Todeliberateistosearchforaroutine’’
[58, p. 188]. Extensive and critical study of the Krister Segerberg’s concept of
routineispresentedinchapter[Elgasem-Ch]ofthisvolumebyDagElgasem.The
chapterintroducescentralelementsofKristerSegerberg’saccountofroutinesand
relatesittootherpositionsinthephilosophyofaction.Itisarguedthattheconcept
of a routine has an important role to play in the theory of action and that Krister
Segerberg’s own formalisation of the concept of intentional action does not meet
the theoretical challenges posed by the routine concept. It is pointed out that to
meetthechallengesitisenoughtobringtheconceptofaroutineexplicitlyintothe
semantic framework of the logic of intentions and actions.
Krister Segerberg introduced manyinteresting dynamic operators and provided
adequate(i.e.,soundandcomplete)axiomatisationforPDL(cf.[47,53]3andmany
otherinterestingformalresultsin[48,52]).Languageofdynamiclogicwithoper-
ators‘‘after’’and‘‘during’’isdefinedinBackus-Naurnotationasfollows[49,52]:
u::¼p j:uju^uj½a(cid:2)uj½½a(cid:2)(cid:2)u ð1Þ
i
a::¼a ja(cid:3) jataja;a ð2Þ
i
3 DecidabilityofPDLwasprovedin[18].ThehistoryofearlyresultsinPDLcanbefoundin
[20].
