Towards Epistemic Planning Agents

Manfred Eppe

and Frank Dylla

Department of Computer Science and Mathematics, University of Bremen, Bremen, Germany

Cognitive Systems, SFB/TR8 Spatial Cognition, University of Bremen, Bremen, Germany

Keywords:

Planning, Epistemic Reasoning, Action Theory, Event Calculus.

Abstract:

We propose an approach for single-agent epistemic planning in domains with incomplete knowledge. We argue

that on the one hand the integration of epistemic reasoning into planning is useful because it makes the use of

sensors more ﬂexible. On the other hand, deﬁning an epistemic problem description is an error prone task as

the epistemic effects of actions are more complex than their usual physical effects. We apply the axioms of

the Discrete Event Calculus Knowledge Theory (DECKT) as rules to compile simple non-epistemic planning

problem descriptions into complex epistemic descriptions. We show how the resulting planning problems are

solved by our implemented prototype which is based on Answer Set Programming (ASP).

1 INTRODUCTION

Many approaches to AI planning rely on the strong

and unrealistic assumption that complete knowledge

about the world is available. These planning sys-

tems which consider incomplete knowledge usually

don’t consider conditional action effects and infor-

mation acquired by sensing is always used directly.

We point out that if epistemic reasoning (ER) (Black-

burn et al., 2001) is integrated in planning, then sens-

ing provides extra information. Our ﬁrst hypothesis

is: A planning system which accounts for both epis-

temic reasoning and actions with conditional effects

can be used to compensate for missing or broken sen-

sors and to work around expensive sensing actions

using cheaper sensing actions. For example, if one

wants to ﬁnd out whether a liquid is poisonous it is

costly to learn about its poisonousness by drinking

the liquid. Instead, conditional effects of actions can

be exploited to achieve indirect sensing. Assume a

robot with the (sub-)goal to know whether a door is

open or not. If equipped with an appropriate sensor

it will sense the door state and the goal is achieved.

If it does not feature this speciﬁc door sensor or if

the sensor is broken it can still acquire the informa-

tion indirectly, e.g. through a location sensor it might

be equipped with: It tries to drive through the door,

senses its location and infers the door’s open-state via

the location. If it is behind the door then the door

is open and if it is still in front of the door, then the

door is closed. In the following, we use the term epis-

temic planning (EP) when we speak about a single

Epistemic translator

Execution

monitor

PLIK problem

representation

Epistemic EC representation

f2lp

gringo

claspD

Stable models /

Conditional plan

Figure 1: The toolchain of our planning system.

agent which is aware of having incomplete knowledge

about the world, which can sense and which integrates

epistemic reasoning in the planning process. A prob-

lem in EP is that deriving epistemic representations

of planning problems can be cumbersome when done

manually (see Section 4.) Our second hypothesis is:

The automated translation of non-epistemic planning

problem domains into epistemic ones simpliﬁes the

formal description of planning problems. We also ar-

gue that automated translation also guarantees sound-

ness wrt. epistemic theory, and we make the claim that

currently there exists no planning system which au-

tomatically generates epistemic planning domain de-

scriptions and which considers actions with condi-

tional effects. Our main result is the Planning Lan-

guage for Incomplete Knowledge (PLIK) and a tool

which performs the automated translation of PLIK

planning problem descriptions into an epistemic di-

alect of the Event Calculus (EC) (Kowalski, 1986)

using the Discrete Event Calculus Knowledge The-

ory (DECKT) (Patkos and Plexousakis, 2009) (Figure

1). The epistemic problem description is input of the

f2lp-tool by Lee and Palla (2012) which translates the

problem description into an answer set programming

(ASP) problem. We interpret the solutions of the ASP

311

Eppe M. and Dylla F..

Towards Epistemic Planning Agents.

DOI: 10.5220/0004260603110317

In Proceedings of the 5th International Conference on Agents and Artiﬁcial Intelligence (ICAART-2013), pages 311-317

ISBN: 978-989-8565-39-6

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

problem as conditional plans. For details which we

omit in this paper due to space restrictions we refer to

(Eppe and Dylla, 2012).

2 RELATED WORK

The Model Based Planning (MBP) system by Bertoli

et al. (2001) is closely related to our work, as it im-

plicitly accounts for the knowledge-level effects of

actions. That means, one can specify conditional ef-

fects of actions in its input language NPDDL (Bertoli

et al., 2002) and the planner handles their epistemic

effects. However, the authors do not prove that

their underlying action theory is epistemically sound.

The PKS planner by Petrick and Bacchus (2004) is

the only system we know which explicitly regards

for knowledge-level effects of actions. Nevertheless,

knowledge-level effects must be handled manually

and demand a complex problem speciﬁcation.

Planners demand for action theories which de-

scribe properties of the world and how they change.

Prominent examples are the Situation Calculus (SC)

(Reiter, 2001), Event Calculus (EC) (Kowalski, 1986)

and Fluent Calculus (FC) (Thielscher, 1998). Action

theories involving epistemic reasoning are introduced

by (Moore, 1985), who describes the possible-worlds

semantics of knowledge using Kripke structures and

an epistemic K-ﬂuent. (Scherl and Levesque, 2003)

continue this work and solve the frame problem for

epistemic SC. IndiGolog (De Giacomo and Levesque,

1998) and FLUX (Thielscher, 2005) are high-level

programming languages based on SC and FC. In both

languages it is possible to express epistemic effects of

actions but these effects have to be implemented man-

ually and their epistemic accuracy is not guaranteed.

Our work is based on the Event Calculus (EC)

by (Kowalski, 1986) and the Discrete Event Cal-

culus Knowledge Theory (DECKT) by (Patkos and

Plexousakis, 2009). The theory uses the predicate

HoldsAt ( f , t) to state that a ﬂuent f holds at time

t. Happens (e, t) denotes that the event e happens at

t. Initiates (e, f , t) and Terminates(e, f , t) deﬁne ef-

fects of events.

We use ∆ to denote conjunctions of

Happens-statements and γ to denote conjunctions of

HoldsAt-statements. An effect axiom has the form

γ ⇒ π(e, f , t) where π ∈ {Initiates, Terminates}. A

precondition axiom has the form Happens (e, t) ⇒ γ,

Throughout this text, all variables are universally quan-

tiﬁed if not stated otherwise. Variables for events/actions

are denoted by e, for ﬂuents by f , for literals by l and for

time by t. Reiﬁed ﬂuent formulae φ do not contain quanti-

ﬁers or predicates. Second order expressions do not occur.

saying that an event can only happen if condition γ

holds.

Planning in EC is abductive reasoning. (Shanahan,

2000) describes EC planning as follows: Consider Γ

to be the initial world state, Γ

the goal state and Σ a

set of action speciﬁcations. One is interested in ﬁnd-

ing a plan ∆ such that:

CIRC[Σ; Initiates, Terminates, Releases]∧

CIRC[∆; Happens] ∧ Γ ∧ Ω ∧ EC |= Γ

(1)

where CIRC denotes circumscription (Mueller, 2005)

and Ω denotes uniqueness of names axioms.

Patkos and Plexousakis (2009) developed

DECKT, an epistemic theory for EC. They show

that the theory is sound and complete wrt. T

system (Blackburn et al., 2001) of the possible

world semantics.They introduce an epistemic

Knows-ﬂuent using nested reiﬁcation. For example,

HoldsAt (Knows(¬ f ), t) means that at time t the

agent knows that f is false. Knows-ﬂuents are

released from inertia at all times in DECKT. DECKT

also uses a ﬂuent KP(f) which states that f is known

persistently, i.e. KP-ﬂuents are not released from

inertia. DECKT states, that everything which is

KP-known is also Knows-known:

HoldsAt (KP(φ), t) ⇒ HoldsAt (Knows(φ), t) (2)

Reiﬁcation allows for expressing so-called Hidden

Causal Dependencies (HCD). HCDs are implications

like HoldsAt (KP( f ⇒ f

), t), expressing that it is

known that if f is true then f

is also true. DECKT’s

axiom (3) states that a ﬂuent can only be known if it

is KP-known or if it is known through an implication.

HoldsAt (Knows(φ), t) ⇒ HoldsAt (KP(φ), t) ∨ (3)



HoldsAt



KP(φ

), t



∧ HoldsAt



KP(φ

⇒ φ), t



3 EPISTEMIC PLANNING

A problem speciﬁcation consists of a set of types T ,

a set of objects O, a set of ﬂuents F , a set of action

speciﬁcations A, a set of goals G and a set of state-

ments about the agent’s initial knowledge I which

may be incomplete. T , O, F , A, G and I are ﬁnite

and may be empty.

Types are sorts in an EC domain description. A

PLIK type speciﬁcation is e.g.:

(: t yp es Do or Ro o m Ro b ot )

For more details concerning precondition axioms we

refer to (Mueller, 2005).

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312

Objects are elements of a certain sort:

(: ob j e c t s c orr ido r , li v i n g R o o m - R o om

d1 - Doo r wc , v c - Rob ot )

where the “-” is to be read as “element-of”.

Fluents have a set of arguments of a certain type. An

example for the ﬂuent speciﬁcation in PLIK is:

(: fl u e n t s

ha sD o o r ( Room , D o or ) in R o o m ( Robot , R o om )

op e n e d ( Doo r ) i s R o b u s t ( Ro bo t ) )

There may exist a sensing action for a ﬂuent f . There-

fore we deﬁne two deterministic events for each ﬂu-

ent, senseT(f) and senseF(f).

Initiates(senseT ( f ), KP( f ), t)

Terminates(senseT ( f ), KP(¬ f ), t)

Initiates(senseF( f ), KP(¬ f ), t)

Terminates(senseF( f ), KP( f ), t)

(4)

Goals are speciﬁed as follows:

(: g oa l ( and ( or [3] i n R o om ( wc , l i v i n g R o om ) )

( or [ 4 ] ! i nR o o m ( vc , l i v i n g Ro om ) ) ) )

where the numbers in square brackets represents the

time limit until the literal must be known to hold. Its

general form is conjunctive normal form (CNF):

( an d ( o r [t

. . . [t

) . . .

( or [t

. . . [t

) )

It translates to epistemic EC as follows:

i=1

j=1

HoldsAt



Knows(l

), t



(5)

Initial Knowledge is provided as follows:

(: i ni t i n R oo m ( wc , c o r r i d o r ) i nR oo m ( vc , co rr id or )

is Ro bu st ( vc ) h as Do or ( co rri d or , d1 )

ha sD o o r ( l iv in g Ro o m , d1 ) )

It is a set I of literals which are known to hold at time

0. They translate to epistemic EC as:

∈I

HoldsAt (KP(l

), 0) (6)

EC does not use negation-as-failure, so we also have

to explicitly state what the agent does not know:

∈I

l 6= l

⇒ ¬HoldsAt (KP(l), 0) (7)

where the l

are these literals the agent knows.

Action Speciﬁcations. We illustrate the translation

of action speciﬁcations with the following example:

(: ac t io n m o v e R o o m T o R o o m

: p a r a m e te rs (? ro b o - R o bo t ? d o or - Doo r ? f r om

? to - Ro o m )

: p r e c on d i t i o n ( a nd

in R o o m (? robo ,? fr o m ) ! i n R o om (? robo , ? to )

ha sD o o r ( ? from , ? d o or ) h a sD oo r (? to , ? d o or )

( or i s R o b u s t (? rob o ) o pe n ed (? do o r ) ) )

: e ff e c t

( if ( an d o pe n e d (? do o r ) i n R oo m (? robo , ? f ro m ) )

the n ( an d i n R oo m ( ? robo , ? to )

! i nR o o m (? robo , ? f r om ) ) ) )

It describes the conditional effect that if a robot exe-

cutes this action it will end up in the target room if the

door to the room is open. The precondition states that

the agent will only consider this action if it knows that

the door is open or that the robot is robust (so crash-

ing against a closed door does not cause harm). It

consists of a parameters section, a precondition spec-

iﬁcation and a conjunction of conditional effects. The

parameters are variables (denoted with the preceding

?) and quantiﬁed over the scope of their sort. An ac-

tion’s precondition is given in CNF:

( an d ( o r l

. . . l

) . . . ( o r l

. . . l

) )

Let e be the action’s name, then we have in EEC:

Happens(e, t) ⇒

i=1

j=1

HoldsAt



Knows(l

), t



(8)

This states, that an event can only happen if its pre-

conditions are known to hold. In terms of planning, it

means that the planner will only consider actions in a

plan when it knows that their preconditions hold.

A conditional effect of an action has the form:

( if ( an d l

. . . l

) th e n ( a n d l

. . . l

) )

It can be represented as a pair (E, C) where C =

, . . . , l

} is a set of condition literals and E =

, . . . , l

} is a set of effect literals. Even though

we consider epistemic planning, the physical non-

epistemic effects of actions are still valid. Thus, we

have to add one non-epistemic effect axiom for each

∈ E to our theory:

∈C

HoldsAt (l

, t) ⇒ π(e, f

, t)

(9)

where l

∈ C are the condition literals, f

are

the ﬂuents of the literals l

∈ E and π ∈

{Initiates, Terminates}.

DECKT states that if all condition literals of a condi-

tional effect are known to hold, then its effect literals

are also known to hold. For every effect literal l

in a

TowardsEpistemicPlanningAgents

313

conditional effect of an action we add:

i=1

HoldsAt (Knows(l

), t)

⇒ Initiates(e, KP(l

), t) (10)

Knowledge about an effect ﬂuent is lost if a) at least

one of the conditions is unknown and if b) there is no

condition which is known not to hold and if c) the new

truth value of the effect ﬂuent is not already known.

Thus, for every l

∈ E we add the effect axiom:

∈C

¬HoldsAt (Knows(l

), t)

∧

∈C

¬HoldsAt (Knows(¬l

), t)

∧

¬HoldsAt (Knows(l

), t)

⇒ Terminates(e, KP(l

), t)

(11)

DECKT deﬁnes how knowledge about the effect of an

action is obtained through knowledge about its con-

dition. This is useful, e.g. if for some reason sensing

a door’s open-state is not possible in certain rooms.

In this case one can send the robot through the door,

sense its open-state after the execution and retroac-

tively infer the robot’s location.

At the current state we only account for the case

where one condition is unknown. If knowledge about

the unknown condition is acquired later and the con-

dition is revealed to hold, then knowledge about the

effect is revealed indirectly.

Thus, for every effect literal l

∈ E and for every

potentially unknown condition literal l

∈ C we have

the following clause:





∈C\{l

}

HoldsAt (Knows(l

), t)





∧

¬HoldsAt (Knows(¬l

), t)∧

¬HoldsAt (Knows(l

), t)

⇒ Initiates (e, KP(l

⇒ l

), t)

(12)

The event initiates an implication, stating that if l

true then l

must also be true.

In order to acquire knowledge about a condition

through an effect, the effect of an action must be

known not to hold at the action’s execution time, and

there must be no condition which is known not to

hold. If the effect later becomes known to hold, then

all conditions of the actions must also hold. Thus,

for each condition literal l

∈ C and each effect literal

∈ E, we add the following clause to our theory:

¬HoldsAt (Knows(l

), t)∧

¬HoldsAt (¬Knows(l

), t)∧

¬HoldsAt (Knows(l

), t)

⇒ Initiates (e, KP(l

⇒ l

), t)

(13)

where e is the action’s name.

DECKT uses the predicate KmAffect to express

that an event may affect a ﬂuent. The predicate holds

for each effect l

∈ E of a conditional effect (C, E) of

an event e if there is no condition which is not known

not to hold:

Happens(e, t) ∧

∈C

¬HoldsAt (Knows(¬l

), t)

⇒ KmAffect(e, f

, t)

(14)

where f

is the ﬂuent in the literal l

An implication is terminated if one of the involved

ﬂuents may be affected.

HoldsAt



KP(l ⇒ l

), t



∧

KmAffect(e, f , t) ∨KmAffect(e, f

, t)

⇒ Terminates



e, KP(l ⇒ l

), t



(15)

There are four more axioms we do not explicitly men-

tion in this paper for brevity reasons. One states that

Knows-ﬂuents are always released from inertia. The

epistemic truthness axiom says that everything which

is known to hold does indeed hold. Another axiom

determines how knowledge which is gained through

an implication becomes persistent if the implication

is terminated and the last axiom handles transitivity

of implications which sometimes must be made ex-

plicit. We point the interested reader to (Patkos and

Plexousakis, 2009) and refer to these two axioms as

−

Observations are a key element of epistemic theories.

They provide the agent’s basis for knowledge acqui-

sition. In PLIK we use the keyword :observation to

describe sensing effects. For example:

(: ac t io n s e n se In R o o m

: p a r a m e te rs (? ro b o - R o bo t ? r o om - Ro o mf )

: o b s e rv at i o n ( and in Ro om (? r o b o , ? ro o m ) ) )

This action does not have a precondition or a physical

effect and is thus a pure sensing action.The observa-

tions are provided as a conjunction (and f

. . . f

|O|

For each observed f

we add the event axiom:

Happens(e(v), t) ⇒ (16)

Happens(senseT ( f

), t) ∨ Happens(senseF( f

), t)

with f

∈ v. Intuitively, if a sensing action happens,

then either positive or negative sensing will happen.

Solving Epistemic Planning Problems. Given a

planning problem description in PLIK, we generate

an EEC representation as follows:

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314

1. Objects, types and ﬂuents are declared.

2. For each ﬂuent we declare and specify senseT and

senseF events Σ

as described in (4).

3. Initial knowledge Γ is speciﬁed as described in

(6), (7); goals Γ

are speciﬁed as described in (5).

4. Action speciﬁcations Σ are generated through (8),

(9), (10), (11), (12), (13), (14) and (16).

The pair (∆, Γ

∗

) is a possible solution to the planning

problem with incomplete knowledge if the following

holds:

CIRC[Σ ∧ Σ

;Initiates, Terminates, Releases] ∧ (17)

CIRC[∆; Happens] ∧ Γ ∧ Γ

∗

∧ Ω ∧ EC ∧DECKT |= Γ

where DECKT = (2) ∧ (3) ∧ (15) ∧ (D

−

) represents

the domain-independent DECKT axioms which are

not generated by our translation. Γ

∗

can be inter-

preted as a possible world in which the plan ∆ is a

solution to the planning problem, i.e. Γ

∗

is a conjunc-

tion of HoldsAt statements which can be seen as a

condition under which ∆ solves the planning prob-

lem. Figure 2 shows how Γ

∗

and ∆ are included in

the stable models generated by the ASP tools. The

complete solution of the planning problem is the set

of all n pairs (∆

, Γ

∗

) for which the entailment (17)

holds. This solution can be interpreted as a condi-

tional plan with the conditions represented by Γ

∗

and

the actions to be executed under a certain condition by

∆

. The execution of this plan then demands for an ex-

ecution monitor which compares the possible worlds

∗

with the agent’s knowledge about the world. At ex-

ecution time, the agent non-deterministically chooses

a plan ∆

and follows it as long as the condition Γ

∗

is not inconsistent with the agent’s knowledge about

the world. If Γ

∗

becomes inconsistent due to sensing

actions, then the agent has to choose another branch

(∆

, Γ

∗

) with a Γ

∗

that is consistent with the agent’s

knowledge about the world. If no such Γ

∗

exists, then

the problem is unsolvable.

Implementation Issues. Lee and Palla (2012) pro-

pose to use Answer Set Programming to solve EC

reasoning problems and show that their approach out-

performs existing solutions like the DECreasoner by

(Mueller, 2005). We make use of their f2lp tool to

translate the EEC planning problem description into

an ASP representation of the problem. We use the

tool gringo (Gebser et al., 2011) to generate the Her-

brand Models of the problem and claspD (Drescher

et al., 2008) as the ASP solver. Unfortunately, not

the f2lp-tool we use nor any other reasoner we know

about supports reiﬁcation. Therefore, we had to sac-

riﬁce completeness of our planner and deﬁne special

predicates which translate as follows:

Knows( f , t) := HoldsAt (Knows( f ), t)

KnowsNot( f , t) := HoldsAt (Knows(¬ f ), t)

KP( f , t) := HoldsAt (KP( f ), t)

KPNot( f , t) := HoldsAt (KP(¬ f ), t) (18)

ImpliesTT( f , f

, t) := HoldsAt



KP( f ⇒ f

), t



ImpliesTF( f , f

, t) := HoldsAt



KP( f ⇒ ¬ f

), t



ImpliesFT( f , f

, t) := HoldsAt



KP(¬ f ⇒ f

), t



ImpliesFF( f , f

, t) := HoldsAt



KP(¬ f ⇒ ¬ f

), t



We deﬁne the persistence laws for the KP and Implies

predicates equivalently to the persistence laws for the

HoldsAt predicate in the DEC axiomatization and use

special Initiates and Terminates predicates for each of

the KP and Implies which follow the very same ax-

ioms as the original DEC Initiates and Terminates do.

Contraposition and transitivity rules for the implica-

tion predicates is also implemented manually. Using

these special predicates and the additional persistence

and effect axioms for each predicate, our approach is

sound. This is easy to see as none of our translation

rules generates an implication which involves more

than two ﬂuents. However, it is not complete as we do

not include HCD expansion as described in (Patkos,

2010), and we do not consider retroactive knowledge

gain about effects if more than one condition is un-

known.

4 EVALUATION

Reduction of the Planning Problem Speciﬁcation.

Looking at the translation of PLIK to non-epistemic

EC, we ﬁnd that through (9), for each conditional ef-

fect (C, E), |E| effect axioms of the form γ ⇒ π(e, f , t)

are generated; one for each effect literal l ∈ E. Look-

ing at the translation into the epistemic EC, we ﬁnd

that many additional epistemic effect axioms are gen-

erated: (10) generates |E| effect axioms, (11) gen-

erates another |E| axioms and (12), (13) generate

|E| · |C| axioms each. Thus, each conditional effect

(C, E) of an action speciﬁcation demands specifying

|E| non-epistemic effect axioms and |E| · (2 · |C|+ 2)

epistemic effect axioms.

For example, consider extending the above

moveRoomToRoom action by adding only two more con-

ditions (robot’s battery must be full and robot must

not be blocked) to the effect:

: e ff e c t ( if ( an d

op e n e d (? d oo r ) b at t e r y F ul l (? r ob o )

! b lo ck ed (? rob o ) i nR o o m (? robo , ? f r om ) )

the n ( an d i n R oo m ( ? robo , ? to )

! i nR o o m (? robo , ? f r om ) ) ) )

TowardsEpistemicPlanningAgents

315

Then, the epistemic EC version of the action is more

than 100 lines (11 000 bytes) of axioms which would

be very circumstantial to implement manually.

Use case: Move-through-door. We implemented a

use case with several robots moving through rooms

and one central planning agent controlling the robots.

Some robots are equipped with bumpers, so it is safe

to send them through a door without knowing whether

the door is open. The planning agent can only send a

robot through doors if it knows that the door is open

or that the robot has a bumper.

We investigated the stable models which are gen-

erated by the reasoner and it turned out that the

knowledge-level effects of actions are correctly han-

deled. Figure 2 shows how implications (I), plan (∆),

assumptions about the world (Γ

∗

), direct knowledge

gain (K

) as well as indirect knowledge gain (K

)

are successfully generated and modeled. The output

is that of a simple scenario with two robots, wc and

vc, where vc is robust and wc is not. The generated

plan involves sending the robust vc through a door at

t = 0, sensing its location at t = 1 and then, knowing

that the door must be open at t = 2, safely sending wc

through the door.

Figure 2: The output of the reasoner for the move-through-

door example with two robots (vc,wc).

Use Case: Poisonous Liquid. We adopted the poi-

sonous liquid-example from (Petrick and Bacchus,

2004). A thirsty agent has a liquid and does not know

whether it is poisonous. He can perform a drink-

action. If he drinks the liquid he will not be thirsty

anymore but he will get poisoned if the liquid is poi-

sonous. The agent can also pour the liquid on the

lawn, and if the liquid is poisonous the lawn will be

dead. Finally the agent can sense whether the lawn is

See the corresponding move-action in section 3.

alive. In the initial state, the agent only knows that he

is thirsty and not poisoned. The goal is that the agent

always knows that he is not poisoned and knows that

in the end he is not thirsty. The result is exactly 1 sta-

ble model, because there is only one possible world

in which the goal can be achieved: This is the world

where the liquid is not poisonous. The plan considers

that the agent ﬁrst pours the liquid on the lawn, then

senses whether the lawn is dead, and ﬁnally, if the

lawn is not dead, drinks the liquid. For details con-

cerning the implementation of this use case we refer

the reader to (Eppe and Dylla, 2012).

5 CONCLUSIONS

In this paper we provide a method for the formaliza-

tion of epistemic planning problems. The main con-

tribution of our approach lies in the automated trans-

lation of planning problem speciﬁcations demanding

complete knowledge about the world into planning

problems which allow for incomplete knowledge. We

show that this translation safes a problem designer

the work of specifying additional |E| · (2 · |C| + 2)

knowledge-level effect axioms.To the best of our

knowledge there is currently no other planning system

which takes ordinary planning domains as input and

automatically compiles them into epistemic planning

domains, such that epistemic effects of actions can be

exploited to compensate missing or broken sensors.

Our approach is sound but not complete wrt.

DECKT and the possible worlds semantics of knowl-

edge. To achieve completeness we have to introduce

actions with non-deterministic effects, e.g. like toss-

ing a coin. Another issue that we need to consider

is knowledge acquisition about effects if more than

one condition is unknown. This goes along with what

(Patkos, 2010) calls HCD-expansion. However, this is

hardly possible without true reiﬁcation and we don’t

know of any reasoner which supports this.

ACKNOWLEDGEMENTS

We thank Theodore Patkos who was always happy to

help us with details concerning DECKT and related

work. Funding by the German Research Associa-

tion (DFG) under the grants of International Research

Training Group on Semantic Integration of Geospa-

tial Information (IRTG SIGI) and SFB/TR8 Spatial

Cognition is gratefully acknowledged.

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