Planning Speech Acts in a Logic of Action and Change∗
Martin Magnusson and Patrick Doherty
Department of Computer and Information Science
Linköping University, 581 83 Linköping, Sweden{marma,patdo}@ida.liu.se

Abstract
Cooperation is a complex task that necessarily involves
communication and reasoning about others’ intentions andbeliefs. Multi-agent communication languages aid designers of cooperating robots through standardized speech acts,
sometimes including a formal semantics. But a more direct
approach would be to have the robots plan both regular andcommunicative actions themselves. We show how two robots with heterogeneous capabilities can autonomously decide to cooperate when faced with a task that would otherwise be impossible. Request and inform speech acts are formulated in the same first-order logic of action and change as
is used for regular actions. This is made possible by treating
the contents of communicative actions as quoted formulasof the same language. The robot agents then use a natural
deduction theorem prover to generate cooperative plans foran example scenario by reasoning directly with the axiomsof the theory.

1 Introduction
Autonomous agents reason about the world to form plans
and affect the world by executing those plans. Thus, agents’plans have an indirect effect on the world, and it becomes
important for reasoning agents to take other agents’ plans
into account. Furthermore, they would do well to plan actions that affect other agent’s plans and thereby (doubly indirectly) affect the world. Philosophers of linguistics haverealized that we humans do this all the time through communication. In particular, Searle’s speech acts [24] characterize natural language utterances as actions with conditions
upon their execution and effects on the mental states of others.
Perrault, Allen, and Cohen [19] establish a useful connection between speech acts and planning. They formalize
speech acts as planning operators in a multi-modal logic ofbelief and intention. Using these an agent can inform otheragents about some fact, request other agents to perform∗ This work is supported in part by the Swedish Foundation for Strategic
Research (SSF) Strategic Research Center MOVIII, the Swedish ResearchCouncil Linnaeus Center CADICS, and CENIIT, the Center for Industrial
Information Technology.

some action, or ask other agents questions by requestingthem to inform about some fact. They encoded simplified
versions of these actions as STRIPS-like planning operators
and used a backward-chaining algorithm to generate plans
involving both regular actions and speech acts.
Research on software agents [8] has also adopted speechacts. This body of work depends fundamentally on agent
communication languages, which are standardized sets ofspeech acts that ensure interoperability in agent to agent
communication. The two most well known standards,
KQML [5] and FIPA/ACL [6], are both based on speech act
theory. FIPA/ACL also has a logical semantics defined using multi-modal BDI logic. But the semantics is meant only
as a prescriptive guide when implementing software agents.
Some researchers try to obtain, and sometimes even prove,
conformance between the implementation and the semantics, while most programmers are probably not overly concerned with such matters. Moreover, the communication
language is only a wrapper for a content language, which
has to provide its own semantics. There is no integrationof speech acts within a more general framework of action
and change. Instead, these agent communication langauge
technologies remain agnostic as to how to plan speech acts
and other actions to achieve goals.
Morgenstern [16] offers an integrated theory of bothtypes of actions using a syntactic first-order logic that includes quotation. Davis and Morgenstern [2] provide analternative integration using regular first-order logic. The
two theories’ semantics cover both the speech acts and theircontent. However, while the theories were authored withthe aim of applications in multi-agent planning, their use
has so far been mainly of a prescriptive nature, in the implementation of a STRIPS-like planner in the case of theformer theory, and as a specification for future implementations in the case of the latter theory.
In this paper we formalize inform and request speech acts
in first-order logic with quotation. The representation isbased on Temporal Action Logic (TAL), a first-order language with a well developed methodology for representing
time, action, and change. TAL is complemented by syntactic operators that express the modalities of belief and commitment. They take quoted formulas as arguments and allow for the encoding of the effects of speech acts on otheragents’ beliefs and commitments. The resulting formalismcan be used to represent and reason about both speech acts
and their message content, may it be facts, actions, or otherspeech acts. We automate such reasoning through a natural deduction theorem prover that incorporates a form of
abductive planning. The system is applied to a multi-agent
planning problem involving the cooperation between two
robots through planned goal delegation and knowledge acquisition, which is introduced below.

2 Cooperation and Communication
Consider a motivating scenario involving an autonomous
unmanned aerial vehicle named uav1. The robot isequipped with a winch system capable of lifting and dropping supply crates. Suppose it is assigned the task of delivering crate15 to the storage building store23. It would be
unwise (although perhaps spectacular) to have the robot fly
into the building. Instead, UAVs are restricted to operate indesignated fly-zones, and storage buildings are not amongthem.
A class of autonomous unmanned ground vehicles provide services complementary to flying robots. They too can
attach crates, using fork lifts, but stick to driving short distances in and between buildings designated as drive-zones.
One of the UGVs, named ugv3, happens to sit idle in thebuilding store14.
To succeed at its task the UAV will have to request help
from the ground robot to get crate15 into the building,where it can not fly itself. It knows that ground robots
have the capability of delivering crates between locations
in drive-zones, and it might consider delegating its task to
ugv3. But crate15’s current location prevents simply delegating the goal since the crate is far outside any drive-zone
areas where a ground vehicle could fetch it. Instead, uav1
will have to deliver crate15 to a rendezvous point, accessible to both UAVs and UGVs. Only then is it possible torequest ugv3 to see to it that the crate gets to its final destination.
Such a plan is only possible if the two robots manage tocoordinate their actions through communication. We would
like them to figure out the above plan, including both physical actions and communicative speech acts, completely autonomously. This will require a sufficiently expressive representation and reasoning formalism. We present our proposal next.

The origins of TAL are found in Sandewall’s modeltheoretic Features and Fluents framework [23]. Doherty[3] selected important concepts, such as an explicit timeline and the use of occlusion (discussed below), to form
TAL and gave it a proof-theoretic first-order characterization. Many extensions since have turned TAL into a very
expressive language for commonsense reasoning. Doherty
and Kvarnström [4] provide a detailed account of the logic,
but the version presented below includes further extensions
that make TAL suitable for applications in multi-agent planning and reasoning.
In TAL, properties and relations that may change overtime are modeled by fluents. A fluent f is a function of time,and its value at a time point t is denoted (value t f ). When
we talk about a time interval i between two time points t1
and t2 we mean the interval (t1 ,t2 ] that is open on the left
and closed on the right. The functions (start i) and (finish i)picks out t1 and t2 respectively. An agent carrying out anaction a during time interval i is specified by the predicate(Occurs agent i a). But the most important feature of TAL is
probably its occlusion concept. A persistent fluent’s value ispermitted to change when occluded, but must persist during
time intervals when not occluded. The following formula(with free variables implicitly universally quantified and in
prefix form to make the representation of quoted formulas
more convenient) relates a fluent f ’s value at the start andend time points of a time interval i:(→ (¬ (Occlude i f ))(= (value (start i) f ) (value (finish i) f )))(1)

By assuming that fluents are not occluded unless otherwise
specified one is in effect making the frame assumption thatthings usually do not change. Exceptions are specified byaction specifications that explicitly occlude fluents that theaction affects. E.g., if uav1 flies between two locations, its
location fluent (location uav1) would be occluded during
any interval with a non-empty intersection with the movement interval. This prevents any use of Formula 1 for relying on the default persistence of the robot’s location thatconflicts with the robot’s moving about. By exercising finegrained control over occlusion one gains a flexible tool for
dealing with important aspects and generalizations of theframe problem.

3.1

A Syntactic Belief Operator

Previous accounts of TAL lack a representation of agents’mental states and beliefs. Introducing a syntactic belief op3 Temporal Action Logic
erator provides a simple and intuitive notion of beliefs. To
explain this let us first assume that uav1 believes it is at loc1
First-order logic might serve as a solid foundation. But it is at noon. The following formula1 would represent this belief
by itself too noncommittal regarding choices of how to rep- in its knowledge base:resent actions and their effects on time-varying properties of(= (value 12:00 (location uav1)) loc1)(2)
the world. Several alternative logics of action and change
1 Clock times such as 12:00 are not really part of the logic. We assume
are available to aid a logicist researcher. We present worka translation scheme between clock times and integers.
with one such logic, the Temporal Action Logic (TAL).

Similarly, if it was ugv3 that believed that uav1 is at loc1,
Formula 2 would be in its knowledge base. Beliefs aboutothers’ beliefs are then really beliefs about what formulas
are present in others’ knowledge bases. If uav1 believes
that ugv3 believes what Formula 2 expresses, then uav1 believes that ugv3 has Formula 2 in its knowledge base. This
would be represented in the knowledge base of uav1 by thefollowing formula:(Believes ugv3 12:00’(= (value 12:00 (location uav1)) loc1))
The first argument of the Believes predicate is then the agent
holding the belief. The second argument is the time point at
which the agent holds the belief. Finally, the third argument
is a quoted version of the formula expressing the belief, in
this case Formula 2. This is what makes Believes a syntactic
operator.
We use the quotation notation from KIF [7], which isa formal variant of Lisp’s. An expression preceded by aquote is a regular first-order term that serves as a name ofthat expression. Alternatively one may use a backquote, inwhich case sub-expressions can be unquoted by precedingthem with a comma. This facilitates quantifying-in by exposing chosen variables inside a backquoted expression forbinding by quantifiers. E.g., we use quantifying-in to represent uav1’s belief that ugv3 knows its own location, without
uav1 having to know the name for that location:(∃ x (Believes ugv3 12:00‘(= (value 12:00 (location ugv3)) ’,x)))Note that while x ranges over locations2 , it is the name ofa location that should occur as part of the third argumentof Believes. The quote preceding the comma ensures thatwhatever value x is bound to is quoted to produce the nameof that value.
While a quoted formula still looks like a formula, it is infact a term. This means that standard inference rules suchas modus ponens are not applicable to the quoted formulasthat appear as arguments in the Believes operator. There are
two possible solutions to this limitation. Either we could
add axioms that express inference rules for beliefs, or we
could employ a theorem prover with special purpose inference rules for beliefs. We pursue the latter alternative in thetheorem prover described in Section 5, for efficiency reasons. While it should still be possible to characterize these
inference rules in terms of axioms, this is subject to future
work.

3.2

Action Occurrences

An action occurs when it is possible for an agent to execute the action, during some time interval i, and the agent
is committed to the action occurring, at the start of the timeinterval. The predicate (Possible agent i action) represents
2 TAL is an order sorted logic. In our implementation we indicate variable sorts by prefixes, but ignore these here for readability.

physical and knowledge preconditions for an agent carrying out an action during time interval i, while (Committed
agent t p) represents an agent’s commitment at time point t
to satisfy the formula p. Both predicates require a quoted
expression in their third argument position, which precludes
the free use of substitution of equals without regards to theagent’s knowledge. Using these predicates we can formalize the above intuition about action occurrences:(→ (∧ (Possible agent i ‘’,action)(Committed agent (start i)‘(Occurs ’,agent ’,i ’,action)))(Occurs agent i action))
Note the interaction between backquote and quote in‘’, action to make sure that the argument of Possible is thename of the action. The initial backquote turns the following quote into the name of a quote, leaving the variable action free for binding. The resulting expression denotes thequoted version of whatever the variable is bound to rather
than a quoted variable that can not be bound at all.

3.3

Action Specifications

Each one of an agent’s available actions has an action specification that consists of three parts. The first part determines under what conditions an action is possible. It may
include physical preconditions, but also involves knowledge
preconditions on behalf of the agent executing the action.
Consider e.g. a stock market agent that plans to get richby buying “the stock that will increase in value”. Whiletheoretically correct, the plan is of no practical value unlessthe agent knows a name that identifies some particular stockthat it reasonably expects will increase in value. To makethis intuition formal, Moore [14] suggests that an action is
only executable if the agent knows rigid designators for allof the action’s arguments. Morgenstern [15] modifies thissuggestion slightly in her requirement that standard identifiers are known for the action arguments.
Our action specifications follow Morgenstern and use thesyntactic predicate (Identifier x) to single out a name x as astandard identifier. In the stock market example, the actionof buying stock would not be executable unless the agent infact knew the name under which the stock was listed.
The second part of an action specification lists additional
requirements for any agent that decides to execute the action itself. To execute an action the agent must invoke somepiece of computer code implementing it. Since our actions
have an explicit time argument we think of the agent as having an execution schedule to which procedure calls can be
added at specific time points. Executing an action then involves looking up standard identifiers for its arguments andscheduling the procedure call associated with the action.
The effect of deciding to execute an action is that the agent
becomes committed to the action occurrence. An alternative way of ensuring commitment to an action is to delegateits execution to someone else through the use of the request
speech act, as we will see later.
Finally, the third part of an action specification details theeffects of the action on the world and on the mental statesof agents. This allows agents to reason about actions andform plans to achieve goals.

4 Formalization
We are now able to formalize the agent cooperation scenariopresented in Section 2 using TAL. The following unique
names assumptions are needed:(6= l1 l2 )(6= c1 c2 )l1 , l2 ∈ {base, helipad2, store14, store23}
c1 , c2 ∈ {nil, crate15}

The terms in the first set are locations and the second arecrates, where nil denotes a null element of the crate sort.
In addition, quoted expressions are considered equal only
when they are syntactically identical.
The term names in the following set are standard identifiers that can be used as arguments to procedure calls in the
robot’s internal action execution mechanism. We might e.g.
imagine that the procedure for flying to one of the named
locations involves a simple lookup of a GPS coordinate in
an internal map data structure.
(Identifier x)

x ∈ {’uav1, ’ugv3, ’crate15, ’base,’helipad2, ’store14, ’store23}

Operating restrictions on UAVs and UGVs are given by flyand drive-zones:(FlyZone base)(FlyZone helipad2)(DriveZone store14)(DriveZone store23)(DriveZone helipad2)
The above knowledge is common to all agents in our scenario.

4.1

Physical Actions

The bulk of the robots’ knowledge base is made up of theaction specifications. Each of the three specification parts
are given by an implication. Starting with the fly action wenote that it is possible for a UAV to fly to a location in a flyzone if the UAV knows a standard identifier for the location.
Secondly, an agent may commit to flying by scheduling a
fly procedure call. The constant self is a placeholder for theidentifier of the agent in whose KB the formula appears, e.g.
uav1 or ugv3 in our case. This means that, while an agent
can reason about whether it is possible for another agent tofly, it can not schedule a call to the fly procedure in anotheragent’s execution mechanism. Thirdly, at the end of the fly
interval the UAV ends up at its destination.
In addition, modified fluents need to be occluded to overrule their default persistence. Flying should occlude the

UAV’s location fluent in any interval that intersects the flying action since (Occlude i f ) means that f is occluded
somewhere in interval i. This could be expressed as an implication (→ (Intersect i2 i) (Occlude i2 (location uav))).
However, the action specification below uses the contrapositive form of this formula. The reason for this is discussed
further in Section 5.
(→ (∧ (Believes uav (start i) ‘(= ’,to ,x))(Identifier x)(FlyZone to))(Possible uav i ‘(fly ’,to)))(→ (∧ (= to x) (Identifier ‘’,x)(Schedule self i (fly x)))(Committed self (start i) ‘(Occurs self ’,i (fly ’,to))))(→ (Occurs uav i (fly to))(∧ (= (value (finish i) (location uav)) to)(→ (¬ (Occlude i2 (location uav))) (Disjoint i2 i))))
Note that the above might sometimes require the agent toreason about its own beliefs. Suppose, for example, thatuav1 is considering the possibility of flying itself to ugv3’s
location. Its knowledge base might contain the formula (=(value t1 (location ugv3)) helipad2), expressing the belief
that ugv3 is at helipad2. Then uav1 would make the belief
explicit by asserting (Believes uav1 t2 ’(= (value t1 (location ugv3)) helipad2)), where t2 is the current time.
Ground vehicles have a very similar action that allows
them to drive to locations in drive-zones:(→ (∧ (Believes ugv (start i) ‘(= ’,to ,x))(Identifier x)(DriveZone to))(Possible ugv i ‘(drive ’,to)))(→ (∧ (= to x) (Identifier ‘’,x)(Schedule self i (drive x)))(Committed self (start i) ‘(Occurs self ’,i (drive ’,to))))(→ (Occurs ugv i (drive to))(∧ (= (value (finish i) (location ugv)) to)(→ (¬ (Occlude i2 (location ugv))) (Disjoint i2 i))))Both types of agents can carry one crate at a time, and thefluent (carrying agent) indicates which one it is at the moment. To attach a crate the agent must not already be carrying anything, indicated by the value nil, and the agent andcrate must be at the same place. The action effects occlude
the crate’s location (as well as the carrying fluent) since we
can no longer depend on the frame assumption that it willremain in the same place.
(→ (∧ (Believes agent (start i) ‘(= ’,crate ,x))(Identifier x)(= (value (start i) (carrying agent)) nil)(= (value (start i) (location agent))(value (start i) (location crate))))(Possible agent i ‘(attach ’,crate)))(→ (∧ (= crate x) (Identifier ‘’,x)(Schedule self i (attach x)))(Committed self (start i)‘(Occurs self ’,i (attach ’,crate))))(→ (Occurs agent i (attach crate))(∧ (= (value (finish i) (carrying agent)) crate)(→ (¬ (Occlude i2 (location crate)))(Disjoint i2 i))(→ (¬ (Occlude i3 (carrying agent)))(Disjoint i3 i))))Again we follow Allen’s directions and introduce an informRef action designed to facilitate questions of this type.
The informRef action does not mention the value that is unknown to the UAV agent, which instead performs the following request:(request ugv3’(Occurs ugv3 i2 (informRef uav1
(value 12:00 (location ugv3)))))

The above request still contains the unknown time interval
i2, which ugv3 may instantiate in any way it chooses. The
Detaching a crate has the effect that the crate ends up at the
explicit time representation used by TAL opens up the possame location that the agent is currently at:sibility of a general account of the knowledge preconditions(→ (∧ (Believes agent (start i) ‘(= ’,crate ,x))and knowledge effects of action’s start and end time points,(Identifier x)
but formulating it is part of future work.
(= (value (start i) (carrying agent)) crate))
The informRef preconditions require that the informing(Possible agent i ‘(detach ’,crate)))agent knows what the value is, which is being informed
about. The effects assert the existence of a value for which(→ (∧ (= crate x) (Identifier ‘’,x)the speaker knows a standard name.
(Schedule self i (detach x)))
Note that an agent that commits to executing the action(Committed self (start i)schedules an inform procedure call, plugging in the sought‘(Occurs self ’,i (detach ’,crate))))value. In contrast, an agent that only reasons about the ef(→ (Occurs agent i (detach crate))
fects of the informRef action, as in the question example(∧ (= (value (finish i) (carrying agent)) nil)above, knows that the value will become known, but need(= (value (finish i) (location crate))
not yet know its name.
(value (finish i) (location agent)))(→ (¬ (Occlude i2 (location crate)))(→ (∧ (Believes speaker (start i) ‘(= ’,value ,x))
(Disjoint i2 i))(Identifier x)(→ (¬ (Occlude i3 (carrying agent)))(Believes speaker (start i) ‘(= ’,hearer ,y))
(Disjoint i3 i))))(Identifier y))

4.2

Speech Acts

Speech acts can be used to communicate knowledge to,and to incur commitment in, other agents. We reformulate
Allen’s speech acts [1] in TAL using the syntactic belief andcommitment predicates. More complex formulations havebeen suggested in the literature, e.g. to allow indirect speechacts [18]. But our robots will stick to straight answers anddirect requests, without regard for politeness (although see
Section 7 for a discussion of this).
The type of information we will be interested in is knowing what a particular value is. This is straight forwardly
communicated by standard identifiers. E.g., if ugv3 wishes
to inform uav1 that its location is store14 at noon, it mayschedule an action of the following form:(inform uav1’(= (value 12:00 (location ugv3)) store14))(3)

However, this is complicated when uav1 wishes to ask ugv3
what its location is. In accordance with much research inspeech acts, we view questions as requests for information.
The UAV should thus request that the UGV perform theinform action in Formula 3. Though since uav1 does notknow where ugv3 is, which is presumably the reason why
it is asking about it in the first place, it can not know what
action to request.

(Possible speaker i ‘(informRef ’,hearer ’,value)))(→ (∧ (= value x) (Identifier ‘’,x)(= hearer y) (Identifier ‘’,y)(Schedule self i (inform y ‘(= ’,value ’,x))))(Committed self (start i)‘(Occurs self ’,i (informRef ’,hearer ’,value))))(→ (Occurs speaker i (informRef hearer value))(∃ x (∧ (Believes hearer (finish i) ‘(= ’,value ,x))(Identifier x))))Many other formalizations of speech acts restrict requests
to action occurrences. Our formulation of requests supports any well formed formulas, whether they are declarative goals or action occurrences. The effect is that the agent
that is the target of the request is committed to satisfying
the formula.
(→ (∧ (Wff formula)(Believes speaker (start i) ‘(= ’,hearer ,x))(Identifier x))(Possible speaker i ‘(request ’,hearer ’,formula)))(→ (∧ (Wff formula)(= hearer x) (Identifier ‘’,x)(Schedule self i (request x formula)))(Committed self (start i)‘(Occurs self ’,i (request ’,hearer ’,formula))))(→ (Occurs speaker i (request hearer formula))(Committed hearer (finish i) formula))

The Wff predicate determines whether the quoted expression is a well formed formula. While we could write axioms defining it, since quoted expressions are terms in our
language, we find it convenient to view it as defined by semantic attachment.
Finally, to delegate declarative goals an agent must know
something about the capabilities of other agents. In our scenario, UAVs know that ground robots are able to transport
crates between locations in drive-zones. This allows uav1
to delegate its goal task and trust that it will indeed be satisfied.
(→ (∧ (DriveZone (value (start i) (location crate)))(DriveZone to)(Committed ugv (start i)‘(= (value (finish ’,i) (location ’,crate)) ’,to)))(= (value (finish i) (location crate)) to))This concludes our formalization of the robot cooperation
scenario. We turn our attention next towards the question of
how to perform automated reasoning with it.

occlusion, action occurrences, temporal constraints, andpositive or negative holds formulas, depending on the current reasoning task [13]. These are allowed to be assumed rather than proven, as long as they are not counterexplained or inconsistent. As an example, consider thefollowing natural deduction proof fragment, explained below (where the justifications in the right margin denote row
numbers, (P)remises, (H)ypotheses, and additional background (K)nowledge).
1
2
3
4
5
6
7
8
9
10
11

5 Automated Natural Deduction

12

Earlier work with TAL has made use of a model-theoretic
tool for automated reasoning called VITAL [9]. But thistool relies upon the set of actions being pre-specified andconsequently does not support planning. Later work madedeductive planning possible through a compilation of TAL
formulas into Prolog programs [10]. But Prolog’s limited
expressivity makes it inapplicable to interesting planningproblems involving incomplete information and knowledge
producing actions, such as speech acts. Instead, our current work concentrates on an implementation of a theorem
prover based on natural deduction, inspired by similar systems by Rips [22] and Pollock [20].
Natural deduction is an interesting alternative to thewidely used resolution theorem proving technique. A natural deduction prover works with the formulas of an agent’s
knowledge base in their “natural form” directly, rather thancompiling them into clause form. The set of proof rules is
extensible and easily accommodates special purpose rulesthat can make reasoning in specific domains or using a specific formalism like TAL more efficient. We are actively
experimenting with different rule sets so the description below is of a preliminary nature.
Rules are divided into forward and backward rules. Forward rules are applied whenever possible and are designed
to converge on a stable set of conclusions so as not to continue generating new inferences forever. Backward rules,
in contrast, are used to search backwards from the current
proof goal and thus exhibits goal direction. Combined, theresult is a bi-directional search for proofs.
Nonmonotonic reasoning and planning is made possible
in our theorem prover through an assumption-based argumentation system. The set of abducibles consists of negated13(= (value 12:00 (location uav1)) base)P(∧ (= (start i37) 12:00) (= (finish i37) 13:00))
P(¬ (Occlude i37 (location uav1)))H(= (value 13:00 (location uav1)) base)
1-3,K(= helipad2 helipad2)
K(Believes uav1 (start i38) ’(= helipad2 helipad2)) 5(Possible uav1 i38 ’(fly helipad2))
6,K(Schedule uav1 i38 (fly helipad2))
H(Committed uav1 (start i38)’(Occurs uav1 i38 (fly helipad2)))
8,K(Occurs uav1 i38 (fly helipad2))
7,9,K(= (value (finish i38) (location uav1))
helipad2)
10,K(→ (¬ (Occlude i (location uav1)))(Disjoint i i38))
10,K(Disjoint i37 i38)
3,12

The UAV is located at base at noon, as in Row 1. Suppose
it needs to remain at the same location at 1 p.m. One wayof proving this would be by using the persistence formulain Section 3. The location fluent is only persistent if it is
not occluded. While uav1 has no knowledge about whether
it is occluded or not, (¬ Occlude) is abducible and may be(tentatively) assumed. The effect of making non-occlusion
abducible is to implement a default persistence assumption.
Row 2 introduces a fresh interval constant and Row 3 indicates the assumption using a Copi style (described e.g. byPelletier [17]) vertical line in the margin.
Suppose further that uav1 also needs to visit helipad2.
The only way of proving this would be to use the fly action
defined in Section 4. A backward modus ponens rule adopts(Occurs uav1 i38 (fly helipad2)) as a sub goal. Backward
chaining again, on the action occurrence axiom in Section 3,
causes (Possible uav1 i38 ’(fly helipad2)) and (Committed
uav1 (start i38) ’(Occurs uav1 i38 (fly helipad2))) to become new sub goals. These are again specified by the fly
action specification. The first of these sub goals is satisfied
by Row 6 and the fact that helipad2 is both an identifier anda fly-zone. The commitment goal in Row 9 is satisfied by
Row 5, the fact that helipad2 is a viable argument to the fly
procedure, and Row 8, which assumes that uav1 schedules
the procedure call. The implementation of the proof rulethat adds Row 8 performs the actual scheduling by updating
an internal data structure. It is still possible to backtrack, removing the assumption in Row 8, as long as the procedure
call has not yet been executed, i.e. if it is scheduled to occur
at some future time or if execution has not yet reached thispoint. This could happen if something causes the theorem
prover to reconsider flying to helipad2, or if scheduling theflight causes a conflict with some other assumption that wasmade previously. In such cases the procedure call would be
removed from the internal data structure as well.3 Finally,
having proved the robot’s ability and commitment to flying
to helipad2 Row 10 concludes that the flight will occur, withthe effect that uav1 ends up at helipad2 in Row 11.
Flying should occlude the location fluent in any intersecting interval. This would most naturally be expressed by(→ (Intersect i i38) (Occlude i (location uav1))). But, as
noted in Section 4, we use the contrapositive form instead.
The reason is the need for consistency checking when assumptions have been made. It is well known that the problem of determining consistency of a first-order theory is noteven semi-decidable. Our theorem prover uses its forward
rules to implement an incomplete consistency check (moreon this below), and the contrapositive form makes these forward rules applicable. Row 12, which is an effect of the fly
action, together with the assumption in Row 3 trigger theforward modus ponens rule, adding the disjointness constraint in Row 13. This enforces a partial ordering of thetwo intervals to avoid any conflict between the persistenceof the UAV’s location, and its moving about. Another forward inference rule consists of a constraint solver that determines whether the set of temporal constraints is consistent.
If it is impossible to order i37 and i38 so that they do not intersect in any way, then an inconsistency has been detected
and the prover needs to backtrack, perhaps cancelling themost recent assumption or removing the action that was last
added to the schedule.
For some restrictions on the input theory we are able
to guarantee completeness of the nonmonotonic reasoning[13]. But in the general case, when one cannot guarantee
completeness of the consistency checking, we might conceivably fail to discover that one of the assumptions is unreasonable. This would not be a cause of unsoundness,since we are still within the sound system of natural deduction, but it might result in plans and conclusions that rest
on impossible assumptions. A conclusion Φ depending on
an inconsistent assumption would in effect have the logicalform ⊥→ Φ, and thus be tautological and void. This is to
be expected though. Since consistency is not even semidecidable, the most one can hope for is for the agent tocontinually evaluate the consistency of its assumptions, improving the chances of them being correct over time, while
regarding conclusions as tentative. [21].

6 Generated Plans

plans for the robot cooperation scenario. We present theproof goals and the resulting plans below.
Let us initially place the crate and the UAV (carrying
nothing) at base at 12:00:(= (value 12:00 (location crate15)) base)(= (value 12:00 (location uav1)) base)(= (value 12:00 (carrying uav1)) nil)
The goal is to have crate15 delivered to the storage named
store23 at some future time point:
Show (∃ t (= (value t (location crate15)) store23))
The UAV uses theorem proving to reason backwards fromthis goal approximately like what follows. “For the crate to
be at store23 someone must have put it there. I could put it
there myself if I was located at store23 carrying crate15.
But I can’t think of any way to satisfy the fly-zone precondition of flying to store23. Though my knowledge ofground vehicles suggests a completely different possibility.
My goal would also be satisfied if both the crate’s locationand store23 were in drive-zones, and some ground vehicle
had committed to the goal. In fact, helipad2 is a drive-zone,
and it is also a fly-zone, so I can go there and drop the crateoff. Before going there I should attach crate15, which isright here next to me. Then I’ll decided upon some particular ground robot, say, ugv3, and request that it adopts thegoal that crate15 is at store23.”
While the robots are not nearly as self aware as thismonologue suggests, it corresponds roughly to the search
space for the following plan:(Schedule uav1 i1 (attach crate15))(Schedule uav1 i2 (fly helipad2))(Schedule uav1 i3 (detach crate15))(Schedule uav1 i4(request ugv3’(= (value (finish i5) (location crate15)) store23)))(Before i1 i2)(Before i2 i3)(Before i3 i4)(Before i4 i5)
The UAV executes its plan, including sending the goal request to ugv3. We switch to look inside the mind of the
UGV as it tries to prove that the requested formula is satisfied. Suppose that half an hour has passed and that theUGV happens to be at some other storage building, carrying nothing:(= (value 12:30 (location ugv3)) store14)(= (value 12:30 (carrying ugv3)) nil)

The UGV will have to drive to the crate in order to pick
it up and deliver it to store23. But ugv3 does not know
By applying the natural deduction theorem prover to the crate15’s location, and scheduling a drive to (value 12:30
TAL formalization we are able to automatically generate (location crate15)) is prevented by the Identifier requirement on the drive action argument. The restriction is neces3 The link between theorem proving and action execution is an interesting topic. The mechanism described above is one approach, but we are sary since trying to find the coordinate of (value 12:30 (locurrently investigating alternatives.
cation crate15)) will certainly not generate any results given

the robot’s area map. The plan should instead involve finding a standard identifier for crate15’s current location andlooking that up in the map.
We assume that ugv3 believes that uav1 knows wherecrate15 is, and that whatever location that is, it is a drivezone (although see Section 7 for a discussion of this):(∃ x (∧ (Believes uav1 12:30‘(= (value 12:30 (location crate15)) ,x))(Identifier x)))(DriveZone (value 12:30 (location crate15)))
The task is then to prove the content of uav1’s request:
Show (= (value (finish i5) (location crate15)) store23)
The resulting plan makes use of the request and informRef
speech act combination to formulate a question corresponding to “what is crate15’s location”. Furthermore, while thisquestion will equip the robot with a standard identifier, thisidentifier is not yet known at the time the plan is being constructed. Rather than scheduling the drive procedure call,ugv3 instead plans to request itself to carry out the driving
after having asked uav1 about crate15’s location. At thetime at which this request is managed, the required information will be available for scheduling the actual drive procedure call. The rest should be a simple matter of going tostore23 to drop crate15 off at its goal:(Schedule ugv3 i6(request uav1’(Occurs uav1 i7(informRef ugv3
(value (start i5) (location crate15))))))(Schedule ugv3 i8(request ugv3’(Occurs ugv3 i9(drive (value (start i5) (location crate15))))))(Schedule ugv3 i10 (attach crate15))(Schedule ugv3 i11 (drive store23))(Schedule ugv3 i12 (detach crate15))(Before i6 i7)(Before i7 i8)(Before i8 i9)(Before i9 i10)
(Before i10 i11)
(Before i11 i12)
Let us switch our attention back to uav1 and see what
it plans to do about ugv3’s request for information. The
UAV’s current state is described by:(= (value 12:30 (location crate15)) helipad2)(= (value 12:30 (location uav1)) helipad2)(= (value 12:30 (carrying uav1)) nil)
The proof goal is defined by the incoming request:
Show (Occurs uav1 i7(informRef ugv3
(value (start i5) (location crate15))))Since uav1 has first hand knowledge about crate15’s location it schedules an inform procedure call according to thedefinition of the informRef speech act:
(Schedule uav1 i7(inform ugv3‘(= (value (start i5) (location crate15)) helipad2)))
Switching our focus back to ugv3 we find that it has received the formula that uav1 informed it about:(= (value (start i5) (location crate15)) helipad2)
This puts ugv3 in a position where it can prove the content
of its request to itself:
Show (Occurs ugv3 i9(drive (value (start i5) (location crate15))))
The result is that the missing drive procedure call is inserted
at the right place in the execution schedule with the standard
identifier plugged in as its argument:(Schedule ugv3 i9 (drive helipad2))
Once at helipad2, the rest of the scheduled actions will havethe robot attaching crate15, driving to store23, and dropping
the crate off to satisfy the goal and complete the scenario.

7 Limitations and Future Work
The work presented in this paper is far from a complete
solution to the robot cooperation scenario. One unsolved
question regards our assumption that ugv3 believes thatuav1 knows where crate15 is. Maybe there ought to besome commonsense knowledge that would allow it to defeasibly infer uav1’s knowledge from the fact that it delegated agoal that directly involved that knowledge. One might suspect that this is but one instance of a more general problem
of reasoning about who is likely to know what in which situations. An alternative solution would be to have the UAV
reason about the fact that ugv3 needs to know where thecrate is to be able to move it to its destination. The UAV
could then pro-actively inform the UGV about the crate’s
location before requesting the UGV to move it.
An ad hoc move that we were forced to make was to remove the informRef speech act from the UAVs knowledge
base while generating the first plan. While this particularaction is not needed for that particular plan, the UAV clearly
ought to have access to all its actions at all times. The reason for our move has to do with the fact that uav1 must
attempt to solve the goal itself before considering delegating it. What makes our scenario interesting is that it is notpossible to solve without cooperation. But uav1 can not
know that trying to deliver crate15 by itself is futile until
it has explored all alternative ways of doing so. Unfortunately, the informRef speech act made for a rather unwieldy
search space, which was more than our theorem prover hadtime to explore while we cared to wait. This prevented

uav1 from giving up on the prospect of managing the delivery by itself within a reasonable amount of time. We suspect that as the agents are equipped with more knowledge
and actions, more possibilities will open up in the theorem
prover’s search space, and the need for some kind of heuristic to help guide search will increase.
The speech acts themselves are subject to some limitations. One is our disregard of any physical preconditions tocommunication such as geographical closeness constraints.
Our robots are assumed to have a radio link at all times. Another limitation is that we do not consider indirect speechacts. This seems reasonable as long as we are thinking ofcommunication between our robots. But there is no denyingthat many of the speech acts uttered by humans are indirect.
A human UAV operator uttering “Could you make sure thatcrate15 is in store23?” is presumably requesting the UAV
to make sure the goal is satisfied rather than querying about
its ability to do so. Another serious limitation is our assumption that other agents always accept requests. Some
rejected requests could reasonably be handled during plan
execution through re-planning or plan repair. But others
should be considered already during planning and would
result in conditionally branching plans or plans with loops
that repeat requests until accepted.
A future development could be the inclusion of composite actions, which would make it possible to explicitly represent informRef as a macro action that includes an informspeech act. This is in contrast to our current formalization
where inform is only a procedure call and not a stand alone
action. Another possibility for development exists with regards to the execution schedule mechanism. While we thinkthat it is a promising method for integrating planning andexecution, the description of its workings that we have provided here is rather sketchy and needs further elaboration.
In particular we would like to take advantage of our integrated temporal constraint solver to calculate action durations and schedule actions at explicit clock times.
Finally, an agent architecture based exclusively on logical reasoning raises efficiency concerns. Both plans in ourrunning example were automatically generated by the theorem prover in 2 minutes and 35 seconds on a Pentium M 1.8
GHz laptop with 512 MB of RAM. That might or might not
be reasonable, depending on the application. But, in either
case, it was admittedly a small problem, which begs thequestion of whether the architecture will scale up to realworld problems. Alas, we do not yet know. But there are atleast some reasons to be optimistic.
One reason is, as already mentioned, the use of a temporal constraint solver for reasoning with time. More generally, one can view special purpose algorithms as additional
natural deduction rules that make certain types of inferences
efficient. Another reason is the choice of an interruptible algorithm for nonmonotonic reasoning. In a real-time setting
the agent can act, at any time, to the best of its knowledge
given the reasoning it has performed up to that point.
But most encouragingly, achieving satisfactory perfor-

mance in certain domains is already possible. E.g., our theorem prover was applied to UAV surveillance and quickly
generated plans for realistic size problems [11]. Furthermore, the agent architecture was used to the control thecharacters in a computer game that requires real-time interaction [12]. We believe computer games to be a particularly suitable domain for empirical studies of logical agentson the road from tiny benchmark problems towards larger
real-world applications.

8 Conclusions
We have described a scenario involving communication andcooperation between two robots. The solution required one
robot to plan to delegate a goal through communication using a request speech act. The other robot had to plan toachieve knowledge preconditions, again through communication using a nested request and informRef speech act.
These speech acts were formalized in an extension of Temporal Action Logic that includes syntactic belief and commitment operators, which were made possible through theuse of a quotation mechanism. The formalization made it
possible to generate a plan involving both cooperation andcommunication using automated theorem proving. Finally,a novel scheduling mechanism provided a tightly coupledintegration between planning and the execution of generated plans.
The formalization used quotation, which seems most befitting of a logicist framework. The robots’ explicit representation of beliefs as formulas in a knowledge base motivates their representation of others’ beliefs as quoted formulas. Further benefits may be gained by using quotationin the context of speech acts. A fuller theory of communication will presumably also include locutionary acts, i.e.
the actual utterances that encode messages between agents.
These are most naturally thought of as strings consisting ofquoted formulas from the agents’ knowledge bases.
Our philosophy is based on the principle that logic is anintelligent agent’s “language of thought”. The formalization of the speech acts are similar to their corresponding
semantics proposed in the literature. But unlike many otherapproaches that view the semantics as normative, such as
agent communication languages, we put the formulas in our
agents’ heads where the agents can reason with them using
theorem proving. In fact, our use of a prefix notation for formulas makes the correspondence between the theory in thispaper and its Lisp implementation exact, save for some logical symbols that are not available for use as Lisp identifiers.
Through this approach we hope to construct an agent architecture based on logical planning with a level of flexibility
that would be difficult to match using agent programming
languages.

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