Towards Active Logic Programming

03/21/2014 ∙ by Stefania Costantini, et al. ∙ Università degli Studi dell'Aquila 0

In this paper we present the new logic programming language DALI, aimed at defining agents and agent systems. A main design objective for DALI has been that of introducing in a declarative fashion all the essential features, while keeping the language as close as possible to the syntax and semantics of the plain Horn--clause language. Special atoms and rules have been introduced, for representing: external events, to which the agent is able to respond (reactivity); actions (reactivity and proactivity); internal events (previous conclusions which can trigger further activity); past and present events (to be aware of what has happened). An extended resolution is provided, so that a DALI agent is able to answer queries like in the plain Horn--clause language, but is also able to cope with the different kinds of events, and exhibit a (rational) reactive and proactive behaviour.

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1 Introduction

In this paper we address the issue of defining a logic programming language for reactive and proactive agent systems, with a clear procedural and declarative semantics. The motivation of this paper is that, while it is quite straightforward to build logical agents which are in some way rational, it is much more difficult to build logical agents that interact with the environment, and perform actions either on their own initiative (i.e. they are proactive) or in response to events which occur externally (i.e. they are reactive).

A lot of work has been done in order to equip logical agents with more and more sophisticated forms of rationality. Logical agents can represent (and communicate) their own as well as other agents’ thinking processes, and are able to build arguments by means of their own inference rules where: either each agent has a logic associated with it, [14], [18], with rules of inference which relate the different logics of the different agents; or, each agent is defined together with its specific inference rules and communication modalities [3].

Logical agents are able to combine belief updating, goal updating and practical reasoning in a BDI fashion (“Belief, Desires, Intentionality”) [20], [19]. Logical agents are able to interact with an environment on which they have limited [22] or no [1] expertise. Logical agents can reason about actions ([11] and subsequent extensions) and can manipulate not simply logical formulas, but complex data types, and are able to act in accordance with a specific, declarative policy [10]. Many of these approaches are related to logic programming, either syntactically or semantically, others are based on theorem–proving or transition systems as an operational semantics.

Reactive and proactive agents typically achieve their functionality by means of condition–action rules, where the condition constitutes a stimulus that causes the agent to perform some kind of action as response. The approach of [15] is aimed at combining rationality and reactivity in logic: it proposes that reactivity is achieved, in a rational agent, by modeling reactive rules as integrity constraints in the proof procedure. By combining the approaches of [15] and [3], the approach of [8] obtains rational reactive agents by treating communication primitives as abducibles. There are, however, few approaches in logic programming for representing not only the actual behavior of one agent in a detailed way, but also the behavior of complex multi–agent systems, with few notable exceptions. A relevant approach is the concurrent logic programming language ConGolog [16], [21], based on situation calculus, where properties of multi–agent systems can be formally proved. At present, ConGolog has been less useful as an implementation language, although further developments are under way. Another one is the Constraint Logic Programming language CaseLP, which can also be used in the context of a Multi-Agent-System specification methodology based on linear logic [2], [7].

In this paper we focus on representing reactivity and proactivity in logic programming in the simplest possible way, with the objective of introducing in a declarative fashion all the essential features, while keeping the language as close as possible to the syntax and semantics of logic programming [17]. The resulting language (that we call DALI) should then be easy to understand, easy to implement, and easy to use. To this aim, we introduce:

distinct atoms to represent external events; whenever an event takes place (it can be an action or a message from another agent, or something which changes in the external world), the corresponding event atom becomes true;

distinct atoms to represent internal events; an internal event corresponds to a conclusion reached by the agent, which can trigger some kind of activity in the agent itself;

distinct atoms to reason about past events, and present events, the latter being events which have already taken place, to which the agent has however not yet responded;

distinct atoms to represent actions that can be performed by the agent;

reactive rules that have an event (either external or internal) as conclusion; a reactive rule can be understood as the agent’s reaction to the event;

action rules that have an action as conclusion; an action rule can be understood as defining the preconditions for an action to be performed;

active rules that have actions in their body, so as to model proactive behavior, where an agent performs an action with the aim of reaching some kind of objective, and reactive behavior where an agent acts in response to stimuli, since a reactive rule can be active.

Procedural semantics is based on an easy–to–implement, extended resolution. Declarative semantics of agents and agent systems is based on “snapshots” of the current stage of the computation, which consist in the Least Herbrand Models on a suitably modified versions of the logic programs representing agents. Snapshots can then be organized so as to represent “evolutions” of the agent system.

In order to keep the discussion as simple as possible, we take as basic language the plain propositional Horn-clause language, and we just consider “events” and “actions” without even trying any finer distinction. We are conscious of the fact that, when introducing variables and time, there will be many related issues to be coped with. Also for lack of space, we leave these topics out of the scope of the present paper. In perspective, however, the practical logic language DALI will have all the useful features of real languages, though still remaining (in our opinion) as simple and clean as to be easily integrated, if needed, with most of the previously mentioned approaches.

2 Reactive Logic Programming

2.1 External Events

In order to illustrate the extension we propose to the Horn–clause language, it is useful to take into consideration about how rules are understood in logic programming. Consider for instance the following logic program:

:-

The second rule is by no means necessary to prove the truth of , that is an immediate consequence of the first rule (which is a fact). In this case, clearly truth of is not conditioned by truth of . It is important to notice however that the second rule is still a candidate for resolution of goal , and it will be finally selected by any fair interpreter, and will be applied by the immediate consequence operator . Then, since we already know that is true, we can interpret the resolvent as a reaction of the interpreter in response to the stimulus .

Let us now assume that is an external event, i.e. something which occur outside (and independently of) the program that we are considering. External events, or stimuli, could be messages, or actions (performed by some other entity) which affect the agent, or observations, depending of the environment where the program is put at work. At present, we do not distinguish between these cases.

Similarly to most logical approaches to agents, we leave to the language developer to decide how the agents are made conscious that an event took place, and how to suitably represent an event to a given agent (for instance, if you call me on the phone, I see this action the other way round, i.e. in my view I am being called).

We simply assume that, as soon as this event happens, somehow assumes value true for every agent Ag which is able to observe this event. Then, any rule defining in the program of agent Ag, can be interpreted as a stimulus–response rule, i.e. a rule that determines some actions to be executed in response to the stimulus .

Enhancing logic programs with some kind of modules of agents (or, more generally, of multiple theories) is a well studied topic. Following [3], we assume we have a form of modularization available, that allows a program to be divided into separate modules, or agents, each one endowed with its own name (this without affecting the standard semantics). In the following, when referring to agent , we will implicitly refer to the logic program defining .

Then, we associate to a set of distinct atoms

representing external events. We call each of the ’s an event atom. According to [3], whenever event takes place, atom becomes true for all the other agents. We assume that events which have taken place are recorded in a set

For each , may possibly provide only one rule of the form:

where the ’s can be understood as responses to the stimulus .

We call this rule a reactive rule. Notice that having a single reactive rule for each event is not really a restriction, since the ’s may have multiple definitions.

We assume that events are ”consumed” by reactive rules. I.e., the application of the reactive rule causes to be removed from

We state the limitation that the ’s do not appear in the body of other rules. Then, when happens, we are in a situation fairly analogous to that of the above example, since we have a true atom, and a rule which is by no means aimed at proving this fact, but that, instead, specifies activities (internal inferences and/or actions) to undertake as response. Then, atoms in the body should not be intended as determining the truth of , but, vice versa, as predicates that should be proved whenever becomes true. In a sense, it is like if the opposite side of the implication is being used. However, notice that we do not say that truth of implies truth of , but that on truth of , truth of should be checked.

To make this interpretation more intuitive, and in order to make it recognizable that rules with conclusion are stimulus–response rules, a slightly different notation may be used, for instance by replacing the token “:-” with “:”, Then the syntax of a reactive rule becomes:

For the sake of readability, given predicate , the fact that , i.e. that represents an external event, is stressed by an explicit subscript, by denoting as .

Example 2.1

If an event determines some behavior, then stimulus–response rules are adequate, like for instance

rains :
open_umbrella :-

where . The rule says that in case it rains, the agent opens an umbrella. Then, on truth of event rains, we check the truth of (i.e. try to prove) the related condition open_umbrella. This is done as usual in logic programming, i.e. using the second rule, and try proving its condition have_umbrella.

Notice that, if there are several atoms in the conditions of a reactive rule, their order may be relevant.

Example 2.2

Consider the following variation of previous example.

rains :

In this case, it is better to open the umbrella before deciding what to do next (which for instance could be going home, or instead entering a shop).

2.2 Actions

Since is reactive and proactive, we also associate to the set of distinct atoms

which represents the actions that Ag is able to perform. We call each of the ’s an action atom.

Actions can be performed in response to external events, but also on the agent’s own initiative (proactivity). The ’s can appear in the body of rules, and may have an explicit definition, i.e. there can be (optionally) only one rule with head , that we call action rule. In this case, the body of this rule expresses preconditions for the action to be performed. Action rules are the same as ordinary rules, and in fact are treated by DALI resolution in exactly the same way. However, in order to make it visible that, conceptually, action rules express preconditions for actions, we add again some syntactic sugar so as to distinguish action rules from the others. An action rule will have in particular the form

It is left to the implementation that, whenever succeeds, on the one hand atom becomes true (as an external event) to all the other agents (according to [3]), and, on the other hand, the corresponding action is performed in practice, in case actually interacts with an environment. If there are several rules with the same action in their body, then this action can be potentially performed several times.

Given predicate , the fact that , i.e. that represents an action, is stressed by an explicit subscript, by denoting as .

Example 2.3
danger :
ask_for_help :-
ask_for_help :-
call_police :

In this case, we have the external event danger , to which the agent reacts with ask_for_help (which is an ordinary predicate). This implies possibly performing one or both of the two actions scream or call_police where scream , call_police . The latter one however can be performed upon precondition have_a_phone, as specified by the corresponding action rule.

Notice that it is somewhat arbitrary to decide which are the predicates that are to be inserted into the set of actions. In principle, the distinction between actions and ordinary predicates is that actions affect the environment, and/or are observable from the other agents.

From the declarative point of view, action subgoals without a corresponding action rule always succeed, while action subgoals with an action rule succeed or fail (in which case the action is not performed) according to the standard procedural semantics of the Horn clause language. In practice however, an action may be unsuccessful in the sense that, for some reason, it is not possible to achieve the intended effect on the external environment. For instance, referring to the above example, the action call_police might in practice be prevented by the phone being out of order. In some cases, the agent itself might cope with this kind of failures, by following some protocol in the interaction with other agents. In other cases, the implementation should make the agent aware of the failure of an action. A possibility is that of specially generated external events: in this way the agent might provide, whenever necessary, suitable ”recovery” event rules.

2.3 Internal Events: Reacting to Conclusions

Assume that, whenever some conclusion is reached, this triggers some kind of activity (internal reaction) in the agent. This is possible by defining another set of distinct atoms, , which contains those predicates which are to be considered as events, and then can possibly appear as the conclusion of only one reactive rule.

This kind of predicates will be called internal events. From the procedural point of view, we assume the conclusion happy, obtained by means of the ordinary rule, is recorded in a set , and then reconsidered later to trigger the reactive rule. Similarly to external events, the internal events which are ”consumed” by reactive rules, are removed from .

Given predicate , the fact that , i.e. that represents an internal event, is stressed by an explicit subscript, by denoting as .

Example 2.4

Assume that we want to express the fact that Henry, when happy, merrily sings a song. Then, Henry’s theory might become:

happy :-
happy :

where . For defining the reactive rule, we let , i.e. we state that the internal conclusion happy may be interpreted as an event, and determine an action.

Internal events can play an important role whenever the agent makes some kind of planning for achieving its goals. In fact, by means of reactive rules related to internal events, plans can be “tuned” according to the subgoals that have been actually achieved.

Also, internal events may help simulate a sort of ”consciousness” in the agent, which is able to recognize, reason about and react to its own conclusions. To this aim, subgoals corresponding to predicates belonging to should be automatically attempted from time to time. Referring to the above example, the subgoal happy should be attempted every now and then, so as to apply the reactive rule in case of success. Which ones to attempt, and how frequently, can be left to the implementation, possibly guided by suitable directives.

An action atom may be considered as an internal event, and therefore the agent can “react” to its own actions.

Example 2.5

Assume now that Anne is invited by her friends to go out with them. She checks for the possibility of going by car, and if the car is not available, then she takes the bus. If she take the car, she calls on her friend Susan in order to ask her to join. This is represented by the following rules.

invitation :
go_out :-
go_out :-
go_by_car :
go_by_car :

2.4 Drawing Conclusion from Past Events

It may be useful to allow event atoms in the body of rules. In fact, it may be the case that there is a conclusion to draw, depending on what has happened before.

Then, we suppose that external and internal events are recorded. In particular, for every event atom , we add another distinct atom (where stands for ), meaning that event has happened in the past. We call the set of these atoms.

Example 2.6

For instance, if we want to express that George is happy if his girlfriend has called, then we need a rule such as:

happy :-

where girlfriend_call .

Notice that this is a source of nonmonotonicity in the observable behavior of the agent. In fact, query ?-happy to agent Henry may initially fail, and may later succeed when the event girlfriend_call will have happened. In our interpretation, an event becomes a past event whenever the agent has reacted to it, i.e. as soon as the corresponding reactive rule has been applied.

We do not mean past events ad an ”ad hoc” way of handling time. Rather, we see the set of past events as a sort of “state” of the agent, although it is important to notice that the facts that are recorded are either external events which have happened, or conclusions that have been proved, or actions that have been performed. The set of past events constitutes a repository for lemmas, and therefore is no harm from the declarative point of view. From the practical point of view, it is a sort of ”memory”, useful to the agent to enforce a coherence in its interactions with the external environment. Notice however that the set of past events is by no means similar to the memory of imperative languages, where one can record arbitrary statements.

2.5 Drawing Conclusion from Present Events

It can also be useful to reason about an external event which ”has already taken place”, and to which the agent has not yet reacted. I.e., we would like atoms to be allowed into the body of rules, which correspond to events that are already available to the agent, although the corresponding reactive rule has not been applied yet. This because we want to distinguish between reasoning about events, and reacting to events.

In particular, for every event atom we add another distinct atom (where stands for ), meaning that event has happened but has not been considered yet. We call the set of these atoms.

Example 2.7

In this example Mary is awakened by the alarm clock. Then, she realizes it is time to stand up, and also switches the alarm clock off.

my_god_its_late :-
my_god_its_late :
alarm_clock_rings :

In this case, alarm_clock_rings is an external event, while my_god_its_late is an agent’s conclusion, which is interpreted as an internal event. Notice that the ring of the alarm clock is first reasoned about, by means of the special predicate alarm_clock_rings, which allows a conclusion to be reached, and then gives rise to a reaction. Precisely, , , , and

Present events may help reasoning about the effects of actions.

3 Procedural Semantics

What we need for building a DALI interpreter is the possibility of monitoring external and internal events, so as to actually respond to stimuli. We propose to do that by means of an extension to SLD–resolution.

We assume to associate the following sets to the goal which is being processed by a DALI interpreter:

  • the set of the external events that are available to the agent (stimuli to which the agent can possibly respond);

  • the set of internal events which have been proved up to now (internal stimuli to which the agent can possibly respond);

  • the set of past events (both internal and external).

The procedural behaviour of a DALI agent may consist of the following activities. First, trying to answer a query (like in plain Horn–clause language). Second, responding to either external or internal events. Third, trying to prove a goal corresponding to an internal event (as suggested before, these goals should be attempted from time to time). These different kinds of activities are in principle independent of each other, and should be somehow interleaved: for instance, while trying to answer a query, an external or internal event may occur, to which the agent should in the meanwhile respond.

Therefore, a goal in DALI is a disjunction of component goals. Every is a goal as usually defined in the Horn–clause language, i.e. a conjunction. The meaning is that the computation fails only if all disjuncts fail.

The suggested strategy for proving a goal is the interleaving, i.e. the interpreter at each step should be able to pick up a subgoal from any of the ’s, or to add a new , that in particular will be an external or internal event. The resolution strategy adopted in a DALI implementation will specify how to perform the interleaving among the component goals. The precise definition of a resolution strategy is however out of the scope of this paper. Instead, we concentrate in defining which are the resolution steps that the interpreter can perform.

In fact, below is the formal definition of the extended resolution. Notice that a resolution step will also update (whenever necessry) the sets , and . The definition is composed of six different cases. In cases (i)-(iii) the selected atom belongs to one of the existing component goals. In cases (iv)-(vi) instead, an atom is chosen from the set of external (resp. internal) events, and is added to the given goal, as a new component goal. At each stage of the inference process, more than one case will be in general applicable. The resolution strategy will state in which order the different cases should be applied, and how often to consider the different classes of events.

Definition 3.1 (DALI Resolution)

Given a logic program defining agent (with associated sets of external events , internal events , actions , past events , present events ), given sets , and , and goal of the form

where each is of the form:

DALI resolution derives a new goal and new sets , and by means of one of the following steps.

  • Select atom and a corresponding defining clause , and apply SLD–resolution with as the selected atom and as the input clause, thus obtaining . Let , and .

  • Select atom where , without defining clauses, and derive the new goal where the component goal is replaced by

    Let , and if then , else .

  • Select atom , and derive the new goal where the component goal is replaced by

    Let , and .

  • Choose atom , and join it to the given goal, thus deriving the new goal with the new component goal Let , and .

  • Choose atom , and join it to the given goal, thus deriving the new goal with the new component goal Let , and .

  • Choose atom , and join it to the given goal, thus deriving the new goal with the new component goal .

Given a goal , according to the above definition, DALI resolution can do one of the following.

(i) Pick up a subgoal from any component goal , and proceed with the refutation as usual. This case is also adequate if the subgoal is an action atom with a defining clause, or an event atom with a corresponding reactive clause.

(ii) Perform an action without preconditions, which means select an action atom without a defining clause, and just remove it from the goal. I.e., an action without preconditions always “succeeds”. It is left to the implementation perform the action, and to make the action atom true (in the form of an external event) to all the other agents. If this action is among the internal events, then it must be included into the set since it has taken place, and then it can possibly trigger some internal reaction.

(iii) Consider an atom corresponding to an event , i.e corresponding to an external event which has happened, but that has not been considered yet. This atom can simply be removed from the goal, i.e. “succeeds”, while remains unchanged, since the agent has still to react to . Intuitively, the agent asks itself whether has happened, so as to use this knowledge in its reasoning. Later, it will possibly react to .

(iv)–(v) React to any of the external or internal events, by inserting the corresponding new component goal in the overall goal. The event has to be removed from the set of the events which are still to be considered, and inserted into the set of past events.

(vi) Insert a new component goal which corresponds to an internal event. In this way, in case this component goal succeeds, it becomes possible to ”react” to this conclusion (intuitively, the agent asks itself whether holds, so as to act consequently if this is the case).

It is left to the resolution strategy which case to apply at each step (if there are several possibilities). I.e., it is left to the resolution strategy to choose how often to consider external and internal events, and in which order, and how to organize the interleaving among the component goals.

What is not considered in the previous definition is the fact that, whenever a subgoal corresponding to an internal event is proved, it should be inserted into the set . This is for the sake of simplicity, but notice that the definition can be made precise by introducing nested refutation for these atoms. A nested subgoal is a subgoal of the form . When resolving , it would become and so on. Any subgoal corresponding to an internal event should be a nested subgoal. On obtaining the empty nested subgoal , i.e. on proving , we would let .

Notice that represents some kind of input channel for the agent. As a further extension, we could have several “channels”, according to some classification of different events (e.g. messages or observations or other interactions with the external environment). Also, the resolution strategy could take as input some kind of declaration about the priority for selecting among different possibilities.

4 Declarative Semantics

Work is under way for a complete definition of declarative semantics, able to consider in general terms the evolutions of multi–agent systems. At present, we are able to specify the declarative semantics of an agent given a certain initial situation, i.e., in a sense, a “snapshot” of the agent’s behavior. We are also able to sketch how to describe the evolution of a set of interacting agents, but we have only an initial idea on how to study properties of the system as a whole.

In the following, we first specify semantics of a single agent, and then introduce a concept of evolution of an agent system.

The first objective is to declaratively model reactive rules for external and internal events. Consider for a moment the plain Horn–clause language, and the following program:

:-

Its least Herbrand model is , like for the following slightly modified version:

:-

Since is true by means of a unit clause, the second rule for does not change the meaning of the program, since it differs from the previous version only in that there is itself in the body.

This is exactly the trick that we will use for our reactive Horn–clause programs. Precisely, given (external or internal) event , we assume to transform rule:

into the new rule:

Syntactically, we have added itself in the body of its own rule. The meaning is that, since there is no other rule in Ag defining , then the conditions of this rule may become true only if the truth of comes from some other agent, i.e. if event has happened. We also add rule

which models the fact that as soon as the reactive rule for is applied, a corresponding past event is generated.

The second objective is to declaratively model actions, without or with an action clause. The point is, an action atom should become true (given its preconditions, if any) whenever the action is actually performed in some rule. Consider another simple program written in the plain Horn–clause language:

:-

Its least Herbrand model is , since both and are given as facts. If we modify the program as follows:

:-
:-

its least model is . Assuming that is an event atom and is an action atom with no defining clause, this modification ensures that the action atom becomes true whenever the action is actually performed, i.e. if the clause defining is applied, and its condition is true. Similarly, let us assume that has a defining clause, like in the program:

:-
:-

Its least Herbrand model is , since , and are given as facts. We modify the program as follows:

:-
:-

Its least model is still , but, interpreting as an action atom, we state then can be derived only if the corresponding action is actually performed in the rule defining . More generally, for every action , with action rule

and for every other clause where appears in the conditions, of the form

with , we assume to add the new rule

If has no defining clause, we instead add clause:

The meaning is that is been performed (if its preconditions hold) by the clause with head , provided that the conditions in the body of this clause are true.

Finally, for every external or internal or past event that we want to be true at the beginning, we add corresponding unit clauses

We define the “snapshot” declarative semantics of a program written in our enhanced Horn–clause language DALI, as the standard declarative semantics of a program , obtained from by means of the modifications specified above. Work is under way for proving DALI resolution correct and complete w.r.t. this declarative semantics, by means of an adaptation of standard proofs.

It is important to notice that we have defined the semantics of our new language by modifying the program, while leaving the semantic approach unchanged. In this way, we keep all the useful properties of the Horn–clause language, thus we are still able to exploit all the technical machinery related to it (such as methods for program analysis and optimization, abstract interpretation, partial evaluation, debugging, etc.) which remains applicable on .

If we want to be more precise in our “snapshot” of the behavior of agent , we can simulate a resolution strategy by taking a program , where differs form in that only the clauses that should select are left, while the others are cancelled. Of course however, several can be obtained from .

We can extend this semantic approach by defining the following procedure for modeling evolutions of a multi–agent system:

  1. Given logic programs (agents) , build .

  2. Given computation rule , from , build .

  3. Compute the least Herbrand models of , say .

  4. Taken as starting point the set of events contained in , change the unit clauses of accordingly, and go back to step 3.

In this way, we obtain possible evolutions of our agent system. In order to study these evolutions, we can for instance pick up the suggestion by [13], of adopting well–established techniques from the field of model–checking.

5 Concluding Remarks

An agent as defined above, is completely characterized by its input channels, resolution strategy and Horn–clause theory. About the input channels, of course we recognize the need, as emphasized by [12], of an underlying “transducer” integrated in the implementation, that converts all the incoming “stimuli” into a form that is intelligible to the agent and inserts them into the right channel.

A lot of implementation issues have been left open in this paper. An important point is that of timely response to events, possibly guided by directives specifying time constraints. These constraints should influence the resolution strategy. It is not clear however how one could prove that a DALI program satisfies given real–time requirements.

Metareasoning is important for agents: as remarked in [2], an agent can reason on the basis of meta–goals, which possibly require sophisticated strategies to be achieved. Then, it would be interesting to take as basis for DALI an enhanced Horn–clause language with self–reference and reflection like Reflective Prolog ([4] which is the basic language for [3] and [8]). On the lines of [9] and [3], metalevel information could also be used to construct agent interfaces, and to record information about heterogeneous information sources, in view of the integration of heterogeneous information systems.

It is important to notice that we have not considered negation. Negation is instead really important from the expressive and practical point of view, at least since it allows exceptions to be stated to general reactive rules. In the following example, where we assume to have negation as failure, we define a situation where birds can fly for trying to avoid a predator (while the other animals run away), except for abnormal birds, like penguins or road–runners.

Example 5.1
predator_Attacks :
try_to_Escape :-
try_to_Escape :-
fly :

Negation adds further complication to both declarative and procedural semantics. Nevertheless, adding negation to DALI is a main topic of future research.

Since this is work in progress, a suitable comparison with related work is missing. We mean to add the comparison in the final version of the paper.

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