Much effort has been dedicated to provide a general model of agents working in complex environments. This research focuses on the high level cognition used in determining the behavior of the agent.
The language of the Situation Calculus represents a very useful way of modeling an agent’s knowledge of its environment. One of its advantages is that there exist methods to derive an executable program from a basic set of axioms. This program can then be used to determine the actions that are necessary in order to accomplish certain goal states. The main objective of this line of work is to obtain an automatic way of deriving such an executable program.Eje: Inteligencia artificialRed de Universidades con Carreras en Informática (RedUNCI

Filocamo, Gabriel R.

García, Diego R.

Simari, Guillermo Ricardo

Servicio de Difusión de la Creación Intelectual

A General Approach to the Implementationof Action TheoriesGerardo I. Simari Diego R. Garc´ıa Gabriel R. FilocamoLaboratorio de Investigacio´n y Desarrollo en Inteligencia ArtificialDepartamento de Ciencias e Ingenier´ıa de la Computacio´nUniversidad Nacional del Sur. Av. Alem 1253, (8000) Bah´ıa Blanca, ArgentinaTel: ++54 291 4595135 - Fax: ++54 291 4595136{gis,drg,grf}@cs.uns.edu.arAbstractMuch eﬀort has been dedicated to provide a general model of agents working in complexenvironments. This research focuses on the high level cognition used in determining the behaviorof the agent.The language of the Situation Calculus represents a very useful way of modeling an agent’sknowledge of its environment. One of its advantages is that there exist methods to derive anexecutable program from a basic set of axioms. This program can then be used to determinethe actions that are necessary in order to accomplish certain goal states. The main objectiveof this line of work is to obtain an automatic way of deriving such an executable program.1 Introduction and BackgroundAn important goal in the research programme of Artificial Intelligence is to develop autonomousentities called agents. This autonomy is of utmost relevance for an agent to be consideredintelligent in the environment that it occupies; the study of the relationship among beliefs,actions, and their consequences is one way to go in obtaining this objective.The research we are conducting in the LIDIA lies within the area of Cognitive Robotics.Work in this field is directed towards the provision of a uniform theoretical and implementationframework for autonomous robotic or software agents that reason, act, and perceive in com-plex environments. The diﬀerence between “traditional” robotics and cognitive robotics is theemphasis placed on higher level cognition in determining agent behaviors.One way of modeling an agent’s beliefs about the world, the possible actions it can take,and its eﬀects on the environment is the Situation Calculus [11, 12].1.1 A Brief Introduction to the Situation CalculusWe will briefly introduce the Situation Calculus in order to provide the framework necessaryin the rest of the presentation.The Situation Calculus is a second order language, quite suitable for representing dynam-ically changing worlds. Each change in the world is the result of a specific action, which isdefined in the language. A situation stands for a history of the actions taken in the world(simply a sequence of actions), and is represented as a first order formula. A special situation,the constant s0, is used to represent the initial state. Every other situation is denoted by thespecial functional symbol do(α, s); this means that action α executed in situation s leads to anew situation, called do(α, s), where s is a situation built in the same way, or s0. For exam-ple, for action grab(x) (which denotes grabbing object x), do(grab(x), s) is the situation whichresults from grabbing object x in situation s.There exists a certain type of relations that may vary from situation to situation, whichare called Relational Fluents. These are represented by predicates that take a situation termas their last argument. Functions whose values depend on the situation are called FunctionalFluents, and also take a situation term as their last argument. For example, the relational fluentnextTo(x), which holds in s0, no longer holds in do(walk(y), s0), where object x is diﬀerentfrom object y.Another type of relations, which do not depend on the situation, are represented by pred-icates without a situation parameter, and are called Non-Fluent predicates. Similarly, thosefunctions that are situation independent are called Non-Fluent functions.The theory is completed by a variety of axioms, which capture the diﬀerent aspects of theworld that is being modeled. These axioms are:• Action Precondition Axioms:The Action Precondition Axioms specify the requirements that must be satisfied for anaction to be executed. For this reason, there will be one axiom for each action. Inthe definition of these axioms the predicate poss(a, s) is used, meaning that action a ispossible (can be executed) in situation s.An Action Precondition Axiom will have the following general form poss(a, s) ≡ Υ, whereΥ is a first order formula.• Eﬀect Axioms The Eﬀect Axioms specify how the relational and functional fluents’values change after the execution of an action. In this case, there will be at least oneaxiom for each fluent.An Eﬀect Axiom for a relational fluent f will have the following general form:φf → f(tn, do(α, s)), and for a functional fluent g, γg → g(tn, do(α, s)) = r, wheretn = t1, t2, ..., tn are terms, and φf ,γg are first order formulas. The Eﬀect Axioms forrelational fluents can be subdivided into positive and negative axioms. An axiom ispositive if the relational fluent f is not negated in• Successor State AxiomsThe Successor State Axioms provide a complete way of describing how the world evolvesas a response to the execution of actions. Each axiom describes how to compute a thevalue of a fluent for the next situation, given its value for the current situation. Intuitivelythe successor state axiom for a fluent f has the following structure:True afterwards ⇔ [An action made it true ∨True already and no action made it false]The use of ⇔ means that the axiom will be true after the execution of the action if it ismade true or it stays true; and that it will be false otherwise. For each relational fluentf , the successor state axiom has the following form:f(xn, do(a, s)) ≡ γ+f (xn, a, s) ∨ f(xn, s) ∧ ¬γ−f (xn, a, s)where γ+f (xn, a, s) → f(xn, do(a, s)) and γ−f (xn, a, s) → f(xn, do(a, s)) are the positiveand negative normal form eﬀect axioms for the fluent f , respectively.2 ObjectivesCentral in this work is the goal of making the process of obtaining an executable implementationof the action theory an automatic one. Therefore, what we want is to be able to compile thelanguage of the Situation Calculus into an object language such as Prolog. There are manyadvantages to having such a compiler; the implementation of an action theory can be quitetedious, and having an automatic processor can ease the design of such a theory. For example,if the initial axioms suﬀer modifications, the final result can be quickly visualized.There exists a process, based on work done by Lloyd and Topor [10], that can be used toobtain a prolog program from the initial Situation Calculus axioms. They propose a set oftransformations suggested by Clark’s theorem [1] which reformulate the Action Preconditionand Successor State axioms in a way that results in a direct translation into Prolog clauses.Once the basic axioms are specified, the automatic process should generally consist of thefollowing steps:• Transform the Action Precondition Axioms:— Obtain the if-halves from the Action Precondition Axioms.— Apply the Lloyd-Topor transformation rules to the if-halves in order to obtain for-mulas that are easy to implement (Lloyd-Topor normal form).• Transform the Successor State Axioms:— Obtain the if-halves from the Successor State Axioms.— Apply the Lloyd-Topor transformation rules to the if-halves in order to obtain for-mulas that are easy to implement (Lloyd-Topor normal form).• Initial Database definition: Obtain the if-halves from the initial database definition.These definitions obey the form:F (xn, s0) ≡ ΨF (xn, s0)where F (xn, s0) will not be negated in this case. This is due to the fact that negativeinformation is represented in Prolog by the Closed World Assumption (CWA). It shouldalso be noted that F cannot be a functional fluent in this case because this type of fluentcannot be directly implemented in Prolog. Notwithstanding, an n-ary functional fluentcan be implemented as a (n+ 1)-ary Prolog predicate, where the last argument representsthe value of the fluent.• Non-Fluent Predicate definition: Obtain the if-halves from the definitions, and thenapply the Lloyd-Topor transformation rules to these if-halves.• Obtain a program in a given object language: Using the formulae obtained in theprevious steps, derive a fully functional program that models the specified action theory.3 Current Research LineCurrent work is being dedicated to the study of the applications of the Situation Calculus. Oneway of understanding the implementation of an action theory seems to be the resolution of asimple problem that covers all of the details of the process. One such problem is the Monkeyand Bananas ProblemThe Monkey and Bananas Problem is a classic planning problem. It was proposed by JohnMcCarthy in 1963, and later reprinted in [11]. A monkey is in a room that contains a bunch ofbananas hanging from the ceiling, and a chair. The monkey can’t reach the bananas from thefloor. Nevertheless, if the chair were below the bananas, and the monkey were standing on topof it, then the bananas would become reachable. One possible setup for an initial state is themonkey not standing next to the chair, and the chair not sitting below the banana bunch.One advantage to using this problem as a first approach is that, with a simple world like theone described, there shouldn’t be obstacles that obscure the process of obtaining an executableprogram from an initial formulation. Because there are few objects and actions, the numberof axioms needed to formalize an action theory will be reduced, which is useful in dealing witherrors committed in the initial stages of the resolution.Once the program is obtained, it can be used to obtain plans in which a set of fluents arevalid (or not). For example, it could be used to obtain a plan which the monkey can use tograb the bananas and get down from the chair.Having solved a simple problem like the one described, it will be easier to approach broaderproblems that could contain special cases that must be taken into account in the constructionof an automated tool.References[1] Clark, K. L. Negation as failure. In Logic and Databases (New York, 1978), H. Gallaireand J. Minker, Eds., Plenum Press, pp. 293—322.[2] Elkan, C. Reasoning about action in first-order logic. In Proceedings of the Conferenceof the Canadian Society for Computational Studies of Intelligence (Vancouver, BritishColumbia, May 1992).[3] Finzi, A. I., Pirri, F., and Reiter, R. Open world planning in the situation calculus.In Proceedings of the 7th Conference on Artificial Intelligence (AAAI-00) and of the 12thConference on Innovative Applications of Artificial Intelligence (IAAI-00) (Menlo Park,CA, July 30— 3 2000), AAAI Press, pp. 754—760.[4] Gelfond, M., and Lifschitz, V. Representing action and change by logic programs.Journal of Logic Programming 17, 2,3,4 (1993), 301—323.[5] Gelfond, M., Lifschitz, V., and Rabinov, A. What are the limitations of thesituation calculus? In Automated Reasoning: Essays in Honor of Woody Bledsoe, R. Boyer,Ed. Kluwer Academic Publishers, Dordrecht, 1991, pp. 167—179.[6] Hintikka, J. Knowledge and Belief. Cornell University Press, Ithaca, New York, 1977.[7] Kowalski, R. A., and Sergot, M. J. A logic-based calculus of events. New GenerationComputing 4 (1986), 67—95.[8] Lespe´rance, Y., Levesque, H. J., Lin, F., Marcu, D., Reiter, R., and Scherl,R. B. A logical approach to high-level robot programming–A progress report. In Controlof the Physical World by Intelligent Systems, Papers from the 1994 AAAI Fall Sympo-sium (Menlo Park, California, 1994), B. Kuipers, Ed., American Association for ArtificialIntelligence, American Association for Artificial Intelligence, pp. 79—85.[9] Lespe´rance, Y., Levesque, H. J., and Reiter, R. A situation calculus approach tomodeling and programming agents. In Foundations of Rational Agency, M. J. Wooldridgeand A. Rao, Eds. Kluwer Academic Pub;ishers, Dordrecht, 1999, pp. 275—299.[10] Lloyd, J. W. Foundations of Logic Programming, Second Edition. Springer-Verlag, 1987.[11] McCarthy, J. Situations, actions, and causal laws. In Semantic Proceedings of thetri-annual IFIP Conf, Minsky (ed), Machine Intelligence, eds: Meltzer, and Michie, vars.PublishersT Press. 1968.[12] McCarthy, J., and Hayes, P. J. Some philosophical problems from the standpoint ofartificial intelligence. Machine Intelligence 4 (1969), 463—502.[13] Moore, R. Reasoning about knowledge and action (technical report 191). Tech. rep.,SRI AI Center, 1980.[14] Pylyshyn, Z. W. Computation and cognition : toward a foundation for cognitive science.Cambridge, Mass. : MIT Press, 1984, 292 p., CALL NUMBER: BF311 .P93 1984, 1984.

A general approach to the implementation of action theories

SEDICI - Repositorio de la UNLP

A General Approach to the Implementation
of Action Theories
Gerardo I. Simari Diego R. Garc´ıa Gabriel R. Filocamo
Laboratorio de Investigacio´n y Desarrollo en Inteligencia Artificial
Departamento de Ciencias e Ingenier´ıa de la Computacio´n
Universidad Nacional del Sur. Av. Alem 1253, (8000) Bah´ıa Blanca, Argentina
Tel: ++54 291 4595135 - Fax: ++54 291 4595136
{gis,drg,grf}@cs.uns.edu.ar
Abstract
Much effort has been dedicated to provide a general model of agents working in complex
environments. This research focuses on the high level cognition used in determining the behavior
of the agent.
The language of the Situation Calculus represents a very useful way of modeling an agent’s
knowledge of its environment. One of its advantages is that there exist methods to derive an
executable program from a basic set of axioms. This program can then be used to determine
the actions that are necessary in order to accomplish certain goal states. The main objective
of this line of work is to obtain an automatic way of deriving such an executable program.
1 Introduction and Background
An important goal in the research programme of Artificial Intelligence is to develop autonomous
entities called agents. This autonomy is of utmost relevance for an agent to be considered
intelligent in the environment that it occupies; the study of the relationship among beliefs,
actions, and their consequences is one way to go in obtaining this objective.
The research we are conducting in the LIDIA lies within the area of Cognitive Robotics.
Work in this field is directed towards the provision of a uniform theoretical and implementation
framework for autonomous robotic or software agents that reason, act, and perceive in com-
plex environments. The difference between “traditional” robotics and cognitive robotics is the
emphasis placed on higher level cognition in determining agent behaviors.
One way of modeling an agent’s beliefs about the world, the possible actions it can take,
and its effects on the environment is the Situation Calculus [11, 12].
1.1 A Brief Introduction to the Situation Calculus
We will briefly introduce the Situation Calculus in order to provide the framework necessary
in the rest of the presentation.
The Situation Calculus is a second order language, quite suitable for representing dynam-
ically changing worlds. Each change in the world is the result of a specific action, which is
defined in the language. A situation stands for a history of the actions taken in the world
(simply a sequence of actions), and is represented as a first order formula. A special situation,
the constant s0, is used to represent the initial state. Every other situation is denoted by the
special functional symbol do(α, s); this means that action α executed in situation s leads to a
new situation, called do(α, s), where s is a situation built in the same way, or s0. For exam-
ple, for action grab(x) (which denotes grabbing object x), do(grab(x), s) is the situation which
results from grabbing object x in situation s.
There exists a certain type of relations that may vary from situation to situation, which
are called Relational Fluents. These are represented by predicates that take a situation term
as their last argument. Functions whose values depend on the situation are called Functional
Fluents, and also take a situation term as their last argument. For example, the relational fluent
nextTo(x), which holds in s0, no longer holds in do(walk(y), s0), where object x is different
from object y.
Another type of relations, which do not depend on the situation, are represented by pred-
icates without a situation parameter, and are called Non-Fluent predicates. Similarly, those
functions that are situation independent are called Non-Fluent functions.
The theory is completed by a variety of axioms, which capture the different aspects of the
world that is being modeled. These axioms are:
• Action Precondition Axioms:
The Action Precondition Axioms specify the requirements that must be satisfied for an
action to be executed. For this reason, there will be one axiom for each action. In
the definition of these axioms the predicate poss(a, s) is used, meaning that action a is
possible (can be executed) in situation s.
An Action Precondition Axiom will have the following general form poss(a, s) ≡ Υ, where
Υ is a first order formula.
• Effect Axioms The Effect Axioms specify how the relational and functional fluents’
values change after the execution of an action. In this case, there will be at least one
axiom for each fluent.
An Effect Axiom for a relational fluent f will have the following general form:
φf → f(tn, do(α, s)), and for a functional fluent g, γg → g(tn, do(α, s)) = r, where
tn = t1, t2, ..., tn are terms, and φf ,γg are first order formulas. The Effect Axioms for
relational fluents can be subdivided into positive and negative axioms. An axiom is
positive if the relational fluent f is not negated in
• Successor State Axioms
The Successor State Axioms provide a complete way of describing how the world evolves
as a response to the execution of actions. Each axiom describes how to compute a the
value of a fluent for the next situation, given its value for the current situation. Intuitively
the successor state axiom for a fluent f has the following structure:
True afterwards ⇔ [An action made it true ∨
True already and no action made it false]
The use of ⇔ means that the axiom will be true after the execution of the action if it is
made true or it stays true; and that it will be false otherwise. For each relational fluent
f , the successor state axiom has the following form:
f(xn, do(a, s)) ≡ γ+f (xn, a, s) ∨ f(xn, s) ∧ ¬γ−f (xn, a, s)
where γ+f (x
n, a, s) → f(xn, do(a, s)) and γ−f (xn, a, s) → f(xn, do(a, s)) are the positive
and negative normal form effect axioms for the fluent f , respectively.
2 Objectives
Central in this work is the goal of making the process of obtaining an executable implementation
of the action theory an automatic one. Therefore, what we want is to be able to compile the
language of the Situation Calculus into an object language such as Prolog. There are many
advantages to having such a compiler; the implementation of an action theory can be quite
tedious, and having an automatic processor can ease the design of such a theory. For example,
if the initial axioms suffer modifications, the final result can be quickly visualized.
There exists a process, based on work done by Lloyd and Topor [10], that can be used to
obtain a prolog program from the initial Situation Calculus axioms. They propose a set of
transformations suggested by Clark’s theorem [1] which reformulate the Action Precondition
and Successor State axioms in a way that results in a direct translation into Prolog clauses.
Once the basic axioms are specified, the automatic process should generally consist of the
following steps:
• Transform the Action Precondition Axioms:
— Obtain the if-halves from the Action Precondition Axioms.
— Apply the Lloyd-Topor transformation rules to the if-halves in order to obtain for-
mulas that are easy to implement (Lloyd-Topor normal form).
• Transform the Successor State Axioms:
— Obtain the if-halves from the Successor State Axioms.
— Apply the Lloyd-Topor transformation rules to the if-halves in order to obtain for-
mulas that are easy to implement (Lloyd-Topor normal form).
• Initial Database definition: Obtain the if-halves from the initial database definition.
These definitions obey the form:
F (xn, s0) ≡ ΨF (xn, s0)
where F (xn, s0) will not be negated in this case. This is due to the fact that negative
information is represented in Prolog by the Closed World Assumption (CWA). It should
also be noted that F cannot be a functional fluent in this case because this type of fluent
cannot be directly implemented in Prolog. Notwithstanding, an n-ary functional fluent
can be implemented as a (n+ 1)-ary Prolog predicate, where the last argument represents
the value of the fluent.
• Non-Fluent Predicate definition: Obtain the if-halves from the definitions, and then
apply the Lloyd-Topor transformation rules to these if-halves.
• Obtain a program in a given object language: Using the formulae obtained in the
previous steps, derive a fully functional program that models the specified action theory.
3 Current Research Line
Current work is being dedicated to the study of the applications of the Situation Calculus. One
way of understanding the implementation of an action theory seems to be the resolution of a
simple problem that covers all of the details of the process. One such problem is the Monkey
and Bananas Problem
The Monkey and Bananas Problem is a classic planning problem. It was proposed by John
McCarthy in 1963, and later reprinted in [11]. A monkey is in a room that contains a bunch of
bananas hanging from the ceiling, and a chair. The monkey can’t reach the bananas from the
floor. Nevertheless, if the chair were below the bananas, and the monkey were standing on top
of it, then the bananas would become reachable. One possible setup for an initial state is the
monkey not standing next to the chair, and the chair not sitting below the banana bunch.
One advantage to using this problem as a first approach is that, with a simple world like the
one described, there shouldn’t be obstacles that obscure the process of obtaining an executable
program from an initial formulation. Because there are few objects and actions, the number
of axioms needed to formalize an action theory will be reduced, which is useful in dealing with
errors committed in the initial stages of the resolution.
Once the program is obtained, it can be used to obtain plans in which a set of fluents are
valid (or not). For example, it could be used to obtain a plan which the monkey can use to
grab the bananas and get down from the chair.
Having solved a simple problem like the one described, it will be easier to approach broader
problems that could contain special cases that must be taken into account in the construction
of an automated tool.
References
[1] Clark, K. L. Negation as failure. In Logic and Databases (New York, 1978), H. Gallaire
and J. Minker, Eds., Plenum Press, pp. 293—322.
[2] Elkan, C. Reasoning about action in first-order logic. In Proceedings of the Conference
of the Canadian Society for Computational Studies of Intelligence (Vancouver, British
Columbia, May 1992).
[3] Finzi, A. I., Pirri, F., and Reiter, R. Open world planning in the situation calculus.
In Proceedings of the 7th Conference on Artificial Intelligence (AAAI-00) and of the 12th
Conference on Innovative Applications of Artificial Intelligence (IAAI-00) (Menlo Park,
CA, July 30— 3 2000), AAAI Press, pp. 754—760.
[4] Gelfond, M., and Lifschitz, V. Representing action and change by logic programs.
Journal of Logic Programming 17, 2,3,4 (1993), 301—323.
[5] Gelfond, M., Lifschitz, V., and Rabinov, A. What are the limitations of the
situation calculus? In Automated Reasoning: Essays in Honor of Woody Bledsoe, R. Boyer,
Ed. Kluwer Academic Publishers, Dordrecht, 1991, pp. 167—179.
[6] Hintikka, J. Knowledge and Belief. Cornell University Press, Ithaca, New York, 1977.
[7] Kowalski, R. A., and Sergot, M. J. A logic-based calculus of events. New Generation
Computing 4 (1986), 67—95.
[8] Lespe´rance, Y., Levesque, H. J., Lin, F., Marcu, D., Reiter, R., and Scherl,
R. B. A logical approach to high-level robot programming–A progress report. In Control
of the Physical World by Intelligent Systems, Papers from the 1994 AAAI Fall Sympo-
sium (Menlo Park, California, 1994), B. Kuipers, Ed., American Association for Artificial
Intelligence, American Association for Artificial Intelligence, pp. 79—85.
[9] Lespe´rance, Y., Levesque, H. J., and Reiter, R. A situation calculus approach to
modeling and programming agents. In Foundations of Rational Agency, M. J. Wooldridge
and A. Rao, Eds. Kluwer Academic Pub;ishers, Dordrecht, 1999, pp. 275—299.
[10] Lloyd, J. W. Foundations of Logic Programming, Second Edition. Springer-Verlag, 1987.
[11] McCarthy, J. Situations, actions, and causal laws. In Semantic Proceedings of the
tri-annual IFIP Conf, Minsky (ed), Machine Intelligence, eds: Meltzer, and Michie, vars.
PublishersT Press. 1968.
[12] McCarthy, J., and Hayes, P. J. Some philosophical problems from the standpoint of
artificial intelligence. Machine Intelligence 4 (1969), 463—502.
[13] Moore, R. Reasoning about knowledge and action (technical report 191). Tech. rep.,
SRI AI Center, 1980.
[14] Pylyshyn, Z. W. Computation and cognition : toward a foundation for cognitive science.
Cambridge, Mass. : MIT Press, 1984, 292 p., CALL NUMBER: BF311 .P93 1984, 1984.


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A general approach to the implementation of action theories

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