Knowledge Acquisition and Problem Solving

CS 785 Fall 2004 Knowledge Acquisition and Problem Solving Agent Problem Solving Gheorghe Tecuci tecuci@gmu.eduhttp://lac.gmu.edu/ Learning Agents Center and Computer Science Department George Mason University

Overview Knowledge-based agents Knowledge base: Object ontology + Rules Rule-based problem solving Control of the problem solving process

What are intelligent agents • An intelligent agent is a system that: • perceives its environment (which may be the physical world, a user via a graphical user interface, a collection of other agents, the Internet, or other complex environment); • reasons to interpret perceptions, draw inferences, solve problems, and determine actions; and • acts upon that environment to realize a set of goals or tasks for which it was designed. input/ sensors IntelligentAgent output/ user/ environment effectors

The architecture of an intelligent agent Implements a general problem solving method that uses the knowledge from the knowledge base to interpret the input and provide an appropriate output. Intelligent Agent Implements learning methods for extending and refining the knowledge in the knowledge base. Input/ Problem Solving Engine Sensors Learning Engine User/ Environment Output/ Ontology Rules/Cases/… Knowledge Base Effectors Data structures that represent the objects from the application domain, general laws governing them, actions that can be performed with them, etc.

Problem Solving Approach: Task Reduction Knowledge Base Object Ontology Reduction Rules Composition Rules • A complex problem solving task is performed by: • successively reducing it to simpler tasks; • finding the solutions of the simplest tasks; • successively composing these solutions until the solution to the initial task is obtained.

The structure of the knowledge base Knowledge Base = Object ontology + Task reduction rules The objectontology is a hierarchical description of the objects from the domain, specifying their properties and relationships. It includes both descriptions of types of objects (called concepts) and descriptions of specific objects (called instances). The task reductionrules specify generic problem solving steps of reducing complex tasks to simpler tasks. They are described using the objects from the ontology.

The structure of the knowledge base (cont.) Knowledge Base = Object ontology + Task reduction rules A task reduction rule is an IF-THEN structure that expresses the condition C under which a task T1 can be reduced to the simpler tasks T1a, or to a set of simpler tasks T11, … , T1n. T1 T1 C C T1a T11 T12 … T1n

Fragment of the object ontology governing_body ad_hoc_ governing_body established_ governing_body other_type_of_ governing_body state_government group_governing_body feudal_god_ king_government other_state_ government dictator other_ group_ governing_ body democratic_ government monarchy deity_figure representative_ democracy parliamentary_ democracy government_ of_Italy_1943 democratic_ council_ or_board autocratic_ leader totalitarian_ government government_ of_US_1943 government_ of_Britain_1943 chief_and_ tribal_council theocratic_ government police_ state military_ dictatorship fascist_ state religious_ dictatorship theocratic_ democracy communist_ dictatorship religious_ dictatorship government_ of_Germany_1943 government_ of_USSR_1943

The instances and the concepts are organized into generalization hierarchies like this hierarchy of governing bodies. Notice, however, that the generalization hierarchies are not always as strict as this one, where each concept is a subconcept of only one concept. For instance, the concept “strategic_raw_material” is both a subconcept of “raw_material” and a subconcept of “strategically_essential_resource_or_infrastructure_element”.

Fragment of feature ontology has_as_controlling_leader D: agent R: person has_as_religious_leader D: governing_body R: person has_as_god_king D: governing_body R: person has_as_monarch D: governing_body R: person has_as_military_leader D: governing_body R: person has_as_political_leader D: governing_body R: person has_as_commander_in_chief D: force R: person has_as_head_of_government D: governing_body R: person has_as_head_of_state D: governing_body R: person

An object feature is itself defined as a subconcept of another object feature, as illustrated in the previous slide. Therefore, the object features are also hierarchically organized. Notice that if feature1 is a subconcept of feature2, than the domain of feature1 should be less general than or at most as general as the domain of feature2. The same condition should hold between the ranges of the two features. For instance, “has_as_political_leader” is a subconcept of “has_as_controling_leader”. The domain of the first feature is “governing_body” which is less general than the domain of the second feature, which is “agent.” Also, the range of “has_as_political_leader” is the same as the range of “has_as_controling_leader”.

Object expressions One can define more complex concepts as logical expressions involving the basic concepts from the object ontology. In the following expression, for instance, ?O1 represents a force that has as industrial factor an industrial capacity that generates essential war materiel from the strategic perspective of a multi-member force that includes ?O1. ?O1 is forcehas_as_industrial_factor ?O2 ?O2 is industrial_capacity generates_essential_war_materiel_from_ the_strategic_perspective_of ?O3 ?O3 is multi_member_force has_as_member ?O1

Ontology matching Ontology matching allows one to answer complex questions about the knowledge represented in the ontology, as illustrated in the following: Question: Is there any force ?O1 that has as industrial factor an industrial capacity that generates essential war materiel from the strategic perspective of a multi-member force that includes ?O1? Answer: Yes, US_1943 is a force that has as industrial factor industrial_capacity_of_US_1943 that generates essential war materiel from the strategic perspective of the Allied_Forces_1943 which is a multi-member force that includes US_1943.

Ontology matching: example Object ontology Question Answer ?O1  US_1943 force ?O2  industrial_capacity_ of_US_1943 subconcept-of force single_member_force ?O3  Allied_forces_1943 subconcept-of instance-of single_state_force ?O1 industrial_capacity instance-of has_as_industrial_factor instance-of US_1943 industrial_capacity ?O2 has_as_industrial_factor multi_state_force instance-of generates_essential_war_materiel_from_ the_strategic_perspective_of has_as_member Industrial_capacity_of_US_1943 multi_state_force instance-of subconcept-of multi_state_alliance ?O3 subconcept-of generates_essential_war_materiel_from_ the_strategic_perspective_of equal_partner_multi_state_alliance Is there any force ?O1 that has as industrial factor an industrial capacity that generates essential war materiel from the strategic perspective of a multi-member force that includes ?O1? has_as_member instance-of Allied_forces_1943

This slide illustrates how the previous question has been answered. The question is represented by the ontology fragment from the left hand side of the slide. Answering the question is equivalent with finding values for the variables from this ontology fragment. To find these values, the agent maps this ontology fragment with the agent’s ontology, as illustrated bellow. The agent attempts to match ?O1 with US_1943. For this, it has to check that US_1943 and ?O1 have the same features. ?O1 is a Force. US_1943 is a single state force, which is a single-member force, which is a force. Therefore US_1943 is also a force. ?O1 has as industrial factor ?O2. US_1943 has as industrial factor industrial_capacity_of_US_1943. Therefore ?O2 has to match industrial_capacity_of_US_1943. ?O2 is an industrial capacity. Industrial_capacity_of_US_1943 is also an industrial capacity. However, ?O2 also generates essential war materiel from the strategic perspective of ?O3. Industrial_capacity_of_US_1943 generates essential war materiel from the strategic perspective of the Allied_Forces_1943. Therefore ?O3 has to match Allied_Forces_1943. ?O3 is an instance of a multi-member force and has as member ?O1, which has previously matched with US_1943. Allied_Forces_1943 is also multi-member force and has as member US_1943. Therefore, the question: Is there any force ?O1 that has as industrial factor an industrial capacity that generates essential war materiel from the strategic perspective of a multi-member force that includes ?O1? Has the answer: Yes, US_1943 is a force that has as industrial factor industrial_capacity_of_US_1943 that generates essential war materiel from the strategic perspective of the Allied_Forces_1943 which is a multi-member force that includes US_1943.

Sample task A task is a representation of anything that an agent may be asked to perform. General task: Identify and test a strategic COG candidate corresponding to the ?O1 Identify and test a strategic COG candidate corresponding to the economy of a force The economy is ?O1 Condition ?O1 is type_of_economy INFORMAL STRUCTURE OF THE TASK FORMAL STRUCTURE OF THE TASK Instantiated task: Identify and test a strategic COG candidate corresponding to the economy of a force The economy is economy_of_US_1943 Identify and test a strategic COG candidate corresponding to the economy_of_US_1943 INFORMAL STRUCTURE OF THE TASK FORMAL STRUCTURE OF THE TASK

Exercise How could the agent generate plausible formalizations? Identify and test a strategic COG candidate for Sicily_1943 Identify and test a strategic COG candidate for a scenario The scenario is Sicily_1943 What kind of scenario is Sicily_1943? Sicily_1943 is a war scenario Identify and test a strategic COG candidate for Sicily_1943 which is a war scenario Identify and test a strategic COG candidate for a scenario which is a war scenario The scenario is Sicily_1943

A task is a representation of anything that an agent may be asked to perform. The informal structure of a task is a phrase in free-form English with variables. The formal structure of a task contains a task name and several task features. The task name is an abstract English phrase with no variables. The task features are also phrases, but they may contain variables, such as ?O1. The formal structure of the task contains also a condition that restricts the values that the variable can take. For example, in the case of the task from this slide, ?O1 has to be an instance of the concept type_of_economy. Replacing the variables with objects that satisfy the condition leads to the creation of specific tasks, as illustrated at the bottom of this slide.

Sample task reduction rule A rule is an ontology-based representation of an elementary problem solving process. IF Identify and test a strategic COG candidate corresponding to the ?O1 IF Identify and test a strategic COG candidate corresponding to the economy of a force The economy is ?O1 QuestionWhat is the type of ?O1 ? Answerindustrial_economy Condition?O1 is industrial_economy THEN Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy The industrial economy is ?O1 THEN Identify and test a strategic COG candidate corresponding to the ?O1 which is an industrial_economy INFORMAL STRUCTURE OF THE RULE FORMAL STRUCTURE OF THE RULE

A rule is a representation of a generic problem-solving step. It has an informal structure and a formal structure. Let us look at the informal structure first. It should be read as follows: IF I have to perform the task Identify and test a strategic COG candidate corresponding to the ?O1 And the question “What is the type of ?O1 ?” Has the answer “industrial_economy” THEN I should Identify and test a strategic COG candidate corresponding to the ?O1 which is an industrial_economy Notice that the informal structure of the rule is very similar with the form we used to illustrate problem solving through task reduction. This is because the agent uses the informal structure to communicate with the user. To reason, the agent uses an equivalent IF-THEN formal structure. This structure indicates the condition under which the task from the IF part can be reduced to the task from the THEN part. It should be read as follows: IF I have to perform the task Identify and test a strategic COG candidate corresponding to the economy of a force, where the economy is ?O1 And the following condition is satisfied: ?O1 is an industrial economy THEN I should Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy, where the industrial economy is ?O1

Another task reduction rule IF Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economyThe industrial economy is ?O1 IF Identify and test a strategic COG candidate corresponding to the ?O1 which is an industrial_economy QuestionWho or what is a strategically critical element with respect to the ?O1 ? Answer?O2 because it is an essential generator of war_materiel for ?O3 from the strategic perspective Condition?O1 is industrial_economy ?O2 is industrial_capacitygenerates_essential_war_materiel_from_ the_strategic_perspective_of ?O3 ?O3 is multi_state_force has_as_member ?O4 ?O4 is force has_as_economy ?O1 has_as_industrial_factor ?O2 THEN Identify ?O2 as a COG candidate with respect to the ?O1 Test ?O2 which is a strategic COG candidate with respect to the ?O1 THEN Identify a strategically critical element as a COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 Test a strategically critical element which is a strategic COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 INFORMAL STRUCTURE OF THE RULE FORMAL STRUCTURE OF THE RULE

Let us consider the informal structure of this more complex rule. It should be read as follows: IF I have to perform the task Identify and test a strategic COG candidate corresponding to the ?O1 which is an industrial economy And the question “Who or what is a strategically critical element with respect to the ?O1 ?” Has the answer “?O2 because it is an essential generator of war materiel for ?O3 from the strategic perspective” THEN I should perform the following two tasks Identify ?O2 as a COG candidate with respect to the ?O1 Test ?O2 which is a strategic COG candidate with respect to the ?O1 The formal structure should be read as follows: IF I have to perform the task Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy, where the industrial economy is ?O1 And the following condition is satisfied: ?O1 is an industrial economy, and ?O2 is an industrial capacity that generates essential war materiel from the strategic perspective of ?O3, and ?O3 is a multi-state force that has ?O4 as one of its members, and ?O4 is a force that has as economy ?O1, and as industrial factor ?O2 THEN I should perform the following two tasks Identify a strategically critical element as a COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 Test a strategically critical element which is a strategic COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 Notice that the elements of the condition are concepts and relationships from the object ontology.

The generality of the ontology and rules Which are more general, the object descriptions from the object ontology, or the rules?

The generality of the ontology An object ontology is characteristic to an entire application domain, such as military or medicine. In the military domain the object ontology will include descriptions of military units and of military equipment. These descriptions are most likely needed in almost any specific military application. Because building the object ontology is a very complex task, it makes sense to reuse these descriptions when developing a knowledge base for another military application, rather than starting from scratch.

The generality of the rules The rules from the knowledge base are specific to a particular application and even to a particular subject matter expert. Consider, for instance, the agents discussed before, the agent that critiques courses of action with respect to the principles of war, and the agent for center of gravity analysis. While both agents need to reason with opposing forces, their reasoning rules are very different, being specific not only to their particular application (course of action critiquing versus center of gravity analysis), but also to the subject matter expertise whose knowledge they encode.

Illustration of rule-based task reduction Identify and test a strategic COG candidate corresponding to the economy of a force The economy is economy_of_US_1943 ?O1  economy_of_US_1943 IF Identify and test a strategic COG candidate corresponding to the economy of a force The economy is ?O1 Rule condition industrial_economy Condition?O1 is industrial_economy instance_of ?O1 = economy_US_1943 THEN Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy The industrial economy is ?O1 Object ontology ?O1  economy_of_US_1943 industrial_economy instance_of Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy The industrial economy is economy_of_US_1943 economy_US_1943

Let us now see how the agent uses the rules in problem solving. Let us suppose that the current problem solving task is: Identify and test a strategic COG candidate corresponding to the economy of a force The economy is economy_of_US_1943 The agent will look into its knowledge base for a rule that has this type of task in the IF part. Such a rule is shown in the right hand side of the slide. As one can see, the IF task becomes identical with the task to be performed if ?O1 is replaced with economy_of_US_1943. Next the agent has to check that the condition of the rule is satisfied for this value of ?O1. The left hand side of the slide shows the rule’s condition. This is satisfied because the object ontology contains the information that economy_of_US_1943 is an industrial economy. Therefore the IF task can be reduced to the THEN task: Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy The industrial economy is economy_of_US_1943

Rule application Identify and test a strategic COG candidate corresponding to the economy_of_US_1943 ?O1  economy_of_US_1943 IF Identify and test a strategic COG candidate corresponding to the ?O1 QuestionWhat is the type of ?O1 ? Answerindustrial_economy What is the type of economy_of_US_1943 ? industrial_economy THEN Identify and test a strategic COG candidate corresponding to the ?O1 which is an industrial_economy Identify and test a strategic COG candidate corresponding to the economy_of_US_1943 which is an industrial_economy ?O1  economy_of_US_1943

As discussed before, there is also an informal structure of the rule, containing the informal structure of the tasks, a question and an answer. The right hand side of this slide shows the instantiation of the informal structure of the rule. This instantiation produces the reduction from the left hand side of the slide. Therefore, the agent can show the user the informal structure of the task reduction steps, which are in English, and therefore easier to follow.

Illustration of rule-based task reduction Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy The industrial economy is economy_of_US_1943 ?O1  economy_of_US_1943 Rule condition IF Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economyThe industrial economy is ?O1 industrial_economy instance-of force Condition?O1 is industrial_economy ?O2 is industrial_capacitygenerates_essential_war_materiel_from_ the_strategic_perspective_of ?O3 ?O3 is multi_state_force has_as_member ?O4 ?O4 is force has_as_economy ?O1 has_as_industrial_factor ?O2 economy_of_US_1943 instance-of has_as_economy ?O4 industrial_capacity has_as_industrial_factor instance-of ?O2 multi_state_force generates_essential_war_materiel_from_ the_strategic_perspective_of has_as_member THEN Identify a strategically critical element as a COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 Test a strategically critical element which is a strategic COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 instance-of ?O3

Let us continue the illustration of the task reduction process. The new problem solving task is: Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy The industrial economy is economy_of_US_1943 The agent will look in its knowledge base for a rule that has this type of task in the IF part. Such a rule is shown in the right hand side of the slide. As one can see, the IF task becomes identical with the task to be performed if ?O1 is replaced with economy_of_US_1943. Next the agent has to check that the condition of the rule is satisfied for this value of ?O1. The left hand side of the slide shows what conditions need to be satisfied by economy_of_US_1943, ?O2, ?O3 and ?O4. This condition is satisfied if there are instances of ?O2, ?O3 and ?O4 in the object ontology that satisfy all the relationships specified in the left hand side of the slide.

Matchings Object ontology Rule condition force industrial_economy subconcept-of instance-of single_member_force force industrial_economy economy_of_US_1943 subconcept-of instance-of instance-of single_state_force has_as_economy economy_of_US_1943 ?O4 instance-of industrial_capacity has_as_economy has_as_industrial_factor instance-of US_1943 industrial_capacity has_as_industrial_factor ?O2 multi_state_force instance-of generates_essential_war_materiel_from_ the_strategic_perspective_of has_as_member Industrial_capacity_of_US_1943 multi_state_force instance-of subconcept-of multi_state_alliance ?O3 subconcept-of generates_essential_war_materiel_from_ the_strategic_perspective_of equal_partner_multi_state_alliance ?O2  industrial_capacity_of_US_1943 ?O3  Allied_forces_1943 has_as_member ?O4  US_1943 instance-of Allied_forces_1943

The partially instantiated condition of the rule, shown in the left hand side of the slide, is matched successfully with the object ontology fragment shown in the right hand side of the slide. ?O4 matches US_1943 because both have the same features and the corresponding values of these features also match. Both ?O4 and US_1943 are forces. Indeed, US_1943 is an instance of a single-state force, which is a subconcept of a single-member force, which is a subconcept of a force. Therefore, using the transitivity rule discussed above, US_1943 is a force. Both ?O4 and US_1943 have the feature has_as_economy with the value economy_of_US_1943. Finally, both ?O4 and US_1943 have the feature has_as_industrial_factor and the corresponding values are ?O2 and industrial_capacity_of_US_1943, respectively. Now one has to show that ?O2 and industrial_capacity_of_US_1943 match. ?O2 is an industrial capacity, and industrial_capacity_of_US_1943 is an industrial capacity. Both ?O2 and industrial_capacity_of_US_1943 have the feature generates_essential_war_materiel_from_the_strategic_perspective_of, with the values ?O3 and Allied_forces_1943, respectively. Therefore one has to show that ?O3 and Allied_forces_1943 match. ?O3 is a multi_state_force. Allied_forces_1943 is an equal_partner_multi_state_alliance, which is a multi_state_alliance, which is a multi_state_force. Therefore Allied_forces_1943 is also a multi_state_force. Finally, both ?O3 and Allied_forces_1943 have the feature has_as_member with the values ?O4 and US_1943, respectively. Moreover, ?O4 and US_1943 have already matched. Therefore the entire matching was successful. As the result of these matching, the rule’s variables are instantiated as follows: ?O2  industrial_capacity_of_US_1943 ?O3  Allied_forces_1943 ?O4  US_1943

Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economy The industrial economy is economy_of_US_1943 ?O1  economy_of_US_1943 IF Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economyThe industrial economy is ?O1 Rule condition industrial_economy Condition?O1 is industrial_economy ?O2 is industrial_capacitygenerates_essential_war_materiel_from_ the_strategic_perspective_of ?O3 ?O3 is multi_state_force has_as_member ?O4 ?O4 is force has_as_economy ?O1 has_as_industrial_factor ?O2 instance-of force economy_of_US_1943 instance-of has_as_economy ?O4 industrial_capacity has_as_industrial_factor instance-of ?O2 multi_state_force THEN Identify a strategically critical element as a COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 Test a strategically critical element which is a strategic COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 generates_essential_war_materiel_from_ the_strategic_perspective_of has_as_member instance-of ?O3 Identify a strategically critical element as a COG candidate with respect to an industrial economy The strategically critical element is industrial_capacity_of_US_1943 The industrial economy is economy_of_US_1943 Test a strategically critical element which is a strategic COG candidate with respect to an industrial economy The strategically critical element is industrial_capacity_of_US_1943 The industrial economy is economy_of_US_1943 ?O1  economy_of_US_1943 ?O2  industrial_capacity_of_US_1943 ?O3  Allied_forces_1943 ?O4  US_1943

The rule’s condition is satisfied for the following instantiations of the variables: ?O1  economy_of_US_1943 ?O2  industrial_capacity_of_US_1943 ?O3  Allied_forces_1943 ?O4  US_1943 Therefore the IF task can be reduced to the following THEN tasks: Identify a strategically critical element as a COG candidate with respect to an industrial economy The strategically critical element is industrial_capacity_of_US_1943 The industrial economy is economy_of_US_1943 Test a strategically critical element which is a strategic COG candidate with respect to an industrial economy The strategically critical element is industrial_capacity_of_US_1943 The industrial economy is economy_of_US_1943 Disciple uses the informal structure of this rule to generate the sentences to be shown to the user, as illustrated in the next slide.

Generating the informal reduction Identify and test a strategic COG candidate corresponding to the economy_of_US_1943 which is an industrial_economy ?O1  economy_of_US_1943 IF Identify and test a strategic COG candidate corresponding to the ?O1 which is an industrial_economy QuestionWho or what is a strategically critical element with respect to the ?O1 ? Answer?O2 because it is an essential generator of war_materiel for ?O3 from the strategic perspective Who or what is a strategically critical element with respect to the economy_of_US_1943? industrial_capacity_of_US_1943 because it is an essential generator of war materiel for Allied_forces_1943 from the strategic perspective THEN Identify ?O2 as a COG candidate with respect to the ?O1 Test ?O2 which is a strategic COG candidate with respect to the ?O1 Identify industrial_capacity_of_US_1943 as a COG candidate with respect to the economy_of_US_1943 Test industrial_capacity_of_US_1943 which is a strategic COG candidate with respect to the economy_of_US_1943 ?O1  economy_of_US_1943 ?O2  industrial_capacity_of_US_1943 ?O3  Allied_forces_1943 ?O4  US_1943

Successive rule applications Identify and test a strategic COG candidate corresponding to the economy_of_US_1943 Rule_1 What is the type of economy_of_US_1943 ? industrial_economy Identify and test a strategic COG candidate corresponding to the economy_of_US_1943 which is an industrial_economy Rule_2 Who or what is a strategically critical element with respect to the economy_of_US_1943? industrial_capacity_of_US_1943 because it is an essential generator of war materiel for Allied_forces_1943 from the strategic perspective Identify industrial_capacity_of_US_1943 as a COG candidate with respect to the economy_of_US_1943 Test industrial_capacity_of_US_1943 which is a strategic COG candidate with respect to the economy_of_US_1943

Task reduction rule with “Except when” conditions In addition to the regular rule condition that needs to be satisfied, a rule may contain one or several except when conditions that should not be satisfied for the rule to be applicable. IF <task> Condition<condition 1> Except when condition<condition 2> Except when condition<condition n> THEN <subtask 1> … <subtask m>

Plausible version space rule IF Identify and test a strategic COG candidate corresponding to the economy of a force which is an industrial economyThe industrial economy is ?O1 Plausible upper bound condition?O1 is type_of_economy ?O2 is economic_factorgenerates_essential_war_materiel_from_the_strategic_perspective_of ?O3 ?O3 is multi_state_force has_as_member ?O4 ?O4 is force has_as_economy ?O1 has_as_industrial_factor ?O2 Plausible lower bound condition?O1 is industrial_economy ?O2 is industrial_capacitygenerates_essential_war_materiel_from_the_strategic_perspective_of ?O3 ?O3 is multi_state_alliance has_as_member ?O4 ?O4 is single_state_force has_as_economy ?O1 has_as_industrial_factor ?O2 THEN Identify a strategically critical element as a COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1 Test a strategically critical element which is a strategic COG candidate with respect to an industrial economy The strategically critical element is ?O2 The industrial economy is ?O1

A rule may be partially learned. In this case it will have two applicability conditions, a plausible upper bound condition that is likely to be more general than the exact condition, and a plausible lower bound condition, that is likely to be less general than the exact condition. The plausible upper bound condition allows the rule to be applicable in many analogous situations, but the result may not be correct. The plausible lower bound condition allows the rule to be applicable fewer situations but the result is very likely to be correct. The agent will apply this rule to solve new problems and its success or failure will be used to further refine the rule. In essence, the two conditions will converge toward one another (usually through the specialization of the plausible upper bound condition and the generalization of the plausible lower bound condition), both approaching the exact applicability condition of the rule. Rule refinement could lead to a complex task reduction rule, with additional Except-When conditions which should not be satisfied in order for the rule to be applicable.

Overview Knowledge-based agents An agent for center of gravity determination Problem solving through task reduction Knowledge base: Object ontology + Rules Rule-based problem solving Control of the problem solving process Tools for representation and reasoning

The search space for problem solving Let us consider the problem solving task 'Pa‘ and let R1, R2, and R3 be the applicable rules which indicate the reduction of 'Pa' to ‘C(Pb,Pc)', to 'Pd', and to ‘C(Pe,Pf,Pg)', respectively. Therefore, to solve the problem 'Pa', one may either: - solve the problems 'Pb' and 'Pc', or - solve the problem 'Pd', or - solve the problems 'Pe', 'Pf' and 'Pg'. One may represent all these alternatives in the form of an AND/OR tree.

The search space for problem solving (cont.) The node 'Pa' is called an OR node since for solving the problem 'Pa' it is enough to solve ‘C(Pb, Pc)' OR to solve 'Pd' OR to solve ‘C(Pe, Pf, Pg)'. The node ‘C(Pb, Pc)' is called an AND node since for solving it one must solve both 'Pb' AND 'Pc'. The AND/OR tree may be further developed by considering all the rules applicable to its leaves (Pb, Pc, Pd, Pe, Pf, Pg), building the entire search space for the problem 'Pa'. This space contains all the solutions to 'Pa'.

Solution tree To find a solution one needs only to build enough of the tree to demonstrate that 'Pa' is solved. Such a tree is called a solution tree. A node is solved in one of the following cases: - it is a terminal node (a primitive task with known solution); - it is an AND node whose successors are solved; - it is an OR node which has at least one solved successor.

Solution tree (cont.) Once the problem solver detects that a node is solved it sends this information to the ancestors of the node. When the node 'Pa' becomes solved, one has found a solution to 'Pa'. solved solved solved solved solved

Solution tree (cont.) • A node is unsolvable in one of the following cases: • - it is a nonterminal node that has no successors (i.e. a nonprimitive problem to which no rule applies); • - it is an AND node which has at least one unsolvable successor; • - it is an OR node which has all the successors unsolvable.

Solution tree (cont.) Once the problem solver detects that a node is unsolvable it sends this information to the ancestors of the node. If the node 'Pa' becomes unsolvable, then no solution to 'Pa' exists. unsolvable solved unsolvable

Knowledge Acquisition and Problem Solving