Prepared for: STIDS 2014

18 November 2014

Presented by:Erik Thomsen

Ontology-Driven Planning

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Motivations and Approach Types Typed Ontologies Typed Ontology-driven Planning Systems Conclusions

Agenda

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Motivations and Approach Types Typed Ontologies Typed Ontology-driven Planning Systems Conclusions

Agenda

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Rather than locked in time, or until explicitly updated, a Living Plan is continuously and increasingly maintained in a state of satisfactory Coherence and Relevance in response to significant changes in the actual or anticipated execution environment.

President Obama

Inauguration Address 2012

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The “Living Plan”

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Key Definitions: Coherence

Coherence: mutually-supportive related/associated plans as well as independent plans (i.e. other component, allied, service, etc. plans).

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Key Definitions: Coherence

Coherence: mutually-supportive related/associated plans as well as independent plans (i.e. other component, allied, service, etc. plans).

Example: Space and Cyber planning in-coherent

Non-kinetic planning: preservation of a particular cell phone tower and associated links for listening for intelligence value.

Kinetic planning (ATO): destruction of the same tower. The cell tower is on an approved target list.

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Key Definitions: Relevance

Relevance: a satisfactory plan with respect to significant external factors such as changes in weather, enemy activity, new weapon systems on the battlefield, Commander’s intent, and so on.

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Key Definitions: Relevance

Relevance: a satisfactory plan with respect to significant external factors such as changes in weather, enemy activity, new weapon systems on the battlefield, Commander’s intent, and so on. Example of insignificant change

Increased movement of surface-to-surface missiles (SSM) from known garrisons to known launch locations in western Area of Operations (AO)

Expected moves to and from known locations.

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Key Definitions: Relevance

Relevance: a satisfactory plan with respect to significant external factors such as changes in weather, enemy activity, new weapon systems on the battlefield, Commander’s intent, and so on. Example of insignificant change

Increased movement of surface-to-surface missiles (SSM) from known garrisons to known launch locations in western Area of Operations (AO)

Expected moves to and from known locations. Example of significant change

Detected movement of previously undetected SSMs Newly identified threat requires updated planning in order to service and

meet change in updated CC’s intent. Would induce changes in aircraft numbers, weapons availability, ISR

support, timing, etc.

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Plan phase Development Execution Post execution

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Key Definitions

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A “Smart Information Grid” for Living Plans

Plan A

Plan B

Assessment

Planning

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Motivations and Approach Types Typed Ontologies Typed Ontology-driven Planning Systems Conclusions

Agenda

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Is a semantically rich typing system Qualitative and quantitative information

Full support for units of all kinds Hierarchies, Networks..

Links external messages with internal models Types have logical and physical form

Symbols are physical representations of logical type roles

LC Type Logic

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Types Collections of values of some unit, with orderings and

potential operators associated with those values, Number system, Dimension, Hierarchy, Measure, Attribute, Variable, Data

type, Network, Directed graph, subject or predicate, function/argument

Schemas Particular collections of ordered types capable of supporting

the definition and execution of expressions. Model, Multidimensional hypercube or multi-cube, Relation, Class diagram,

Frame, Script, System of equations, Shape file, Process, application and Program

LC Type Logic: Types and Schemas

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Query and calculation Queries , Assertions Calculations Representation specification

Schema-defining Type ordering relationship Schema-manipulating Operation specification

Type-defining Units specification Value specification Representation specification

LC Type Logic: Expressions

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Type labels vs. Values vs. operators vs. meta operators

Color.green = Get_color(Object.ball) Integer.9 = Sum(Int.7, Int.2) Profit{$}.1000 = Avg((Obj.Shoes, Profit) , (Obj.Socks, Profit)) Ops_assess_score.0.9 = Assess(Plan_id.72, Phase.post_exe) Author_name.Scott = Get_author_name(Book.Waverly)

Anatomy of a typed expression

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LC Expression Structures

L = LocationC = Content

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LC Expression Structures

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LC Expression Structures

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LC Model Architecture Overview

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Info artifactLogical rep

Info artifact

Phys rep

Logical rep

Phys rep

Phys rep

Logical rep

Phys rep

Logical rep

Verbal Agent 1 Verbal Agent 2

• Any

• Categorical

• Boolean

• Natural#

• Exp#

• Truthvalue

Processing schema

Processing schema

Types

ExpressionsSchemasIn Use

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1st order: Operators that apply to 1+ typed values

Sum/Difference/Product/Quotient Parent, child Next, prev

2nd order: Operators that apply to 1+ typed expressions

Truth functions Truth tests Propositional attitudes

Belief, want, source Sometime attitudes

Heard, felt, said

Expression Classes

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Named collections and ranges

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1.1.1 Type-based functions A value of a Rational = R.unit.instance

A named collection of instances of some unit “Collection_n” = R.unit.(instance, instance, instance)

A named collection of instance-unit pairs “Mixed collection_n” = R.(unit.instance), (unit.instance), (unit.instance)

1.1.2 Named instance ranges for a given unit A named range is a kind of abstract object whose id should be handled in the same way as other object ids.

A named range of instances of some unit w/ step size =1: Range_1 = R.unit.(range: instance, instance) where the first instance listed is the first instance in the range and the second instance listed is the last instance in the range.

Range_1 = R.1.(range:5, 15)

Read: Range_1 is defined as the range of instances from 5 to 15 inclusive of the unit size 1. The values 5 and 15 (i.e. the instances 5 and 15 of unit 1) are boundary values for the named range. The lower valued boundary is called the lower boundary value. The upper valued boundary is called the upper boundary

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Functions on named instance ranges

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1.1.1.1 Functions on named instance ranges Intra_unit_Set_compare (Range_1, Range_2) > Range classification

//For two ranges that share the same unit, ‘Intra_unit_Set compare’ compares the instances of the two ranges//. Possible classifications highlighted in red are as follows:

If two named ranges defined on the Rationals share the same unit and step size and

share the same boundary values, the two ranges are equivalent. the upper boundary of range 1 is equivalent to the lower boundary of range two, the two

ranges are adjacent 2 or more values in range 1 have equivalent values in range 2 and at least one value in range 1

has no equivalent in range 2 and vice versa (Alternatively one could state that the count of values in the intersection of ranges 1 and 2 >= 2 and the count of disjuncts for each of ranges 1 and 2 >=1) the two ranges are overlapping

Every value in range 1 has an equivalent value in range 2 And there exists at least 1 value in range 2 that is lower than the lower boundary of range 1 And there exists at least one value in range 2 that is greater than the upper boundary of range 1, Range 1 is contained within range 2

Every value in range 1 has an equivalent value in range 2 And there exists at least 1 value in range 2 that is lower than the lower boundary of range 1 OR greater than the upper boundary of range 1 And one of the boundary values for Range 1 is equivalent to a boundary value in range 2, Range 1 is contained in and shares a boundary with range 2

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Functions on named unit ranges

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Inter_unit_Set_compare (Range_1, Range_2) > Range classification

//For two ranges defined on the Rationals, ‘Inter_unit_Set compare’ compares the units of the two unit ranges//. Possible classifications highlighted in red are as follows:

If for two named unit ranges with equivalent step sizes are defined on the Rationals and

They share the same boundary units, the two unit ranges are equivalent. the upper boundary of range 1 is equivalent to the lower boundary of range two, the two unit

ranges are adjacent 2 or more units in range 1 have equivalent units in range 2 and at least one unit in range 1 has

no equivalent in range 2 and vice versa (Alternatively one could state that the count of units in the intersection of ranges 1 and 2 >= 2 and the count of disjuncts for each of ranges 1 and 2 >=1) the two ranges are overlapping

Every unit in range 1 has an equivalent unit in range 2 And there exists at least 1 unit in range 2 that is lower than the lower boundary of range 1 And there exists at least one unit in range 2 that is greater than the upper boundary of range 1, Range 1 is contained within range 2

Every unit in range 1 has an equivalent unit in range 2 And there exists at least 1 unit in range 2 that is lower than the lower boundary of range 1 OR greater than the upper boundary of range 1 And one of the boundary units for Range 1 is equivalent to a boundary unit in range 2, Range 1 is contained in and shares a unit boundary with range 2

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Functions on Ragged Categorical hierarchies

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1.1.1 Type-based functions A value of a Ragged Categorical Hierarchy ‘RCH’ = RCH.value

A named range of values relative to a given ‘seed’ value “RCH_Range_n” =

RCH.value.@under RCH.value.up.X RCH.value.Down.X RCH.value.children RCH.value.parent

A named collection of explicit values “Collection_n” = RCH.(value, value, value)

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Functions of named RCH ranges

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Value_Set_compare (RCH_range_1, RCH_range_2) > Range classification

//For two RCH_ranges, Value_Set compare compares the values of the two ranges//

Possible classifications highlighted in red are as follows:

If two named RCH_ranges share the same seed value and

Share the same function, the two ranges are equivalent. Do not share the same function then

o If values match.. equivalent o

Every value in range 1 has an equivalent value in range 2 And there exists at least 1 value in range 1 that is not included in range_2 Range 2 is contained in and shares a boundary with range 1

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Value The temperature value in the room = 68 {degrees}

Label The type defined by the OA team today

= Sentiment penetration{Type_id} The types used as contents in my OA schema

= Hit/Target , civilian casualties/enemy casualties

Operator The operator that converts Int.7, Int.2 into Int.9 = SUM The operator ‘SUM’ is not available to the type List

Expression Flavors

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Primitive Requirement:Supporting assertions and negations

Any Type must have two or more values There must be at least one unit to which the instances belong Every instance must be identifiable and exclusively ORed with

every other in the unit All values must be fully connected via the Type’s atomic

operators: For numeric types, values and atomic operators are co-defined

Well-Formed Types

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External Reps• Create Type Color

With Units CategoricalConstraint = {1, 2, 3, 4, 5}Phys Rep AS English symbolsRed, Blue, Green, Orange, Yellow

• [Obj.i] ~ Action.protect, Objec.master

Phys rep AS ‘BARK’

Internal Reps• Create Type Product

With Units CategoricalPhys rep AS 8 BYTE STRING

• Create Type CostWith Units DollarsPhys Rep AS INT

• Create Type SalesWith Units DollarsPhys Rep AS IEE754 FLOAT

Logical specification vs. physical representation

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Type Grammar

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Senseful AS IS Why sensefulTnv, Tmv AssertionTnv, Tmv Q about Tmv Tnv Tmf Command to execute f on vTnv, Tmf Question about f in f(x)Tnv, Tmf Question about x in f(x)

Sensefulcombinations

Senseless AS IS No assertion, question, command: e.g.,Tnv Tmv Color shapeTnv, Tmf Color actionTnf, Tmf Sit sitTnf, Tmf Sit actionTnf, Tmf Action action

Senselesscombinations

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Built-in processes that determine how the system behaves based on new interpreted information. • Purported expression = f(2+ type values |operators, type_ids)

• Logical state = f(purported expression)

• Equivalent locations = f(Given location)

• Confidence = f(Expression.Assertion)

• Related assertions = f(Given Expression.Assertion(s))

• Answer = f(Expression.Question)

Grammatical Schemas

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Motivations and Approach Types Typed Ontologies Typed Ontology-driven Planning Systems Conclusions

Agenda

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Slot managing

Nesting Nested Schema Role

Slot filling

Substance

Thingevent

Objects

Actions

Attribute

Monadic

Complex

Location/Void

Time Space

For any Verbal Representational Interaction that is constructed from typed expressions

Root Types

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Space Types and Structures

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1.1.1 “1-Space” ‘Distance’ {{Meter}, {Kilometer}, {Centimeter}, …}, {{Foot}, {Mile}, {Inch}, …}, …

‘Angle’ {Degrees}, {Radians}

1.1.2 “2-Space” ‘2DCoordinate’ {Planar Coordinate}, {Polar Coordinate}

‘Planar Coordinate’ {(Distance, Distance)}

‘Polar Coordinate’ {(Angle, Distance)}

‘Area’ {* Distance Distance}

1.1.3 “3-Space” ‘3DCoordinate {SphereCoordinate}, {BlockCoordinate}, {CylinderCoordinate}

‘Block Volume’ {* Distance Distance Distance}

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Translating between Subjective and Objective Coordinates

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Time _1

Time _2

Object-centric coordinatesEnvironment-centric coordinates

Obj_1Obj_2

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ThingEvent Hierarchy

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Physical ThingEvent

Lifeform ThingEvent

Instinctual ThingEvent

Perceptual ThingEvent

Verbal ThingEvent

Object Part Action Part

Object Part

Object Part

Object Part

Object Part

Action Part

Action Part

Action Part

Action Part

Legend part-of links is-a links

Lesser Complexity

Greater Complexity

Physical ThingEvent

Lifeform ThingEvent

Instinctual ThingEvent

Perceptual ThingEvent

Verbal ThingEvent

Object Part Action Part

Object Part

Object Part

Object Part

Object Part

Action Part

Action Part

Action Part

Action Part

rodent hides

digests

falls

Physical ThingEvent

Lifeform ThingEvent

Instinctual ThingEvent

Perceptual ThingEvent

Verbal ThingEvent

Object Part Action Part

Object Part

Object Part

Object Part

Object Part

Action Part

Action Part

Action Part

Action Part

hidesrodent

cat

person

Physical ThingEvent

Object Part Action Part

• natural physical object• rock• air

• manufactured physical object• bomb• road• vehicle

• plane• building

• hospital• barracks

• food

• hit• move

• drift• explode• drop• destroy• miss• roll• melt• burn• enter• exit• evaporate

Objects Actions

Lifeform ThingEvent

Object Part Action Part

Energy Processing

System

Reproductive System

Inflow System

Outflow System

Seed Germinator

System

Seed Generator

System

• plant• tree

• amoeba• mushroom

• metabolize• photosynthesize• intake• expel

Objects Actions

Instinctual ThingEvent

Object Part Action Part

Sensor System

Decision System

Sensor System

• insect• spider• beetle

• reptile• snake

• amphibian• frog

• swim• grasp• hold• push• fly• crawl

Objects Actions

Perceptual ThingEvent

Object Part Action Part

Sensor System

Perceptual System

Motor System

Sensor World Space

Knowledge Space Motor

• dog• cat• infant

• hear• see• remember• forget

Objects Actions

Verbal ThingEvent

Object Part Action Part

Sensor System

Perceptual System

Motor System

Motor 2Motor 1Knowledge Space

World SpaceSensor 2Sensor 1

Symbol• Word symbol• Sentence symbol• Document

input output

Symbol• Word symbol• Sentence symbol• Document• person

• man• woman• civilian

• read• suggest• analyze• explain

Objects Actions

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Interpreting expressions in LC form

E:

<Time/Space> unknown

Loc:

Con:

Loc:

Con:

“plane” (Tr: Object.mech_obj.vehicle, v: plane)“red” (Tr: Attribute.color, v: red, t: “before”)Con:

Loc:

“missed” (Tr: Action, v: miss, t: “before”)“target” (Tr: Object, v: target)

Expression:

The red plane missed the target.

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Reasoning with thingevent temporal containment

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Motivations and Approach Types Typed Ontologies Typed Ontology-driven Planning Systems Conclusions

Agenda

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Iterations on Plan Phases: Joint Air Warfare

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LessonsLearned

Development

Execution

Post Execution

OPLAN Joint AirOperations

Plan

Air OperationDirective

Air TaskingOrder

Damage RepsOp Assess.

JFCGuidance

Air Tasking Cycle

Master AirAttack Plan

Fly

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Planning Phase Metrics Over Time and Across Plans

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Develop Execute Post-Execution

PlanA.1

Develop Execute Post-Execution

PlanA

Develop Execute Post-Execution

PlanA.2

Information Grid

Environmental Sources

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Examples of Planning Metrics per Phase

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Relevanceoutside

Coherenceinternal

PlanningAssessment

process

MetaMetricLearningmetrics

Development Execution Post-Execution

Predicted weatherEnemy Order of Battle

Assets AvailableTiming

Branches consideredTime to completion

Correct projectionsAverage belief

Actual WeatherEnemy intent

AttritionSync success

Missions on timePlan changes over time

Timelinessprecision

Intent achievedSustainability

Overall efficiencyAffordances

MOPs/MOEs quantifiedLessons learned

Correlation of MOPsWith MOEs

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Plan Phase Interaction Example

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ApportionmentDecisionmaking

“How many SEAD missions are we going to need to fly early on?”

“Change in SEAD missions actually flown over the first week.”

Development

Post-Execution

Execute

informs

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Ideal Query

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“What’s the historical drop in SEAD missions actually flown over the first week in similar campaigns?”

For Plans with:- Class eq OPLAN- Area of Operations (OA) intersects with CENTCOM Area of Responsibility (AOR)- Phase eq Post-ExecutionAverage over Plans- Difference

- Percent SEAD Missions flown first day of offensive ops (D0)- Percent SEAD Missions flown D0+6

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Step 1: What is a “Plan”

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For Plans with:- Specification Class eq OPLAN- Specification OA intersects CENTCOM AOR- Actual Phase eq Post-ExecutionAverage over Plans- Difference

- Percent SEAD Missions flown D0- Percent SEAD Missions flown D0+6

OP-11Action

Asset

Actions

Assets

DoctrinalSpecification

(Doc/language)

Computational(IT/formalism)

Mental(neurons/conscious)

Actual(Objects/states)

Plans

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Plan Specification: Information Contained

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Locator: PlanSpec-ID, timeContent:• Owner• Contributors• Approver• Mission value• Contained plans• Containing plans• Complementary component plans• Parent(s) in doctrinal hierarchy• Children in doctrinal hierarchy• Goal state• Predicted outcomes• Trigger condition• Completion condition• Assumed world states• Dissemination• Required Assets• Actions

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A Doctrinal Plan Specification Schema excerpt

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PlanSpec Schema:(PlanSpec-ID[1]+,Time[1]+).* [1]~ Location Structure

(PlanClass[1]+,OA[1]+,ExecCond[1]+,…) [1]+ Content Structure

Types:Plan-ID

categorical

Time

PlanClassragged hierarchical categoricalv = {OPLAN, JAOP, AOD, MAAP, …}F: v.up, .down, .children, .parent

OAStruct (Named-Region, Grid-Polygon)

2D Space (F: .area, .circumference) ->Range (F: .adjacent, .contained_in, .overlap) ->Rational (F: .pred, .succ)

ExecCondTime or Event

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Plan Form Relations

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Plan Process Schema:L(Space[1]+,Time[1]+,Agent[n]+)[1]~[1]C(GoverningDoctrinalPlan,Goal,Phase,Asset-Roles,PredictedOutcome…)

OP-11

Action

Asset

Actions

Assets

Spec-L<Idx,time>C<…>

MentalPlan-L<space,time,agents>C<Idx,assets…>

Actual-L<id,time>C<space,…>

Inferences (not certain)Spec<Idx,time, space>Proc.<Idx,time, space,assets> Actual<time,space, id>

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Step 2: A common framework for location

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For Plans with:- Specification Class eq OPLAN- Specification OA intersects CENTCOM AOR- Actual Phase eq Post-ExecutionAverage over Plans- Difference

- Percent SEAD Missions flown D0- Percent SEAD Missions flown D0+6

Iran(t)

Kuwait(t)

JOA (t)

GHW Bush(t)

A meeting…

Everything is an “Event” in Space-Time

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Operations on thingevents in space-time

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Command Schema:L(Command-ID[1]+,Time[1]+)[1]~[1]+C(AOR,…)

Type:Command-ID

multi-hierarchical categorical

AOR region in time-space

JOA region in time-space

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Step 3: Joining Schemas

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For Plans with:- Specification Class eq OPLAN- Specification OA intersects CENTCOM AOR- Actual Phase eq Post-ExecutionAverage over Plans- Difference

- Percent SEAD Missions flown D0- Percent SEAD Missions flown D0+6

Plan Process Schema:L(Space[1],Time[1],Agent[n])[1]~[1]C(GoverningDoctrinalPlan,Goal,Phase,Asset-Roles,PredictedOutcome…)

PlanSpec Schema:L(PlanSpec-ID[1],Time[1])[1]~[1]+C(PlanClass[1],OA[1],ExecCond[1],…)

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Step 4: Joining actual events to plan schema

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For Plans with:- Specification Class eq OPLAN- Specification OA intersects CENTCOM AOR- Actual Phase eq Post-ExecutionAverage over Plans- Difference

- Percent SEAD Missions flown D0- Percent SEAD Missions flown D0+6

Plan Missions

OPLANCENTCOM

ContainedPlans

Sorties

Roletime

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Plan containment, phases, and execution

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PlanSpec - <PlanSpec-ID1, time…OPLAN,containsPlans>

PlanSpec - <PlanSpec-ID2, time…JAOP,containsPlans>

PlanSpec - <PlanSpec-ID3, time…AOD,containsPlans>

PlanSpec - <PlanSpec-ID4, time…ATO,containsPlans>

PlanMission - <Mission-ID, time … PlanSpec-ID4,OCA…>

Sortie - <Plane-ID, time, Mission-ID,…>

Plane - <Plane-ID, time, wepx, SAM, SEAD…>

Plan containment(embedded phases)

Tactical Execution

Actuality

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Step 5: Aggregation

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For Plans with:- Specification Class eq OPLAN- Specification OA intersects CENTCOM AOR- Actual Phase eq Post-ExecutionAverage over Plans- Difference

- Percent SEAD Missions flown D0- Percent SEAD Missions flown D0+6

OP1 OP2 OP3

PD0

PD+6

Diff

PD0

PD+6

Diff

PD0

PD+6

Diff

SUM(Miss.-SEAD)/SUM(Miss.-all)

SUM(Miss.-SEAD)/SUM(Miss.-all)

Average

Diff

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Aggregation rules for types

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Plan Type…Rule:If plan.v.metric = f(plan.v.a, plan.v.b, …)Then

plan.{v1,v2…}.metric.average ={plan.v1.metric, plan.v2.metric,…}.avg

plan.{v1,v2…}.metric.net =f(plan{v1,v2,…}.a.sum, f(plan{v1,v2,…}.b.sum,…)

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Motivations and Approach Types Typed Ontologies Typed Ontology-driven Planning Systems Conclusions

Agenda

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Improving agility and effectiveness requires a

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Conclusion

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Extensible – mutable type system and schemas enable changing ontologies and semantics as needed

Integration – common space-time locator and thingevent abstractions enable connections to be made

Meta-information – Higher-order expressions, assertions about assertions, enable representation of sources, belief, value, cost, etc., necessary to a “smart” information grid

Explicit distinction of physical and logical representations, and relations between, enable integration of artifacts of various sources and representational systems

Integration of action and object “views” of singular thingevents enables semantics of interactions, movement, transformations, decomposition, etc.

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Toward a Smart Information Grid for Living Plans

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Charles River Analytics Points of Contact

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Presenter NamePresenter Title

617.491.3474 Ext. XXXemail@cra.com

Presenter NamePresenter Title

617.491.3474 Ext. XXXemail@cra.com

Presenter NamePresenter Title

617.491.3474 Ext. XXXemail@cra.com

Should be used as last page

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SBIR Data RightsUse if a SBIR/STTR Related

Appendix/Extras

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Trying to ReduceLogic, Math, and Language to a Common Core

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MathPoints, lines, Numbers, Irrationals Infinity, Variables, FunctionsNumbers

LogicArguments, PredicateTruth functionsSubstitution, IdentityInference

Natural Language

GrammarPhrase structureNouns, verbs,LexiconsMeaning

A potential informatio

n atom

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Outline of Representational levels in LC Model

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Theory/Model

Kernel

Abstract: Numbers, Graphs..

Space-time Physical Objects Life Forms

Instinctual life forms Perceptual life forms

Verbal life forms acquiring & using language forexchanging information about shared perceptions of physical objects unshared perceptions of phys obj shared perceptions of abstract obj. unshared perceptions of abstract obj

Application

Paradox, Info atoms, WFF meaning, equivalence, substitution, color exclusion

Number systems, Irrationals

Time, Space, attribute values Things/objects, processes,

transformations, properties, knowledge, kinds of truth, belief

Extracting meaning from collections of tokens

Combining sensor/verbal data; enhancing meaning, reasoning

Rati

on

al

Em

pir

ical

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Type Hierarchy

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Type Hierarchy as entries in Baked-In Schema

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Continuous planning and assessment Continuous in time: Replace “cycle” with co-operating processes Continuous in level: Replace hard boundaries of levels of planning

with continuum of action Continuous in domain: Replace separate domains of planning and

action (e.g., air, land, cyber, etc.) with integrated plan

Increasingly capable by improving: Action performance through understanding of contributing factors. Projections through assessments of past projections Effectiveness through assessment of impact of past actions Integration of action toward higher goals through assessment of

combined effectiveness Clarification of goals through introspection on outcomes Assessment and planning processes by measuring and modifying Improvement through better measures

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“Continuously and Increasingly”

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WITH Types Time, Store, Sales, Costs, Profit;

Create Schema “Sales Model”

([1]+ Time, [1]+ Store).* Location Structure

[1]- [1]+

(Sales, Costs, Profit) Content Structure

Schema Creation ExpressionsCube-like Schemas

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WITH Types Time, Store, Sales, Costs, Profit;

WITH Schema ([1]+Time, [1]+Store).*[1]-[1]+(Sales, Costs, Profit);

Sales, Store.Cambridge, Time.January = $500Sales, Store.All , Time.*Sales, Store.NY = 2 X (Sales, Store.CA)Profit = Sales - CostsProfit, L.* = (Sales, L.this) - (Costs, L.this)

Sales - Costs AS Profit , Store.MA

Query and Calculation ExpressionsFrom Cube-like Schemas

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WITH Types OrdTime, Step, Quality, Manager

Create Schema “Workflow”

(OrdTime[1]+, Step[1]+).* Location Structure

[1] - [1]+

(Quality, Manager) Content Structure

Schema Creation ExpressionsProcess-like Schemas

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WITH Types OrdTime, Step, Quality, Manager

WITH Schema “Workflow”(OrdTime[1]+, Step[1]+).* [1] - [1]+( Quality , Manager)

Quality, Step.last Quality, Step.all Manager, Step.Quality.Max.*

Query and Calculation ExpressionsFrom Process-like Schemas

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Built-in Types

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• Time • Space • Attribute a lazily constructed type, whose values include all of the values of its sub-types • ThingEventId units Categorical • Object_Geometry units TypeRef

values { Sphere, Block, Cylinder } • FR units SetOf { Object_Geometry.Local_FR, Space } FR stands for Frame of Reference; a

defined Space or the local frame of reference for the Object_Geometry of a given thing event • Coordinate units SetOf { SphereCoordinate, BlockCoordinate, CylinderCoordinate }

Coordinate is the local position within the region defined by the space/object • Sphere units Tuple(Tuple(SphereFR.v, FR), radius) where SphereFR.v.centroid =

FR.v.Coordinate.v (the centroid of the sphere is located at a particular location of the outer frame of reference)

• SphereFR Tuple(zenith, azimuth_reference, centroid) centroid has units Coordinate (the Coordinate.v of the outer FR)

• SphereCoordinate units Tuple(azmuthal_angle, polar_angle, radial_distance)

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Empirical Content

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Multi Scale Integer ‘MSI’ = {Integer Decimal * Integer scale}

Empirical measure = Content_label, MSI , Content unit expression

Content label MSI Content unit expression Soil Moisture Content 12{00} {{ML{1{1}}}/{M3{1{1}}}} SMC 12 {00} ML/ M3 SMC 1200 ML/ M3 SMC 1.2 L/ M3 Profit 53{000,000} {{Sales{${ 1{1}}}} - {Costs{${1{1}}}}} Profit 53 {000,000} Sales{$} - Costs{$} Profit 1.4 Sales{$} /Costs{$} Profit 1.4 {%}

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Core ThingEvent Backbone

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Zoom on Verbal Critter

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An expression instancing physical object thingevents