Prepared for: STIDS 2014 18 November 2014 Presented by: Erik Thomsen Ontology-Driven Planning.
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Transcript of Prepared for: STIDS 2014 18 November 2014 Presented by: Erik Thomsen Ontology-Driven Planning.
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. [email protected]
Presenter NamePresenter Title
617.491.3474 Ext. [email protected]
Presenter NamePresenter Title
617.491.3474 Ext. [email protected]
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