One of the objectives of the ENDSTATE program is to bring together symbolic reasoning, quantitative analysis and detailed simulation in a tightly interleaved process to address the problem of effects-based target generation for highly complex interconnected physical infrastructures. The collaboration between SRI and Alphatech has three main threads:
SRI is concentrating its initial efforts on getting a human readable explanation out of the cross-network analysis results input and output. We are assuming that the AlphaTech and SRI model share the same concepts, structure and "rules of behavior" (or mechanisms), otherwise not only the explanations could be wrong, but the same perturbation on one model could result in different consequences on each model. In other words, we assume the underlying world is the same.
According to our last conference call, the immediate goal of the SRI's team (and therefore SRI's model) will be to produce explanations that arises from the following cycle:
From that cycle of use, the following could be assumed:
Under the assumption that one of the objectives is to use the simulation data from the AlphaTech model, several approaches are possible if the goal is to produce human readable explanation.
Given that no causal information is encoded in the OR model, from the simulation data one could think of discovering causal links by means of different methods. One of them is Structural Equation Modeling [Wright:1921], [Haavelmo:1943], [Koopmans:1950]. SEM was developped so that qualitative causal model could be merged with statistical data to provide causal-effect information.
Causal Ordering [Iwasaki:1986] also tries to achieve the same result by providing an operational definition of independant and dependant variables in self-contained mechanisms.
The advantage of using one of this approaches is that if the difference equations used by AlphaTec are structural in some mechanism sense, we could derive causality relationships that in conjunction with the simulation data could yield interesting results. The disadvantage is that the symbolic abstraction of this approach is non-existant if we perform the causality search at the same level as the OR model.
From the data generated by the simulation, it is possible to construct a probabilistic model either using something like Bayes Nets or evidential theory. Tools for searching the space of possible Bayes Nets [Heckerman:1995] are available, as well as tools for building a predictive model [Spirtes:1993]. In the realm of Evidential Theory, there are such tools as Gister available [Lowrance:1991]. There are also Probabilistic frame-based systems [Koller:1998] which bridge the gap between Frame based representation systems and probabilistic models.
Qualitative reasoning [Kuipers:1994] is a technique building and simulating qualitative models of physical systems where knowledge of that system is incomplete or partially complete. Qualitative simulation guarantees to find the possible behaviors consistent with the knowledge in the model. This expressive power is important in problem-solving for diagnosis and explanation. Compositional modeling and component-connection methods for building qualitative models are available and there has been a lot of work in making the two work together. This is a good trait, given that the current cross network model is naturally decomposable (in nodes, links and so on).
There has been some work on introducing Actions into QR [Forbus:1988] and into bridging the gap between qualitative and quantitative [Berleant:1997] simulations, which seems to be exactly the task at hand for the EndState problem.
A thread of research that might be relevant to explaining things in the cross-network model we are dealing with is Structural Aggregation [Liu:1992]. Given that explanations must pick the appropiate level of granularity to simplify the domain and make the explanation clearer, supressing irrelevant and complex details is key.
Causal knowledge can also be captured in terms of "planning operators". These representations capture the preconditions required for the applicability of an operator and the results of its application. In other words they form an activity-based representation of the behavior of the system. Generative planning technologies can be used to create a sequence of partially-ordered actions to acheive some goals, or endstates [Wilkins:1988]. For the purpose of explanation of a quantitaitve model output, the planning model could be used to search the parially ordered sequence of actions to match the actual outcome of the quantitative model to a sequence of actions [Myers:1996]. However, this depends on the accuracy of the knowledge representation and in particular an understanding of the relationships between actions and effects given a ground truth.
The approach being used for the construction of the SRI model is Qualitative Reasoning. In the qualitative reasoning approach we have a description of the physical situation in terms of components and their interconnections. This is called the device topology. The system is analyzed in terms of its qualitative behaviors, exploiting its relationship to the structure, to obtain a qualitative description and a causal account of how that behavior arises. The above explanation and the relationship to quantitative modeling (and reasoning) could be summarized in the following figure from [DeKleer:1986]:
The key to understanding qualitative reasoning is that we are able to reason about certain properties and events of the real world without having complete knowledge of the quantities involved. If I see an apple falling from a tree, I can tell it's going to hit the ground even if I cannot calculate the exact height from which is falling or the exact velocity at any point.
Under the premise of working with the scenario-subset that was discussed at the SRI meeting we have extracted the following scenario:
The scenario we want to deal with should be a perfect subset ot the "Troy Base" model we have in the Excel spreadsheets, but with the following restrictions:
With the previous submodel, we identified several variables and landmark values that are key in generating an explanation. Because what we want is to generate an explanation, we are only interested in the behavior of certain elements of the system, as well as the important landmark values. For example, when we are talking about oil inventory, the landmark values can be 0 and the maximum capacity of the site, when we are talking about roads an inportant landmark is the maximum throughput of the road, and so on.
Below is a QSIM qualitative model for the space we are interested in:
; Simple-Endstate restricted by food supply, without regeneration.
(define-QDE Simple-Endstate
(text "Simple-Endstate: Coal and Energy in CoalVille and PortVille")
(quantity-spaces
;; Production and Consumption Quantities
(cvm-coal-source (0 max inf) "CoalVille Mine Coal Production")
(cvpp-coal-sink (0 max) "CoalVille Power Plant Coal Consumption")
(cvpp-energy-source (0 max inf) "CoalVille Power Plant Energy Production")
(cv-energy-sink (0 max) "CoalVille Energy Consumption")
(pvpp-coal-sink (0 max) "PortVille Power Plant Coal Consumption")
(pvpp-oil-sink (0 max) "PortVille Power Plant Oil Consumption")
(pvpp-energy-sink (0 max) "PortVille Power Plant Energy Consumption")
(pvpp-energy-source (0 max inf) "PortVille Power Plant Energy Production")
(pv-energy-sink (0 max) "PortVille Energy Consumption")
(pved-coal-sink (0 max) "PortVille Export Dock Coal Consumption")
(pvid-oil-source (0 max) "PortVille Import Dock Oil Production")
;; Flows of Coal and Energy
(cvm-cvpp-coal-flow (0 max) "CoalVille Mine - CoalVille Power Plant Flow")
(cvm-pvpp-coal-flow (0 max) "CoalVille Mine - PortVille Power Plant Flow")
(cvm-pved-coal-flow (0 max) "CoalVille Mine - PortVille Export Dock Flow")
(cvpp-cv-energy-flow (0 max) "CoalVille Power Plant - CoalVille Energy Flow")
(pvpp-pv-energy-flow (0 max) "PortVille Power Plant - PortVille Energy Flow")
(cvpp-pvpp-energy-flow (0 max) "CoalVille Power Plant - PortVille Power Plant Energy Flow") )
(constraints
;; Energy produced is a function of coal/oil consumed
((M+ cvpp-coal-sink cvpp-energy-source) (0 0) (max max))
((M+ pvpp-coal-sink pvpp-energy-source) (0 0) (max max))
;; Energy, oil and Coal conservation
((sum cvpp-coal-sink pvpp-coal-sink pved-coal-sink cvm-coal-source))
((sum cv-energy-sink pvpp-energy-sink cvpp-energy-source))
((sum pv-energy-sink pvpp-energy-source))
((sum pvpp-oil-sink pvid-oil-source))
;; The amount of coal taken from the ground is constant
((constant cvm-coal-source))
;; The amount of energy consumed by the cities is constant
((constant cv-energy-sink))
((constant pv-energy-sink))
;; Rate of change of amounts
((d/dt cvpp-coal-sink cvm-cvpp-coal-flow))
((d/dt pvpp-coal-sink cvm-pvpp-coal-flow))
((d/dt pved-coal-sink cvm-pved-coal-flow))
((d/dt cv-energy-sink cvpp-cv-energy-flow))
((d/dt pv-energy-sink pvpp-pv-energy-flow))
((d/dt pvpp-energy-sink cvpp-pvpp-energy-flow)) ) )
See [Kumar:2000], [Liu:1993] and [Lester:1997].
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