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|Packs (add-ons) for SWI-Prolog|
|Title:||pddl_valoptic_api -- A SWI-Prolog Pack that lets Prolog code seamlessly use PDDL based planners.|
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|Author:||Andrew Dougherty <email@example.com>|
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A SWI-Prolog Pack that lets Prolog code seamlessly use PDDL based planners
Installation using SWI-Prolog 7.3 or later:
!#f03c15 NOTICE: This is a work in progress and is being updated weekly.
This guide is designed for first-time readers, people who need refreshers and others, like myself, who sometimes need some syntax sanity-checking.
If you read anything here that you believe needs improvement, contribute to it on GitHub.
PDDL one of the few languages designed for the purpose of creating a standard for Artificial Intelligence (AI) planning. It was developed in 1998 and was introduced at ICAPS, with improvements and extensions being built into it over the years .
The most popular of PDDL used today are PDDL2.1, which is an extension to PDDL for expressing temporal domains ; PDDL 3  which adds trajectory constraints and preferences to PDDL 2.1, and PDDL+  which allows modelling mixed discrete-continuous domains in PDDL.
A world is described by a set of states, each containing a list of facts and/or objects. A world begins with an initial state, and is governed by a set of rules and constraints that limit which actions can be taken in each state, and each action generally represents a transition to a different state.
There are certain things we need to keep track of in the "world" Workspace.
` ?- optic_add_objects(+Workspace,+[Objects..]).`
` ?- optic_add_objects(+Workspace,+[Predicates..]).`
First thing you need to know, PDDL files usually have the extension `.pddl`.
There are two PDDL files you need to learn the syntax of:
The domain file establishes the context of the world. It determines what sorts of details the states can include (predicates), and what can we do to move between states in the world (actions).
The basic syntax of a domain file is:
(define (domain <domain name>) (:predicates <predicate-list> ) (:action <action-details> ) )
where `<domain-name>` is the name of the world.
Both predicates and actions will become clearer in examples below.
The problem file represents an instance of the world we established in the domain. It determines what is true at the start of the plan (initial state), and what we want to be true at the end of the plan (goal state).
The basic syntax of a problem file is:
(define (problem <title>) (:domain <domain-name>) (:objects <object-list> ) (:init <predicates> ) (:goal <predicates> ) )
where `<title>` is the title of the problem file and `<domain-name>` refers to the name of the corresponding domain file.
Let's imagine we have a robot gripper arm, a cupcake and a plate. The gripper is empty, the cupcake is on the table and we want to put the cupcake on the plate.
Before we model this in PDDL, let's look at the components of the PDDL problem:
First we define the domain.
(define (domain letseat)
Then we define the objects: plate, gripper, cupcake. We will also mark the cupcake and the arm as locatable, a little hack to help us query the locations of these objects using a predicate we'll create later.
(:requirements :typing) (:types location locatable - object bot cupcake - locatable robot - bot )
We also need to define some predicates. Is the gripper arm empty? Where is the cupcake?
(:predicates (on ?obj - locatable ?loc - location) (holding ?arm - locatable ?cupcake - locatable) (arm-empty) (path ?location1 - location ?location2 - location) )
We'll also have to define actions/operators. We need to be able to pick up and drop the cupcake, as well as move the arm between the table and the plate.
(:action pick-up :parameters (?arm - bot ?cupcake - locatable ?loc - location) :precondition (and ; Note how we use the same variable loc ; in both lines below. This is to make ; sure it's looking at the same location. (on ?arm ?loc) (on ?cupcake ?loc) (arm-empty) ) :effect (and (not (on ?cupcake ?loc)) (holding ?arm ?cupcake) (not (arm-empty)) ) ) (:action drop :parameters (?arm - bot ?cupcake - locatable ?loc - location) :precondition (and (on ?arm ?loc) (holding ?arm ?cupcake) ) :effect (and (on ?cupcake ?loc) (arm-empty) (not (holding ?arm ?cupcake)) ) ) (:action move :parameters (?arm - bot ?from - location ?to - location) :precondition (and (on ?arm ?from) (path ?from ?to) ) :effect (and (not (on ?arm ?from)) (on ?arm ?to) ) )
Put all the above into a file, and you have a domain file!
Now we'll look at the problem file. We'll start by letting it know which domain it's associated to, and define the objects that exist in the world.
(define (problem letseat-simple) (:domain letseat) (:objects arm - robot cupcake - cupcake table - location plate - location )
Then, we'll define the initial state: the gripper is empty, the cupcake is on the table, and the arm can move between both.
(:init (on arm table) (on cupcake table) (arm-empty) (path table plate) )
Finally, we define the goal specification: the cupcake on in the plate.
(:goal (on cupcake plate) )
Put that all together and you'll have the problem file!
If you run this using OPTIC, you'll get this solution:
Initial heuristic = 3 Initial stats: t=0s, 4299060kb b (2 @ n=3, t=0s, 4300084kb)b (1 @ n=6, t=0s, 4308276kb) ;;;; Solution Found ; Time 0.00 ; Peak memory 4308276kb ; Nodes Generated: 5 ; Nodes Expanded: 3 ; Nodes Evaluated: 6 ; Nodes Tunneled: 1 ; Nodes memoised with open actions: 0 ; Nodes memoised without open actions: 6 ; Nodes pruned by memoisation: 0 0: (pick-up arm cupcake table)  1: (move arm table plate)  2: (drop arm cupcake plate) 
Here are a few tasks to make it more complex and enforce your understanding.
If you want to check out something a bit more complex, check out the driverlog domain.
If you're a first timer, don't venture into this part until after you've fully understood the basics.
You can actually give actions durations to work in temporal domains.
Each condition and effect is given the time at which it's supposed to happen.
There are a few types of temporal constraints:
`(at start (<condition/effect>))`, which means this must be true or happen at the start of the action. `(at end (<condition/effect>))` , which means this must be true or happen at the end of the action. `(over all (<condition>))`, which means this must be true for the full duration of the action.
Below is an example of the
(move) action from our previous example transformed into a durative action.
(:durative-action move :duration (= ?duration 10) ; Duration goes here. :parameters (?arm - bot ?from - location ?to - location) :condition ; Note how this is "condition" not "pre-condition" (and (at start (on ?arm ?from)) (over all (path ?from ?to)) ) :effect (and (at start (not (on ?arm ?from))) (at end (on ?arm ?to)) ) )
The model files are based on an ontology with multiple layers of abstraction. We design our ontology by combining high level concepts and cross-domain relationships borrowed from three areas: CPS; Agent-Based Model (ABM); and Systems-of-Systems (SoS). The proposed ontology consists of an Upper Ontology, which contains the CPS, ABM, and SoS concepts and relations and a general ITS Domain Ontology. The general ITS Domain Ontology can be further referenced from ontologies that instantiate transport-domain specific transitions and states. It is of course possible to extend the upper ontology with ontologies describing other domains than ITS, for example healthcare, energy and utilities, agriculture, etc.
The objective of breaking the ontology into multiple levels is twofold. First, this approach allows to capture and isolate different levels of properties, attributes and relationships. Higher layers provide broader definitions and more abstract concepts, while lower layers are less abstract and can support specific domains and applications with concepts and relations which might not be present in the upper levels.
Second, ontologies are expected to change, grow and evolve as new domains and techniques are contemplated in them (Davies et al., 2006). Leaving the more abstract and general concepts in an upper layer, and the more specific ones in lower layers, reinforces the idea that altering the most general concepts should be avoided, making them less likely to suffer constant modifications that could lead to unnecessary changes throughout the ontology. This is important because ontologies often reuse and extend other ontologies. Updating an ontology without proper care can potentially corrupt the others depending on it and consequently all the systems that use it.
Upper ontologies should be designed to describe general concepts that can be used across all domains. They have a central role in facilitating interoperability among domain specific ontologies, which are built hierarchically underneath the upper and generic layers, and therefore can be seen as specialization of the more abstract concepts.
Figure above presents a subset of the proposed upper ontology. Its development was prompted by our use cases in management and control of complex systems-of-systems, and was inspired by other ontologies such as SUMO (Suggested Upper Mergerd Ontology) (Niles and Pease, 2001), and W3C SSN (Semantic Sensor Network Ontology) (Compton et al., 2012).
Some important concepts defined on the proposed general ontology include System, Cyber-Physical System, Agent and CPS Agent. A System is a set of connected parts forming a complex whole that can also be used as a resource by other systems. A Cyber-Physical System is a system with both physical and computational components. They deeply integrate computation, communication and control into physical systems. An Agent is a system that can act on its own, sense the environment and produce changes in the world. When an agent is embedded into a cyberphysical system it is called a CPS Agent, or cyberphysical agent.
Important for mathematical desciptions of interrelations between systems are the elements Arc, Node and Graph. Where an Arc is any element of a graph that connects two Nodes, while a Graph is a set of Nodes connected by Arcs.
The concept of System can be further expanded by a number of attributes, such as Capacity, Role and Capability that can also have relationships among them. The System itself is represented within the Declarative Knowledge as an Object. Affordance is a property the defines the tasks that can be done on a specific System, while Capability defines the set of tasks the system can perform. Systems can also have Constraints, which in turn are related to KPIs that are used to measure whether such constraints are satisfied. The higher level of the proposed ontology also provides definitions and relationships between the main Knowlegde Base concepts, the Declarative and Procedural Knowledge.
In our knowledge model, a Transition is a Procedural Knowledge concept that determines how to achieve a certain state (Action) given that an agent observes a particular state (Precondition) as being true in the world and there is an ordered list of effect free function calls in that state (Computation). Meanwhile, both Precondition and Action have a Predicate Set that is directly related to the concept of State from the Declarative Knowledge. The Goal State, which is an specification of State, is related to the concepts of Task and Workflow from the Procedural Knowledge. Where a Workflow is defined as sequence of Tasks, which in turn is defined by a sequence of Goal States assigned to a single Agent.
Figure above presents the main elements of the knowledge base modeling.
With the support of the presented upper ontology model, in this section we propose an ITS domain specific ontology, as depicted in Figure above. One of the central concepts within the ITS domain is the Transport Agent, that extends Agent from the upper ontology. The Transport Agent encompasses agents that are capable of transporting some entity, ranging from physical goods to virtual data. Some important concepts from the upper layers that apply to the Transport Agent include Dynamics and Capacity, among others. Transport Agents in turn are strongly related to the Abstract concept of Transportation Mode which defines the type of transportion scenario (e.g., Roads, Rail, Telco).
Another important concept is the Transportation Infrastructure which encompasses all elements required by a Transportation Mode, such as Routes, Tracks and Transportation Networks. Most elements within the Transportation Infrastructure are extensions of Graph, Arc and Node, abstract concepts from the Upper ontology. Therefore, by using high level graph definitions it is possible to define most of the transportation infrastructure in an ITS Domain. A node inside the transportation infrastructure is referred to as a POI (Point of Interest) and it can be any desired location within the Transportation Network (e.g., a crossing, a specific point in the route, coordinate, a warehouse, a bus stop). A Traffic Semaphore is modeled as a generic Actuator that is used to control and regulate traffic and it can be applied in any transportation scenario. A Transportable Entity encompasses any element that can be transported by a Transport Agent, such as regular Cargo or network Data. A typical Passenger is also a Transportable Entity and extends the upper ontology concept of Human.
 Fox, M. and Long, D. (2003). PDDL2.1: An Extension to PDDL for Expressing Temporal Planning Domains. online] Available at: [http://www.jair.org/papers/paper1129.html [Accessed 20 Nov. 2017].
 Gerevini, A. and Long, D. (2005) Plan Constraints and Preferences in PDDL3. Volume 27, pages 235-297. online] Available at [http://www.cs.yale.edu/homes/dvm/papers/pddl-ipc5.pdf
 Fox, M. and Long, D. (2006) Modelling Mixed Discrete-Continuous Domains for Planning. Volume 27, pages 235-297. online] Available at [http://www.jair.org/papers/paper2044.html
 Davies, J., Studer, R., and Warren, P. (2006). Semantic Web technologies: trends and research in ontology-based systems. JohnWiley & Sons, Chichester,West Sussex, PO19 8SQ, England.
 Niles, I. and Pease, A. (2001). Towards a Standard Upper Ontology. In Proceedings of the International Conference on Formal Ontology in Information Systems - Volume 2001, FOIS ?01, pages 2?9, New York, NY, USA. ACM.
 Compton, M., Barnaghi, P., Bermudez, L., Garcia-Castro, R., Corcho, O., Cox, S., Graybeal, J., Hauswirth, M., Henson, C., Herzog, A., Huang, V., Janowicz, K., Kelsey, W. D., Phuoc, D. L., Lefort, L., Leggieri, M., Neuhaus, H., Nikolov, A., Page, K., Passant, A., Sheth, A., and Taylor, K. (2012). The SSN ontology of the W3C semantic sensor network incubator group. Web Semantics: Science, Services and Agents on the World Wide Web, 17:25 ? 32.
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