Bayesian semantics for the semantic web




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Therefore, even though there is no explicit reference to the “IsA” context nodes from Zone MFrag in the individuals displayed in Figure 31, the object property hasOVariable [3] linking the Zone_MFrag with its respective ordinary variables implicitly conveys that subtyping restriction.

As an example of the mapping between MEBN and PR-OWL depicted in Table 5., representing the context node “z=StarshipZone(st)” requires decomposing it into random variable terms “equal(z, StarshipZone(st))” and “StarshipZone(st)”. In the PR-OWL ontology these RV terms are respectively represented by Z_ZSZoneST_context and Z_ZSZoneST_inner_SZoneST, both individuals of class Context.

The other properties depicted in Figure 31 are the object property hasSkolem [4], which links a quantifier MFrag with its respective Skolem constants, and the properties hasResidentNode [5], hasInputNode [6], and hasContextNode [7], all subproperties of hasNode.

Figure 32 portrays the representation of node ZoneMD(z, t), from the Zone MFrag. Object property isNodeFrom [1] provides the link between the node and its MFrag. Further structural information is provided by the parent list formed with the object property hasParent [2], the object property isResidentNodeIn [6] and the properties that link ZoneMD(z, t) with its “copies” (instances in which the node is used as input and/or context node in other MFrags), which are hasContextInstanceIn [7] and hasInputInstanceIn (not visible in the picture).

ZoneMD(z, t) is a resident node, so it has a probability distribution conditioned on its parents. The link between an individual of class Domain_res and the many possible representations of its probability distribution is provided by the object property hasProbDist [3]. Subsection 5.2.2 explains the different possibilities of representing probability distributions in PR-OWL.

The list of possible states of ZoneMD(z, t) is made using the object property hasPossibleValues [4], while its arguments (ordinary variables z and t) are linked using the hasArgument object property [5]. Note that property hasArgument doesn’t actually point to an individual of class OVariable, which is the class that has the ordinary variables z and t represented (as Z_z and Z_t respectively). Instead, it points to individuals of class SimpleArgRelationship, a subclass of ArgRelationship. These two classes are reified relations specifying the many possibilities of arguments in a random variable. In this specific case (i.e. the ZoneMD(z, t) node), the two arguments are OVariables, so links to both are represented by individuals of the class SimpleArgRelationship, which works as a pointer to individuals of Class OVariable only. When a node has composite arguments, the parent class ArgRelationship should be used, since it works as a pointer to individuals of classes OVariable, Node, Entity, and Skolem.



  1. ZoneMD Resident Node

Object properties isArgTermIn [8] and hasInnerTerm [9] provide further support to reified relations, by keeping track of the complex relationships in which each node is participating. The use of reification is also important for representing probability distributions in PR-OWL, which may be conveyed in different ways.

1.21.2Representing a Probability Distribution

Representing probability distributions is a key issue in achieving a balance between interoperability and conciseness. Proprietary formats usually convey all the necessary information in a compact way, thus simply using that format in a xsd:string to convey that information is an attractive option. However, this option ties the ontology to a specific format that might not be universally known or might be inappropriate to a range of applications. Also, annotating probability distributions might reduce the ability to use that data in complex environments with many systems working with different formats, rules or requirements.

PR-OWL is supposed to facilitate interoperability and thus should be as flexible as possible in terms of how to represent probability distributions. Therefore, it allows using multiple declarative distributions and/or a RDF table format to represent the probability distribution of a given RV.

Each probability distribution can be expressed in different formats using PR-OWL’s declarative distributions represented via the DeclarativeDist class, which is depicted in Figure 33. Possible formats include Netica tables, Netica equations, Quiddity formulas, MEBN syntax, and others. However, the declaration itself is stored as a string so parsers should be compatible with the specific text format of each declaration.

Every individual of class DeclarativeDist has an object property isProbDistOf [1] linking it with their respective resident node. A datatype property isRepresentedAs [2] defines how a given declarative probability distribution is expressed. A datatype property isDefault [3] flags it (or not) as a default distribution. finally, a datatype hasDeclaration [4] includes the probability distribution itself in the format previously defined.



  1. Declarative Distributions in PR-OWL

PR-OWL tables have a different representational scheme. Each individual of class PR-OWLTable is actually a label that links the many components that collectively form a probability distribution of a resident node. As an example, the individual Z_ZoneFShips_table has three properties: isDefault, which states whether or not that individual represents a default probability distribution, isProbDistOf, which links the individual with the node it represents (Z_ZoneFShips in this case), and hasProbAssign, which links the individual with all the individuals of class ProbAssign that collectively form the probability distribution of node Z_ZoneFShips. One of those ProbAssign individuals is Z_ZoneFShips_table_2.3, which is depicted in Figure 34.



  1. A Probabilistic Assignment in a PR-OWL Table

Z_ZoneFShips_table_2.3 corresponds to the probability assigned to the second state of node ZoneFShips (ZFS_1) given that its parent node has value ZN_PlanetarySystem (the third state of that parent). The probability itself (.20) is represented as a xsd:decimal that is linked to Z_ZoneFShips_table_2.3 via the datatype property hasStateProb [1]. The link between the ProbAssign individual and the state of ZoneFShips it refers to is made via the object property hasStateName [2], while property isProbAssignIn [3] links the probability assignment to the table it belongs. Finally, each probability assigned to a state of a variable is conditioned to a combination of states of the parents of that variable. Object property hasConditionant [4] links a ProbAssign individual to the individuals of class CondRelationship that collectively form such a combination of parents. CondRelationship is a reified relation linking a parent with one of its possible states, and a set of CondRelationship individuals represents the combination of parents’ states to which a given probability assignment is conditioned.

ZoneFShips has only one parent, so there is only one conditionant listed (Z_ZoneNature_cond_3.3), which is an individual of the reified class CondRelationship that links node ZoneNature with its third state (ZN_PlanetarySystem). If ZoneFShips had four parents, then four individuals of class CondRelationship (i.e. one for each parent) would have to be listed in order to represent the combination of parents under which that probability assignment is valid.

One issue regarding the probability assignment is the use of xsd:decimal to convey a probability value, when the ideal situation would be to use a datatype that specifically covers the numerical range of probabilities (i.e. 0 to 1, including both extremities). However, at the time of this writing, OWL has no support for user-defined datatypes, so the closest datatype allowed by OWL is xsd:decimal.

Although applications or plugins should be written to prevent invalid entries for probabilities, relying on external plugins to enforce this requirement is not an acceptable option. Therefore, a more robust solution must be sought. In the case of a future consideration of PR-OWL as a basis for a W3C Recomendation for representing uncertainty in the Semantic Web, a special datatype covering the numerical range of probabilities must be included. A very suitable name for such datatype is “prob” (pr-owl:prob), which has already been proposed by other researchers in this field (e.g., Ding & Peng, 2004).

PR-OWL tables represent probabilities in a format that is highly interoperable, since each cell contains links to all the elements that are necessary for specifying the conditions in which the probability inside that cell applies. Also, those elements are available in a non-proprietary, syntax-independent format, which makes it easier to be retrieved by diverse applications without the need for a format conversion. Yet, building PR-OWL tables the way it was done in this work is not a feasible option for a real life application or plugin. Fortunately, all the above steps can be avoided by developing automated tools. The next Section briefly covers such possibilities.

1.22A Proposed Operational Concept for Implementing PR-OWL

In its current stage, PR-OWL contains only the basic representation elements that provide a means of representing any MEBN-based model. Such a representation could be used by a Bayesian tool (acting as a probabilistic ontology reasoner) to perform inferences to answer queries and/or to learn from newly incoming evidence via Bayesian learning.

However, building MFrags and all their elements in a probabilistic ontology is a manual, error prone, and tedious process. Avoiding errors or inconsistencies requires very deep knowledge of the logic and of the data structure of PR-OWL. Without considering the future paths to be followed by research on PR-OWL (i.e. whether it will be kept as an upper ontology or transformed into an actual extension to the OWL language), the framework provided in this Dissertation makes it already possible to facilitate probabilistic ontology usage and editing by developing plugins to current OWL editors.

Figure 35 illustrates an example of such a concept. In that figure, a possible plugin for the OWL Protégé editor (which is itself an OWL plugin) shows a graphical construction of an MFrag being performed in a very similar fashion as a BN is constructed in a graphical package such as Netica™.

In this proposed scheme, in order to build an MFrag a user would only have to select the icon of the node he/she wants to create (e.g. resident, input, context, etc.), connect that node with its parents and children, and enter its basic characteristics (i.e. name, probability distribution, etc.) either by double-clicking on it or via another GUI-related facility.



  1. Snapshot of a Graphical PR-OWL Plugin

The idea of such a plugin is to hide from users the complex constructs required to convey the many details of a probabilistic ontology, such as the reified relationships, composite RV term constructions (with or without quantifiers and Skolem constants), and others. In the figure, the Zone MFrag was selected from the combo box in the top of the viewing area, thus information about its nodes is displayed in a graphical format that allows the user to build more nodes, edit or view the existing ones. and then chose node ZoneEShips(z) so it appears highlighted (a red box around it) and all its data is shown in the lower square.

Tedious tasks such as building a PR-OWL table with many cells could be carried out much more quickly and with fewer errors, thus providing a boost in productivity. In the probability table case, the user would only have to fill the probabilities in the correct cells of a CPT’s graphical display and the plugin would build their respective PR_OWL constructs.

Another point of usage improvement is the intrinsic syntax check provided by a guided construction. As an example, when writing a composite RV term, the user would not have to actually write the complex reified relations (ArgRelationships, Skolem contants, OVariables, Inner terms, etc). Instead, a menu with the allowed connectives would be available so his/her task would be reduced to enter the arguments of the formula and embed the connectives the way he/she wants. The final result would be a valid formula that would then be transformed in PR-OWL syntax by the plugin.

This brief idea of an operational concept barely scratches the surface of the many possibilities for the technology presented here, and its purpose is to point out one such possibility. As previously stated, the present dissertation is focused on defining a coherent, comprehensive probabilistic framework for the Semantic Web, in a way that any probabilistic system could be represented and made available to perform tasks such as plausible inference and Bayesian learning. Therefore, implementing a plugin such as the one envisioned here is a development task that is outside the scope or this dissertation research. Nonetheless, it takes an important first step toward making probabilistic ontologies a reality.  By opening the door to wide use of PR-OWL probabilistic ontologies, the present research makes a significant contribution to realizing the Semantic Web vision.

  1. Conclusion and Future Work

1.23Summary of Contributions

The main objective of this research effort was to establish a framework that enables the use of Bayesian theory for representing and reasoning under uncertainty in the context of the Semantic Web. The key step for achieving such objective was the introduction of probabilistic ontologies, which were formally defined in Chapter 5.

In order to provide the initial conditions for the future spread of probabilistic ontologies, we have developed a complete, modularized set of new definitions for the OWL language, which collectively form a coherent framework for building ontologies that are able to represent uncertainty from concepts of a given domain with full probabilistic first-order logic expressiveness.

Probabilistic ontologies written under this framework achieve a principled representation of uncertainty and allow for the use of different probabilistic reasoning systems as a means to perform plausible reasoning and learning from data on the MTheories represented in PR-OWL format.

The contributions of this research effort also included the development and formalization of a typed version of MEBN logic. This extended version was needed as a means to achieve full compatibility with current Semantic Web languages, including OWL.

A full implementation of MEBN logic and its typed extension does not yet exist. However, Quiddity*Suite is a powerful Bayesian probabilistic reasoning system that is capable of being applied as a PR-OWL reasoner. Therefore, we have also developed a set of rules for translating an MTheory written using the typed version of MEBN into a probabilistic model in IET’s Quiddity*Suite format.

These rules were applied to the Starship MTheory specially developed for this research, and resulted in a running Quiddity*Suite model. The Starship MTheory includes some of the most complex aspects that can be expressed with MEBN logic, such as recursions, nodes with many uncertain parents, context constraints expressed as first-order logic sentences with and without quantifiers, etc. Therefore, having achieved a Quiddity*Suite model capable of building any SSBN based on the original MTheory is a valid proof of concept of the feasibility of using Quiddity*Suite as a PR-OWL reasoner. The source code for the Quiddity Starship model is provided in the Appendix A of this dissertation.

In order to demonstrate the feasibility of representing a complex MTheory using the concepts laid out in Chapter 5, the very same case study was used as a basis for writing a probabilistic ontology containing all the elements from the original model and exploring different possibilities for representing a probability distribution. The resulting PR-OWL ontology is logically equivalent to the original generative MTheory, and thus can be utilized as the basis for generating SSBNs to answer queries posed to the model. In addition, the representation of Finding MFrags was also covered, as a means to demonstrate how PR-OWL ontologies can incorporate new information, either via user insertion or by means of Bayesian learning from data.

Therefore, the upper ontology presented here is capable of representing any MTheory, including both generative and MTheories with findings. In addition, it allows users to define probabilistic ontologies using a RDF-based syntax that is compatible with current OWL ontologies. Furthermore, translators could be written for third-party, of-the-shelf probabilistic reasoners to make use of the ontology to perform Bayesian inference and learning. These capabilities were demonstrated by creating the case study ontology, translating its definitions into Quiddity*Suite and performing probabilistic inferences over it, a process that is documented in the appendices.

1.24A Long Road with Bright Signs Ahead

The proposed framework can be understood as an initial solution situated in a middle ground between the extension approaches employed in OWL-S and SRWL. In common with the first is the fact that no actual extension to OWL semantics and abstract syntax is performed at this time, since it is also an OWL upper ontology. Similarly to the latter, PR-OWL also has the need for specialized tools in order to realize its full potential, while also including concepts (e.g. the prob datatype, FOL connectives, quantifiers, etc.) that could greatly expand OWL expressiveness if adopted as a standard.

Even though it is possible to represent a complex probabilistic system using PR-OWL definitions, performing plausible reasoning and learning from data requires an external tool (e.g. Quiddity*Suite). It is true that some preliminary consistency check and other OWL-DL features are possible using PR-OWL (which is OWL-DL compliant), and that any complex system can still be written in PR-OWL and be interpreted using different probabilistic reasoning systems, provided that PR-OWL plugins are written for capturing the data inside probabilistic ontologies in each package’s native format.

Apart from the need for developing plugins for probabilistic packages so they can be used as plausible reasoners, a specific PR-OWL plugin for current OWL ontology editors remains a priority for future efforts. The process used here for writing probabilistic ontologies can be greatly improved via automation of most of the steps in the ontology building, mainly in the part of writing composite RV terms, but also for consistency checking, reified relations and other tasks that demand unnecessary awareness of the inner workings of the present solution. Once implemented, such plugin has the potential to make probabilistic ontologies a natural, powerful tool for helping to realize the Semantic Web vision.

Furthermore, the technology has the potential to be used in important applications outside the Semantic Web, as we discuss in Appendix C In that discussion, our main point is that the proper use of probability information can help to establish reliable, more general semantic mapping schemas by means of probabilistic ontologies, which can then be applied in applications spanning diverse domains, since it relies on a meta-ontology (i.e. a ontology about ontologies), carrying no domain information, which has the mappings between two or more ontologies as its instances.

That is, PR-OWL has the potential for application in other semantic mapping solutions such as the DTB case study presented in Section C.1 of the appendices. It could also be applied to facilitate interoperability between systems as discussed in the Wise Pilot cases study, presented in Section C.2. The present work thus represents a step toward a general-purpose solution for the semantic mapping problem.

Finally, the most important requirement for adoption of a language is the standardization process. This process goes significantly beyond academic research and thus falls outside the scope of the present work. Nonetheless, we are confident of its feasibility, which we believe having demonstrated in this effort, and of its desirability, given its potential to help solve many of the obstacles that stand in the way of realizing the W3C’s vision for the Semantic Web.


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  1. Source Code for The Starship Model

The source code listed below refers to the probabilistic model that was developed for this research effort. It corresponds to four separate files, namely:

  • Starship_main.spi – It’s the execution manager for the Starship model

  • Starship_framedefs.spi – Defines the model’s frame structure

  • Starship _functions.spi – Defines the functions used in the model

  • Starship_exec.spi – Create instances and built an SSBN

The output of the models is a Netica file that will be saved in each model's respective folder and will be named as Starship_v00_SSBN_00t_00f_00e_00c.dne, where:

  • v00 - the model version

  • 00t - number of time steps

  • 00f - number of friend starships

  • 00e - number of enemy starships

  • 00c - number of enemy starships with cloak mode

This source code was generated using the following configuration:

Hardware:

  • Apple PowerMac Dual G5 – 2.0 GHz – 1.5 GB RAM

Software:

  • Apple Mac OS X Panther (version 10.3.9)

  • Java virtual machine (version 1.4.2_05)

  • IET Quiddity*Suite (version 4.1.5– build Unix-041217T1653)

  • JEdit (version 4.2)

  • Norsys Netica (version 2.17) running on top of MS Virtual PC (version 7.0)

1   ...   5   6   7   8   9   10   11   12   ...   20

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