From Metapattern to Ontoprise

Additionally to the well known OR- and AND-parallelism, polylogical systems offer two main extensions to the logical modeling and implementation of parallelism. First the distribution of the classical situation over several contextures and second, the trans-contextural distributions ruled by the different transjunctional operators. The distribution over several contextures corresponds to a concurrent parallelism where the different processes are independent but structured by the grid of distribution. The trans-contextural parallelism corresponds to a parallelism with logical interactions between different contextures.

"The tree corresponding to the search for a solution to a question seems open to various kinds of parallelism. The most obvious technique, called OR parallelism, allows processes to search disjunctive subtrees in parallel, reporting back to the parent node the result(s) of the search.

The advantage of OR parallelism is that the searches are completely independent of each other and may execute concurrently (except that both may share access to a common data base storing facts and rules). The process performing the search of one subtree does not communicate with processes searching other subtrees." Michael J. Quinn, 212, 1987

Prolog is based not only on its logic, used as an inference machine, but also on its semantics or ontology, realized as a data base. Therefore the process of parallelising has to deal with a deconstructive dis-weaving of the data base´s ontology.

Like in the case above, where the number systems had to be cloned, in the Prolog case, the data base has to be decomposed into disjunct parts. These separated conceptual parts, or conceptual subsystems, have to be distributed over different contextures in a mediated polycontexturality.

Additionally the Prolog parallelism which is based on OR- and AND-parallelism has to be mapped into distributed logics, that is, into a polylogical system.

The Prolog example allows to explain in more a plausible way the decomposition or cloning of the common universe of discourse, that is, the data base of facts, into different subsystems. And secondly it is easier to introduce parallelism based on polycontextural logic than on arithmetics and combinatory logics.

Polycontextural logic is not widely known but more accessible than combinatory poly-logic and poly-arithmetics, which I am just introducing. Additionally there exists since 1992 a working implementation of a tablex proof system of an interesting subsystem of polycontectural logics in ML, running on Unix systems like NeXT.

As an intermediate step in the shift of conceptualization from a hierarchical to a heterarchical way of concept building it maybe helpful to use the strategy of metapattern (Wisse). Metapatterns are used as an new modeling strategy for complex informational systems. Metapatterns are not involved in changing the basic assumptions of programming languages or even their logic as with the PCL approach.

Metapatterns could be helpful to move the process of parallelisation from the OR- and AND-level, that is, from the logical level to the deeper level of the data base, with its facts and rules, shared by the classical parallelism.

She can relax on a fixed object orientation because - the metapattern determines that -situation and object are relative concepts (Wisse 2001). A particular situation is also object in another, higher-level situation. Likewise, an object can act as situation in which another, lower-level object resides. Situation, then, is a recursive function of object and relationship. Wisse

It is this concept of situation that characteristically sets the metapattern apart from traditional object orientation (and provides it with advantages over OO; Wisse 2001). Compared to an object that (only) exists absolutely, an object believed to exist in a multitude a different situations can unambiguously be modeled - to be equiped - with corresponding behavioral multiplicity. Wisse 2001

The radical conclusion from the orientation at situational behavior is that an object's identification is behaviorally meaningless. The modeler does not have to explicitly include something like an original signature in all her models. Essentially a privileged situation may implied. It serves the only purpose of guaranteeing sameness or, its equivalent, persistent identity across (other) situations. Being a situation in its own right, when included in a model it is represented by a seperate context. Made explicit or not, its role is to authenticate an object's identity in other situations by establishing the signature in other contexts.

Traditional object orientation assigns identity at the level of overall objects. Context orientation replaces this view of singular objects with that of plusrality within the object; the object always nneds a context to uniquely identify the relevant part of an overall object, which is what identifying nodes regulate. When behaviors are identical, no distinction between contexts is necessary.

The classical prolog example to prove an "aunt"-relationship can be decomposed from its hierarchical ontology into different situations mapped into different contextures and visualized in the metapattern.

It is also possible that there is some overdetermination because parent and sibling could also be part of kinship.

In Prolog all the facts belong to one ontology or to one semantic general domain or universe. All the rules are based on this mono-contextural ontology and on the corresponding logical operators AND and OR of the again, mono-contextural logic. Everything therefore is linearized and homogenized to a global or universal domain. This, if corresponding fairly with the real world situation is of great practicality and efficiency in both direction, in the case of the formal system, Prolog, and in the case of its data base.

But often, if not always, real world applications are much more complex than this. Even the fairly classical example is presupposing all sorts of facts which are not mentioned in the definition and which would belong to a different real world situation.

I don't criticize this kinship model. It is doing its job to explain in a first step Prolog perfectly. Again, I am using this example for deconstructive reasons, that is for introducing the PCL way of thinking. This is, again a form, I guess, of legitimate abuse of classical models.

Instead of linearizing the above separated contextures kinship, gender, genealogy, ontology into one universal domain, for the example here represented by kinship, the polycontextural modeling is asking for an interweaving and mediating of these different contextures together to a complex poly-contexturality.

Compared to the original mono-contextural modeling this is involving much more complicated mechanisms than it is necessary in the classical case.

Why should we model a simple situation with highly complex tools into a complex model if we can solve the problem with much simpler tools? Simply because the classical approach lacks any flexibility of modeling a complex world. The truth is, that the simple approach needs an enormous amount of highly complicated strategies to homogenize its domains to make it accessible for its formal languages.

To decompose the basic classical ontology into different disjunct domains is a well known procedure and should not be confused with the decomposition, or de-sedimentation of an ontology in the PCL case. In PCL the domains are not simply disjunct and embraced by the general ontology but interwoven in a complex mechanism of interactions.

The metapattern approach has helped to dissolve the hierarchical conception of the "aunt"-relation into different aspects.

The aunt-function is fullfilled and is true, if all components which are connected by the conjunction et (AND) are true.

true(aunt(x,y) iff ( true(female(x)) et true(sibling(x,z)) et true(parent(z,y)))

Metapattern distribute the AND (or: et) over different heterarchical places but gives no formalism to handle this distribution. Polylogics is also distributing these conjucntions but in transforming them at the same time into operators of mediation. Polylogics is shortly defined as a distribution and mediation of classical logics.

In Prolog, each term as such has an identical meaning. If the variable x is denoted with "mary" and mary is female, then the relation or attribute female(mary) is true. Also the variables x, y, z,... are identical. Obviously no "x" will be read as an "y"; we don´t make a "x" for a "u".

In polylogic the situations are happily a little bit more flexible. The variables are flexible to occur as variables in different systems. The variable "x" can occur as the variable x in system S1, that is the variable x can occur as variable x1.

In the same sense the denotation "mary" can occur as female or as sibling or as parent or as something else. Mary as Mary, again something else, maybe a secret.

Also the simultaneity for "mary" of being female and sibling, which is ruled in the Prolog model by the conjunction "et", is realized in the polylogical model, obviously by the mediation rule "§".

This example is very simple because the elements of the partition are simple, there are no composed formulas included. Insofar there is no need to involve polycontextural negations, junctions and transjunctions. Only the operator of mediation "§" between distributed attributes and relations are involved.

Only if we freeze the scenario to a static ontological system all the flexibility of the as-function, not to confuse with the as-if-function, can boil down to the well known non-flexible structure. But to allow a flexible ontology with x as x1, as x2, etc. or mary as female, as sibling, etc. allows to change ontology and to be ready for new situations without starting the system from scratch. It is easy to freeze complexity, but there are no known rules how to make a frozen and dead systems alive. Maybe that's the reason why artificial life is nevertheless so hard.

Prolog refers as it has to do as a programming language based on First Order Logic (FOL) on attributes, relations between attributes and inference rules etc. and not on behaviors and contexts.

To be a parent is classically an attribute of a person, described as a relation to other persons, in PCL this attribute becomes a behavior, maybe of a person, in a complex situation. To be parents is not necessary connected with the attribute to be married, to be a sibling has not to be restricted to have the same parents, to be married has not to involve different gender, and so on. And even that a person is different to another person, or that the person is identical to itself is not as natural as it seems to be. All these presumptions are reasonable, and are corresponding to possible real world models only if all the possible ambiguities and over-determinations are ruled out in favor to a very special model of kinship.

The solution to this situation of complexity is not so much to enlarge the given ontology and to introduce the new differences and attributes to cope with the new situation. Because this strategy is based on the exact same ontological presuppositions and is therefore only repeating the old scenario again.

In the framework of PCL mechanism are offered for a great flexibility in interlocking and interweaving different points of view, situations, and modeling.

The decomposition of an universal domain into its different components is not only introducing a conceptual advantage for the process of modeling but also on a computational level a new form of parallelism is introduced.

The whole manoeuvre is quite similar to what I proposed as a proemial relation between sorts and universes in many-sorted first order logics.

Polycontexturality is not starting somewhere in a complexity, it is virulent at the very beginning of the basic definition of relationships.

Y as child of X and Y as the father of Z has to be mediated, synchronized, realized. Only in a stable hierarchical ontology this relationship of Y as "child of" and "father of" is automatically connected. And therefore "father of father" can be equal to "grandfather" and realized by a conjunction of the two relations, father(X,Y) et father(Y, Z) eq grandfather(X, Z).

In a polycontextural setting this identity of Y, as child and as father, can not be presupposed but has to be established in a possible context. Y as child and Y as father has to be brought together in a way that the transitivity can hold. It is easily possible that the transitivity is broken for some reasons and that it has to be re-established. The reason why the transitivity can be broken lies in the poly-contextural assumption that a entity or a relation is not a simple identity but involved in a cluster or an intersection of a multitude of possible contextures. Only for restricted and regulated situations a complex situation can be reasonably reduced to a mono-contextural one in which transitivity holds unrestricted. Therefore, identity can not be presupposed it has to be realized from case to case.

Because of the relative autonomy of both relations in a complex kinship system, we can calculate and study them simultaneously, realizing some elementary parallelism. This is obviously not possible in a strict biological interpretation of the father-child-relation. There we have to accept the hierarchical dependencies of the relations. But again, we have to be aware that this is the case only because we restrict the setting to a mono-contextural case. In contrast, real world social relations are always highly complex.

Therefore we have two options, the mono- and the polycontextural. The advantage of the later one is flexibility, the advantage of the first one is stability. Both have there weakness, flexibility is risky and dangerous, stability is restricting and killing.

Traditional object orientation assigns identity at the level of overall objects. Context orientation replaces this view of singular objects with that of plurality within the object; the object always neds a context to uniquely identify the relevant part of an overall object, which is what identifying nodes regulate. When behaviors are identical, no distinction between contexts is necessary.

From OO: super-level (type: person) --> sub-level(type: national), (type(foreigner) to

metapattern: (nationalship: person), (foreignship: person), (personship: person).

The class hierarchy of the OO model is transformed to a heterarchical model of behaviors, that is simultaneously ruling contexts.

But metapattern doesn´t offer much mechanism of navigation between simultaneous contexts. What we get is the notion of a pointer, "pointer information objects". They are supporting navigation from one context to another. But these pointers don´t give a hint how they could be implemented.

In contrast to the modelling aspect emphasized by the metapattern approach, from the point of view of implementation of the conceptual models we have to consider the underlying logics of the informational system, here ontologies for the Semantic web.

With this turn we are enabled to show the overwhelming advantage of the PCL approach over the classical modelling and implementing standards. It is the polycontectural, that is the polylogical apparatus which is framing the implementation of the deconstucted ontologies with the help of the metapattern. Without a polylogical implementation, the metapattern is an important modelling device but gives no guidelines for its real world implementation. This can by realized by polylogical funded data base logics.

Normally, the user of say OntoEdit, is not involved in the questions of implementations. But to give the OntoEdit more flexibility, the user is offered a "General Axiom" plugin which allows her to define and edit axioms.

Obviously, the new rules added by the user are only useful if they correspond to FOL.

Based upon a given object base (which can be considered as a set a facts), rules offer the possibility to derive new information, i.e., to extend the object base intensionally. Rules encode generic information of the form: Whenever the precondition is satisfied, the conclusion also is. The precondition is called rule body and is formed by an arbitrary logical formula consisting of P- or F-molecules, which are combined by OR, NOT, AND, <-, -> and <->. A -> B in the body is an abbreviation for NOT A OR B, A <- B is an abbreviation for NOT B OR A and <-> is an abbreviation for (A->B) AND (B<- A). Variables in the rule body may be quantified either existentially or universally. The conclusion, the rule head, is a conjunction of P- and F-molecules. Syntactically the rule head is separated from the rule body by the symbol <- and every rule ends with a dot. Non-ground rules use variables for passing information between subgoals and to the head. Every variable in the head of the rule must also occur in a positive F-Atom in the body of the rule. Assume an object base defining the methods father and mother for some persons, e.g., the set of facts given in Example 2.1.

Is the logic of data, information and records the same as the logic of knowledge? And further, is logic enough for representing knowledge?

I don´t want to go into the interesting discussions about the relationship of logic and knowledge representation languages as developed by the AI researchers long ago. What has to be mentioned is that in their different approaches they all introduced some two-level languages of object-level and meta-level theories.

To give a further motivation to introduce a poly-contextural view of data-base systems it maybe helpful to use the difference between logic of data and logic of knowledge.

The logic of data is quite strict, and well established by the classical systems of logic. Data are strictly non-ambiguous, they maybe not precise, but there is no need for hermeneutical interpretation. Data are in this sense facts. There linguistic model is the name. Facts have names and names are unambiguos, they name an entity. If someone, a person, is called "Meyer", he is not called in the same sense "Mueller". If a data-base consists of data as facts, the rules of logic apply without any restrictions. It is therefore natural to mix these data systems with a hierarchical concept system and to represent them as trees with a single root. The basic names of the Web are URIs, they are based in numbers, and these don´t need any hermeneutics.

But the situation can be considered in a radical different way. If the data-base consists not so much of data as facts but of data as concepts, there is no need to accept the hierarchical system of the classical solution.

If a person is called "Mueller", it´s about facts. If we deal with "persons" it´s not about facts it´s about concepts. Concepts and categories can be understood by the ontological model of names. This is the Aristotelian way. But this is, as we have learned in contemporary philosophy long ago, not the only way. It is a very restricted and obsolete position. Unfortunately it is what we learn from the ontologies of the Semantic Web.

The knowledge about facts is different from the knowledge about concepts. The knowledge about concepts involves some meta-language knowledge which belongs to another logical level than object-language knowledge.

The hierarchic architecture of concepts, as introduced by Aristotle and Porphyr, is a possible but not a necessary solution. It is oriented by object-knowledge. With this approach concepts are produced by abstraction over data sets. Objects, data, records, etc. are first. They have their identity defined on their object-level. There is no change of identity for objects. They are what they are. In this case, concepts are used to produce knowledge about objects and not knowledge about concepts.

Polycontexturality, like the metapattern approach, takes a different strategy. Objects are objects only in relationship to contexts. More adequate, objects are understood by their behavior. Therefore, an abstract object without any behavior, independent of contexts doesn't exist; it is a nil object.

Therefore, classical objects, like data, have a one-level behavior, they exist by being named. They are the result of the process of naming.

Semiotically we are making a shift from the dualistic to a trichotomic semiotics, and further to a chiastic graphematics.

While formalizing the principles governing physical objects or events is (quite) straightforward, intuition comes to odds when an ontology needs to be extended with non-physical objects, such as social institutions, organizations, plans, regulations, narratives, mental contents, schedules, parameters, diagnoses, etc. In fact, important fields of investigation have negated an ontological primitiveness to non-physical objects [7], because they are taken to have meaning only in combination with some other entity, i.e. their intended meaning results from a statement. For example, a norm, a plan, or a social role are to be represented as a (set of) statement(s), not as concepts. This position is documented by the almost exclusive attention dedicated by many important theoretical frameworks (BDI agent model, theory of trust, situation calculus, formal context analysis), to states of affairs, facts, beliefs, viewpoints, contexts, whose logical representation is set at the level of theories or models, not at the level of concepts or relations