SADT (Structured Analysis and Design Technique) has an "SA" graphical language of boxes and arrows that can be used in two complementary ways, called Data Modeling and Activity Modeling, in which the roles of the two graphic features swap -- the adjective specifying the use of the SA Box, for D or A, respectively -- the SA Arrows then being A or D, so that both aspects always are present.
SA Boxes are named and (selected) SA Arrow Segments are labeled with natural-language noun- or verb-forms, as appropriate to the type of modeling and the subject matter of interest. The branching arrow structure of SA boxes' interfacing together naturally yields SA Diagrams (the "sentences" of SA) -- the syntax of which includes a few important additional meaningful annotations that ensure structural integrity of the modeling and enrich the expressiveness of the language, as well. As is characteristic of all of Plex's Picture Language Modeling (PLMing), every visible aspect of SA is linguistic and has a well-determined meaning and role to play.
Any subject's
can be modeled to arbitrary extent and precision. Multiple subjective views of a single objective object of study can be networked together. Digital meaning results, in the sense that although natural language (kown for its ambiguity and imprecision) is used throughout, the graphical structuring constrains all linguistic constructs to comprise a single integrated meaning, squeezing out confusion, like an FM receiver tunes out what would be AM static and distortion. The Reader/Author Cycle that is the centerpiee of the "DT" pragmatics of SADT's SA language encourages "good citizenship" of critiquing and refinement of the modeling to ensure that practical objectives are met fully and economically.
As an interpreted mathematical graph, (probably uniquely) SADT's A and D modeling are Total Duals in that, linguistically, they have exactly the same syntax, semantics, and pragmatics. Activity and data modeling differ only at the pragmatics level -- and then only in an option (that need not be taken). The option applies to any individual SA Box, which is a rectangular box that is integral with and surrounded by an impinging
matching (clockwise, from the left side) the Input, Control, Output, and Mechanism box-sides to which they attach -- only Output being oriented away from the box. Although enigmatic by itself, the Formal Saying for the SA Activity Box is:
which augments the inherited means.
The Saying for the Data box is less elegant; the side roles are the same, and Input is the activity that creates what Output may access or consume, and Control is an activity moderating that. The crucial pragmatics option that really distinguishes totally static from totally dynamic (like particles versus waves in quantum physics) is:
The difference is profound, for it makes Data Labels that are atemporal and definitive (the fundamental think/g-nouns for analysis). Universally it is true that
an SA box's boundary, by definition. This has both profound and interesting consequences,
Outside the boxes of an SA diagram, but inside that child-diagram's boundary, all of the meaning of the entire diagram (inherited from its parent box) is carried by the prescriptively labeled arrow structure -- and hence there is no meaning at all inside the boxes. But on the other hand, before any detailing of any one of those child boxes can take place -- all of that arrow meaning is totally drained out from the arrows and their auras, into the diagram's boxes -- just the appropriate inheritance for each one -- and leaving none at all in the arrow structure. This ensures that every child box has precisely its appropriate inheritance from the parent, so that in a totally fair deliberation, the most worthy child box can be chosen for detailing. In this state, all the meaning is inside the boxes, the trunklines and the auras of arrow meaning having been totally drained into the boxes.
When, through analysis effort and modeling skill, the first chosen child box obtains its detailing and now has become the parent of the grandchildren who are that new detailing -- all festooned with their new prescriptive arrow labels and their connections to all of the other detailing boxes in there -- notice what has happend. That portion of the new parent's original inheritance has been augmented by new, insightful meaning. As each new grandchild has been created and hooked in, the new meaning builds more and more pressure inside that growing diagram of grandchildren siblings. As soon as the last (grand-)child of that first-to-be detailed child box (now the new parent) is complete -- instantly there is a surge of that new meaning bursting forth into the original arrow structure network. With wild shuffling of portions here and there, eventually again, all the meaning resides in the arrow structure, with none left over in the boxes. (It is possible that every original-child's meaning will have been changed, and each one eagerly awaits its turn to be chosen next for detailing.) ... and so the story goes.
The surging of bits of meaning from one box to another amounts to a continual re-calculation of just where those sibling boundaries ought to be. Think of squeegeeing-together various meaning pile-ups and entrapping one pile within a dull cookie-cutter node boundary. Then reset the boundary so that a bit of the pile is on its other side. This mental image matches SA's ancient << "migrating B-box"> SA boundary> model in which, like a cartoon ostrich swallowing an orange --
before | ...A + B |-| C... | >---> | ...A |-| B + C... | after
-- the B sub-box changes its side of the ' |-| ' interface between two parent boxes, changing from siblings A to siblings C.
Profoundly but simply --
(flexibly so that expressiveness of the SA language is enhanced)
to guarantee the integrity of all interfaces.
[ICOM Coding: The impinging I,C,O,M arrows of a Parent box (--or of a Called box) are imagined to be numbered left-to-right or top-to-bottom, and resulting <<letter>#> codes (I1, C3) are attached one of two places: Either
to match them to (-- or to also over-ride selected ICOMs of the thus-being-mated-female-parent Called box, which supplies the Support Model detailing of their mixed-ancestry offspring! See 'These are the two...' slide] In general, then: ICOM-coded matching therefore stages between
- the outside through to
- the inside of a (single or paired) parent box boundary through to
- the inside of the child diagram boundary
-- for by definition, all (two or three) of those boundaries are the same -- the whole construction being that of the (that unique one- or two-) Parent Node (family of multiple offspring). [The above slide also shows upward-pointing SA Support (branching M-arrows; see how they start as "Tunneled Arrows") that distributes permission for many matings of a single Called box, but only with acceptable, selected families!
[An old DTR saying is: "You can't define an interface from just one side." Therefore, if the Called box is an atom, the Call is not a mating (for there are no offspring), but instead is a paremeterization of that atom -- in the sense that in the expression 'Ax + y', 'A' is a Caller-supplied parameter, while the x and y are Called's variables. The SA Reference Language includes provision for Conditional DREs (detail reference expressions) so that a choice of child-diagram detailings is allowed, as well.]
Hence an SA Model is a top-down hierarchy of SA diagrams having a Node Number coordinate system: Every box has a box number (0 - 6), and (starting with A or D and with initial-zero-suppression) the node number of a child is the node number of the parent with that box number appended. Nodes A0 and D0 are the Topmost Ancestor -- the origin for the corrdinate system of the model. The SA Reference Language combines this with ICOM coding to provide complete means of textual reference to, and tracing of, every aspect of the graphic displayed elements.
This completes the profound consequence mentioned above.
The Digital-Meaning of RSADT modeling --The power of Omission
The interesting consequence arises when the hierarchy of the model is displayed either as the Node Tree of the model -- the (brief) box names are graphically portrayed as an upside down tree -- or preferably, in Table of Contents format: the suitably indented and node-numbered (longer) diagram titles, with page numbers.
-- universally accepted and used for all communication purposes! If only visually, the fact that SA's rich arrow structure is in addition to this standard approach to taxonomic organization of information shows that there is much more to expect from this new (to most people) development.
the clear and concise presentation of
definitive and understandable designs, explanations, and analyses of
every sort.
But the true story is much deeper, and has a surprise, as well, for paradoxically,
-- those definitive bounding-arrow-meanings -- networked together by the forks and joins of the branching arrow structure. That structure propagates the prescriptive label-meanings to and through every directed interface between the box nodes right down to the individual atoms that constitute (collectively) the viewpoint of the model. [Those atoms complementarily comprise -- i.e. both encompass and make up, as the ultimate foundation -- all there is to say in that model.] It is important to notice that through each level of detatiling, ICOM coding ensures that the proper connection is made, and that just the right meaning penetrates through the completed interfaces to become "+" requirements that the box's detailing must satisfy. (This is true even for dual-parent Call modeling.) But here is what may be most surprising.
Even at the atomic level (where they have no children)
-- their very emptiness creating a vacuum of unsatisfied requirements -- fiercely searching, like the cups of a huge octopus, to glom onto any real instance of what that modeling actually defines!
Although they are essential in the top-down analysis process, where they provide inordinate (better yet, extra-ordinate) help and guidance in the struggle to get things just right --
That also, however, is why they are an important focus in SA's Reader/Author Cycle, where they do supply extraordinary support and confirmation to aid in the acquisiiton of the proper interpretation of the meaning structure so richly displayed. SADT, practiced well, has no peer.
But the powerful omissions in RSADT/AUT go still deeper, providing the self-consistent, no-external-boundary-conditions, error-free (the ultimate WYSIWYG, so if you don't like what you see, your only recourse is to improve the modeling) perfection of Digital Meaning. It starts with --
From Entry
Omission Arise Definition and Absraction
This is the crucial pragmatics option mentioned that the beginning:
Collectively, Control and Input are called the Entries to an SA box. The total omission of Control makes that individual data box's modeling be both atemporal and definitive:
-- without any conditions or restraint. When carried over to the dual activity modeling, some of the data arrows in activity modeling then not only are prescriptive -- they, too, are definitive, so the activities there also start to become definitive -- which, when carried back over to the dual data modeling, then makes the remaining activity arrows in the data modeling definitive also, so that (finally!) the other data boxes also acquire definitive meaning! [It is all one system so that after sufficient back-and-forth resounding iterations everything settles to a definitive condition.]
In practice, in both instances the "carrying over" actually is performed in the opposite direction. It is called the SA Tie Process, and works as follows: Every SA model of any sort has a topmost ancestral parent box. That box is the opening viewpoint (by definition, being that one atom) -- which is Node 0 -- from which each of its children, and their offspring in turn, derive. Each one acquires its own inheritance from the "Everything" of Node 0. Therefore any meaning of any segment of any arrow in one model must by definition map into at least that topmost box of the other model. From there it similarly may map into just one of the offspring siblings – repeatedly – until finally, either it reaches an atom or its meaning would fit more than one sibling, so it makes no further progress. In either case, the unique stop yields the node number which then is assigned to the arrow-segment meaning (which is unchanged by the process).
Not every arrow segment has a directly-attached meaning-label, of course – but very much the same process applies to that matter, as well. The SA arrow structure is all important. Wherever it may be attached, each prescriptive arrow-label's meaning similarly propagates its effect from the segment to which it is attached, in both branching directions (picture the many root-and-leaf tips of a vine) -- in effect coloring as it goes, until it achieves ICOM status at box boundaries. Whenever a diagram boundary is crossed, ICOM coding continues the progress so the end effect is atom to atom, everywhere. It is those "sticks" of possibility that may be realized to make an actual connection that makes all SA meaning. Those atom-to-atom sticks are bundled together by the branching structure (like cables of insulated wires, above the most-primitive vine level of free choices, all shorted to the same meaning).
These are the facts that set the stage for the Tie Process itself.
The entire semantics of RSADT ultimately derives from the single primitive concept --
in 0, 1, 2, 3, (or more?) dimensions.
The <closed boundary> idea is natural for 2 and 3 dimensions, and maybe for 4, if one is time. For dimensions 1 and 0 the boundary concept degenerates successively to <PAIR of points> (topologically, the 1D sphere, which does have an inside) and POINT (the 0D sphere, with degenerate inside, <nen>), respectively, from the mimal normative 2D case -- where the only-possible three definitive relations between two closed boundaries are
-- which also is the case for dimension 3. 'The Structured Analysis Box', shows (subatomically) the nesting of a <3 half-stick> "sticky blob" (which is the reality-core of SA semantics) inside the SA Box boundary, as well as the open-channel nature(s) of the SA interface arrows.
0D points (called "P1 points" in Plex foundations)
literally are indistinguishable, except for their Identity
-- defined by proposition P4: ‘The identity of a
point is the collection of all other points.' The total
collection of all points (called "the P3 world") being
non-Nothing (for sub-worlds turn out to be distinguishable)
ensures that P1 points are not merely Nothing -- for each
is <relevant nothing> relative to that P3 collection. In
fact, by P5, every
P1 point is the
P3-P5 world! -- a fact that holds by
P2: 'Let there be only points.' (in the proof considerations). [A
P1 point is not the Empty Set of standard
Set Theory (which "exists" only by axiom, requiring the Axiom of
Choice as a repairing axiom, as well -- even in formulations
where the Empty Set is inferred from other axioms.] Then, P6
continues: ‘Let an instant be a world with one
distinguished point.’ -- as the Plex world-view
literally takes off toward the foundations of spacetime.
Realizing a Connection
To tie the above Plex considerations to SA semantics -- the blob itself is a sub-world, of course, and whenever an individual stick is made real (i.e. "is realized") by being completed by its other half-stick, so that two SA-boxes' blobs actually are linked through an interface channel,
This happens precisely through that 1D closed boundary, mentioned above. Before realization, the stick is a mere possibility -- a 1D closed bounary, itself -- a pair of end-points of that stick, one in each blob! -- however remote they may be to each other through that hollow interface arrow! Realization of that possibility creates the Actual Stick of meaning as the 1D INSIDE of that 1D CLOSED BOUNDARY!!! Those two endpoints were
that went through all those coded ICOMs, all the time being
until the other endpoint was reached -- just waiting for this to happen --
no matter how many join- or fork-branchings, or nested boundary-crossings are made (see the <? to !> path ). To be realized, the individual stick must pass muster with every arrow-segment label’s meaning encountered along the way, so that a valid ICOM meaning is presented to both blobs’ boxes, and throughout its length. Should a conflicting label later be attached, that stick will instantly be reduced to a mere possibility -- destroyed by the contradiction, by definition. A realized stick of meaning is a 1D inside, each end of which is (by P5) its <relevant nothing> boundary -- the 0D pair of the 1D sphere, literally "with a foot in each camp"! Those literally are its end-points.
How full is that inside? Start first with "How empty is empty?" assuming that we can use that name for that particular Nothingness state of "inside". In Plex, it has the name "<nen>" which is short for ‘not even nothing’. [Single quotes signify; double quotes name -- and both of those, as well as the ‘< >’ meaning quotes (also called finding quotes, for they match meaning to reality), all come from the primary Formal Saying that provides the foundation for all of meaning in Plex:
-- which has the consequence that "<nothing> quotes" are what quote a word, itself!
So what about consecutive <nothing>-quotations? What separates their <<right><left>> <nothing>s as they abutt? Well, <nen>, of course -- they P1-P5 collapse into just one <nothing> -- thereby providing the proper actual meaning of "word", in Plex foundations, which has no need for "syllable", "phrase", etc. because all such concepts can precisely be < >-parsed! [To make all this rigorous, <nen>’s companion "<nei>" for ‘not even irrelevant’ is necessary, and the pair of them also is sufficient, for
also is a Plex Formal Saying. Notice: Still the Empty Set does not arise, here in Plex, where <nenotation> provides the n-dimensional pre-birth state for any nascent possibility, so that the local relevance context always is explicit.
So How full is that inside? Full enough, by definition, for even <one new P1<<other than the<others>>point> is sufficient. Furthermore, no matter how many times this possibility is realized, twinkling on and off, or how many other SA Box-pairs may have the same stick P1-indistinguishably arise. The bundled sticks now themselves make another P1-P5 world of precisely that ICOM meaning (now-abstracted, because, once established, it is the collection of label-meanings that provides the relevant indistinguishability, not the branching-vine tips). Each time and place a stick is renewed -- each is just as indistinguishably the same BEing as any other, so again P5 holds. [The specifics here may not prove out, in detail, but the gist should be reliable.]
Returning to Plex definitions:
(where BEing is mere non-Nothingness). Furthermore,
The difference made by its non-Nothing realization matters -- What role does it fulfill? What's the difference without and then with <it> included in the state of affairs? That's the meaning of meaning that matters to SA and Plex.
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As shown in the "SADT Time Line" slide, in Part 2 of the ICAM Project, (Integrated Computer-Aided Manufacturing) with SofTech still prime contractor, leading a large coalition of large companies, the ICAM sponsor insisted that SADT's natural Data Modeling (of Things) be omitted, while at the same time, its Activity Modeling (of Happenings) -- renamed IDEF0 (ICAM Definition) -- was to be joined by IDEF1 Database Modeling, and IDEF2 Behavior Modeling (all related name-only!), to be developed by subcontractors under SofTech's contract. The reason? SA's data modeling was deemed to be "too hard" for industry! The cost? Incalculable, for then the mathematical elegance and symmetric completeness of SADT was destroyed, and IDEF0 became merely the best of a competing zoo of other software development CASE tools, none of which were scientifically founded. [For many years the IDEF methodologies were mandated for most manufacturing technology upgrades, and when IDEF0 also then was selected as a "golden nugget" method for all DoD Business Process Reengineering to save $billions annually, IDEF0 and a completely revised IDEF1X were made Federal Standards in 1983. The ad hoc, invented semantics, specified there for IDEF0, definitely is not that of SADT, however.]
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[In fact, S and T Modeling for the States and Transitions of such a complete A and D Modeling of a given subject makes the mathematical structure still more unique and interesting as a open topic for deep natural-systems research, and was a factor in accepting the un-pronounceable name, "SADT", in 1974! In "SADT", "SA" is the Structured Analysis graphical language, proper, and "DT" is the Design Technique pragmatics of its proper application in the "Structured Analysis and Design Technique" methodology trademarked by SofTech.]
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