We covered the key role of attributes in my last blogpost, moving from the blunter scope of groups and roles to the more fine-grained approach of attributes. Now we’re going to take this progression a step further, as we narrow in on my favorite topic: digital context. (If you haven’t already, check out my first two posts on context, where I laid out the roadmap and looked at groups, roles, and attributes.) Our first order today is to travel back to logic class and think about predicates.* But Michel, you’re thinking, what does all this have to do with digital context? Well, one way to describe a context about something is to express it using sentences related to the question. While we will come back to the definition of context in a following post, for now let’s just say that we need some building blocks to express facts about the world, some form of sentences that can be interpreted by a computer, and logic is one of the tools for that.
Subject-Predicate-Object: First Order Logic 101
In my most recent post, we saw how the notions of groups and roles ended up in the increased use of attributes as a way to categorize or define identities. This should not be surprising. Behind this use of attributes lays a fundamental mechanism—a way to represent a simple fact. And it’s the same mechanism that we use when we reason based on the rules of formal logic, which has been in practice forever, or when we represent a fact on a computer (think SQL). In fact, one of the greatest achievements of the early 20th century has been the formalization of logic (needed for mathematic foundation) and computation. This type of logical representation is core to everything we do, as reasoned thinkers and as computer scientists.
But in case you’re a few years removed from logic class, let’s examine this mechanism at work by looking at some very simple diagrams about what we are doing when we associate some attribute with a person or an object, such as assigning a person to a group:
Or assigning a subgroup to a group:
Each of these constructs can be summarized by the following diagram:
In this diagram, a fact can be asserted by the notation: subject-predicate-object. In predicate logic (AKA first order logic), it’s conventionally written as predicate(X,Y), where the variables X and Y could be themselves objects (references to entities) and/or values (arbitrarily “quoted” labels belonging to the initial vocabulary of our logic system). For instance, in our example above, the fact that “Jane is member of the product marketing group” can be written as memberOf(“Jane”,”Product Marketing”) and subGroupOf(“Product Marketing”,“Marketing”).
These kinds of predicates are called “binary” predicates and they are quite common. So if there are binary predicates, the astute reader (that’s you!) might well wonder if there are also unary predicates and, more generally, n-ary predicates. Indeed, the unary predicate exists and generally it’s used to assign a label to an entity—so if we want to say that Jane is an executive, you would write it as executive(“Jane”). As for the n-ary predicate, well here’s where you will find the usual “n-slots” notation of entities/tables as they’re used in the relational/SQL world. So we’d see something like this: age(“Jane”, “33”) or employee(“Jane”, “33”,”product marketing”).
Now, if you look at all those diagrams above, you’ll notice they have a direction, an orientation that tells us which entity plays the role of subject, since the object for a given predicate cannot generally be substituted. This translates into a given order for the different slots of a predicate; for example, in the notation age(“Jane”, “33”), the first slot—“Jane”—is for the person, and the second—“33”—is for her age. Of course, there are always exceptions where the slots are permutable, such as the “brother binary predicate,” where if x is a brother of y—brother(“x”,”y”)— then y is also a brother of x, which could read: brother(“y”,”x”)= brother(“x”,”y”). But in general order, orientation matters.
The diagrams above form directed graphs and the orientation is essential for preserving the semantics of this representation. After all, saying that x kills y—Kill(“x”,”y”)—is very different from saying that y kills x—Kill(“y”,”x”)!
Essential Semantics: Describing Our World in First Order Sentences
So all this is great, but what does it have to do with context? Stay with me here…we’ve seen that when we reduce everything into attributes, we are reducing the world to first principles. But at the same time, by associating attributes to an entity and recombining them progressively through predicates, we are describing a complete world based on “sentences” of first order logic. If you combine those sentences with the usual Boolean operators (Not, And, Or, and the rest of the derived Boolean Zoo members), you get a world that’s pretty complete—complete enough to act as the foundation of mathematics.
And the good news here is that this world is also pretty close to our own “world of discourse” (albeit a lot like my English: awkward and somewhat robotic). Basically, it’s made of simple sentences in the form of subject-predicate-value (where the predicate is the adjective or qualifier), or subject-attribute-object (where the attribute is the verb). Remember our friend Jane from above? Here are some things we know related to Jane:
Jane is member of marketing group.
Product marketing is subgroup of marketing group.
The beauty of the predicate representation is that a huge part of our digital world is already encoded this way. In fact, all of our so-called “structured information”—databases, transactions, etc—runs according to these principles. But the maze of protocols and security representations we’re all dealing with, from SQL, to LDAP, to APIs, to programming languages, has long masked this reality. We need a way to rise above this modern tower of Babel, a way to translate all that structured, transactional data into something more useful, more contextually-driven. In my next post, I’m excited to show you that we’ve done exactly that: returned to first principles to deliver a “contextual and computational language” that’s as easy to interpret at the human level as it is to execute at the machine level. And this is a huge leap forward. We know we can’t teach our marketing teams to think like machines—and believe me, I’VE TRIED—but imagine a world where a business person and an application can both understand, and act on, the exact same notation. Such a world is possible today…so do not miss my next post!
PS: Some of you have been in on this series from the beginning, but all this blogging began as a response to Ian Glazer’s video on killing IAM in order to save it. For those of you just joining the story, you can catch up with the entire story here: one, two, three, four, five, six, seven, eight.
*See what I did there? That was for all the mathematicians…and for Anil John, who’s just as a big a logic geek as I am. 🙂