Bialowieza

{ this chapter is in active development; quite a lot of the technical detail in this chapter at present will probably end up in Implementing, while additional high level and conceptual design, as it develops, will be here. }

Why Bialowieza?

Bialowieza is the second iteration of the Wildwood engine, and this following convention its name should start with ‘B’. Białowieża is Europe’s last great wild wood, and it is currently under threat.

Motivation

The current motivation for restarting work on Wildwood is to provide non-player characters in a game world with sufficient intelligence that they can enter into meaningful unscripted conversations about objects and events in that world.

Major components of Bialowieza

Knowledge Accessors

The wildwood.knowledge-accessor/Accessor protocol defines a bidirectional transducer which can fetch data from whatever storage representation the calling application uses into the representation defined by wildwood.schema.

Advocates

The wildwood.advocate/Advocate protocol describes an agent which can take part in decision processes.

The engine itself

The engine is implemented by the namespace wildwood.bialowieza.

Inference processes

Advocates are entitled to use whatever inference processes they like, but they have access to wildwood.dengine, which is an implementation of the DTree engine described in the chapter on Arboretum adapted to propositions as defined in wildwood.schema.

Propositions

{ TODO read, and follow references from, https://plato.stanford.edu/entries/propositions/ }

As a slightly tendentious first stab, a proposition is a sentence which is either true or false. This is tendentious because two different sentences which have the same underlying semantic import are usually considered to be instances of the same proposition, and seen from the other end, there may be many ways you can validly express a single proposition in a single natural language. However, for the present purpose, the proposition that a proposition is a sentence is good enough.

A sentence generally has the form

<verb subject object>

with possibly a lot of other qualifying material.

So we shall say that a proposition will be represented as a Clojure map with at least the keys:

• :verb - what is asserted
• :subject - of whom (or what)
• :object - to whom (or what)

Thus

{:verb :kill :subject :brutus :object :caesar}

is a proposition which asserts that Brutus killed Caesar.

There may be many other privileged keys, such as

• :location - where did it happen? value might be something from which proximity may be derived;
• :time - when did it happen? This needs to be a value with a canonical order, such as a number;
• :truth - is it true? if present and value false, negates the proposition;
• :confidence - how sure am I? A value, perhaps, in the range -1 to 1, although conventionally if less than 1 we probably set the :truth value to false;
• :data - an argument structure…!
• :authority - id of agent from whom, or rule from which, I know this;

and so on. The exact set of privileged keys is probably actually a matter for particular advocates rather than for the engine itself, although if the advocates in the game don’t broadly share the same set of privileged keys then it won’t work very well.

However…

The attentive reader will note that some of the proposed privileged keys map closely onto the Toulmin schema. Thus we can say:

• that the proposition itself is a claim in the sense of the C term;
• that :data above is precisely data in the sense of the D term in Toulmin’s schema, but may (is likely to) also provide a warrant in the sense of the W term;
• that :truth and :confidence are both qualifiers of the claim in the sense of the Q term;
• that :authority is a form of backing in the sense of the B term.

So what, then, is an ‘argument structure’, as described above? It seems to me that it may be exactly a proposition, with the special feature that the value of the :data key is not minimised.

Recall that in the chapter on Arboretum I observed that the working of the DTree decision algorithm caused precisely those nodes to be collected whose fragments which provided the most relevant explanation to support the decision, in a natural sequence from the general to the particular. I believe that precisely the same fortuitous alchemy will provide the argument structure to provide Toulmin’s D - out :data term. The DTree itself then becomes the W - the :warrant; and the author of the DTree becomes the :authority.

{ TODO: investigate how this notion of a proposition - and a Toulmin structure - relates to situation semantics; especially, consider how locating a proposition in time and space captures the notion of a situation. }

The located proposition

Aristotle’s propositions are essentially two position: they describe a relationship between two entities, a subject and an object. But they’re not located.

Thus:

• Socrates is a man

Tells us that Socrates is always, and everywhere, a man. If Socrates led a double life - if, perhaps, when in Lesbos, he lived as a woman - this simple proposition cannot capture the fact. Let’s draw another example, to make clear.

• Brutus killed Caesar

tells us that, and only that, Brutus killed Caesar. It doesn’t allow us to say how Brutus killed Caesar. If we then say

• Brutus used Dagger₁

It still doesn’t help, because we don’t know how these two propositions relate to one another. Brutus could indeed have used this particular dagger at some time, it might well be the dagger that kille Caesar, but there’s no smoking gun.

But if we say

1. Brutus killed Caesar in the Forum on the Ides of March
2. Brutus used Dagger₁ in the Forum on the Ides of March
3. Dagger₁ caused Wound₁ in the Forum on the Ides of March
4. Caesar died of Wound₁ in the Forum on the Ides of March

then provided the atomicity of our notions of time and space is sufficiently fine, we’re getting pretty close. Adding a notion of location to propositions leads to the notion of an event, a small bundle or ball of time and space which gives them context; and we can reason with this.

The size of an event is, of course, a slightly slippery notion. The inference that Caesar died (at least partly) from the blow struck by Brutus is only possible if the envelope of the event is fairly small - no more than a few metres, no more than a few minutes. But if we replace Dagger₁ with Rifle₁ then the spatial extent of the event can be considerable expanded; and if it’s LandMine₁, then the temporal aspect similarly so.

Are located two-position propositions sufficient?

The reason I like the idea of investigating whether located two position propositions are sufficient is that a very regular knowlege representation is easy to compute over. The reason I think it might not be is this:

Suppose Calpurnia told Drusilla that Brutus killed Caesar in the Forum on the Ides of March. For simplicity, let’s call

• Brutus killed Caesar in the Forum on the Ides of March.

‘Proposition₁’, or ‘P₁’ for short. What is the warrant for believing P₁? Well, it’s that Calpurnia told Drusilla (and presumably, that Drusilla has now told us).

So we have a notional event E₁ such that

• P₁ := ‘Brutus killed Caesar in the Forum on the Ides of March.’
• P₂ := ‘Calpurnia uttered P₁ at E₁.’
• P₃ := ‘Drusilla heard P₁ at E₁.’

And the warrant for the belief that P₁ is the conjunction of P₂ and P₃.

Writing it down like that, it kind of works, but I’m not yet wholly persuaded. It feels clumsy.

As an exercise for the reader, how would we represent ‘Dirck, Joris and I carried the good news from Ghent to Aix’ using only located two position propositions? It feels, as I said, clumsy.

There is, of course, also a lurking combinatorial explosion here. If for each proposition which is learned, two further propositions must be learned as warrant for the first proposition, the world blows up. In an ideal platonic universe we may indeed have turtles all the way down, but in a finite machine we need to say, arbitrarily but ruthlessly, that some classes of proposition will be stored unwarranted.

The event is (like) a situation

I would draw the reader’s attention, here, to the similarity between the notion of an event, discussed above, and the notion of a situation, as discussed by Barwise & Perry. In particular, I’d like to draw attention to similarity between the account I’ve given of how Drusilla’s belief that Brutus killed Caesar is warranted by

• P₂ := ‘Calpurnia uttered P₁ at E₁.’
• P₃ := ‘Drusilla heard P₁ at E₁.’

and the account of explanation as a situation E defined:

E := at I1: understands, a, c; no
    understands, b, c; yes
    enquirlng, a; yes
    addressing, a, b; yes
    saying, a, q; yes
    subject, q, c; yes

  at I2: responding, b, q; yes
    addressing, b, a; yes
    saying, b, u; yes
    subject, u, c; yes

  at I3: understands, a, c; yes
    understands, b, c; yes

  I1 < I2 < I3

where: a, b are some actors; c is some concept; q, u are some utterances.

Explicitly:

• Drusilla => a
• Calpurnia => b
• P₁ => c
• E₁ => I2

I’d argue that these are clearly very similar.

My schema does not specify that “at I1: … understands, a, c; no”, but there’s a reason for that.

Learning, consistency and confidence

Let us suppose that Drusilla already knows the proposition that

• Brutus killed Caesar in Rome in March.

Calpurnia now tells her that

• Brutus killed Caesar in the Forum on the Ides of March.

The two accounts are compatible; this compatibility migh be represented, if you choose, by two further propositions:

• P₄ The Forum is within Rome.
• P₅ The Ides of March is within March.

Philosophers, after Plato, very often argue as though they inhabited ideal universes in which every agent always tells the truth, but the real world is not like that. For any person, there are few other people that that person trusts implicitly. The very notion that we need a warrant for a belief is an explicit recognition of the fact that knowledge is imperfect.

So (unless she witnessed it herself, in which case you’d expect her to have more precise information), Drusilla does not know, in a strong sense, that Brutus killed Caesar in Rome in March. She has some degree of confidence in that proposition, which is likely to be less than perfect.

When she learns from Calpurnia that Brutus killed Caesar in the Forum on the Ides of March, because the two claims are compatible, her confidence in each is likely to increase.

By contrast, if Falco then says ‘No, I heard from Gaius that it happened in April’, then that casts doubt on both the first two claims - but also on this new claim. Because the claims are not compatible, they can’t all be right.

For the time being, I’m going to leave the issue of how confidence is derived and adjusted as an implementation detail; I don’t - yet, at any rate - have an account of how this should work that I can defend. However, there’s one further significant point to make about propositions before we move on.

On the subtext of propositions

Propositions are not atomic. They do not come single spies, but freighted with battalions of inferable subtexts. Suppose Calpurnia says

• Brutus killed Caesar in Rome during the ides of March

I learn more than just that ‘Brutus killed Caesar in Rome during the ides of March’. I also learn that

• Brutus is a killer
• Caesar has been killed
• Rome is a place where killings happen
• The Ides of March are a time to be extra cautious

Suppose Cassius now says

• Longus killed Caesar in Rome during the ides of March

this may cast some doubt on Calpurnia’s primary claim, and on the belief that Brutus is a killer. It doesn’t rule it out - the accounts are compatible - but it certainly doesn’t confirm it. However it does reinforce the beliefs that

• Caesar has been killed
• Rome is a place where killings happen
• The ides of March are a time to be extra cautious.

If Falco then says

• No, I heard from Gaius that it happened in April

the beliefs that

• Caesar has been killed
• Rome is a place where killings happen

are still further strengthened.

In proposing a formalism to express propositions, we need to consider how it allows this freight to be unpacked.

{ TODO: if we receive a new proposition which confirms a proposition we already know, our confidence in both increases. If we learn a new one which contradicts one we already know, our confidence in both decreases. Expand! }

Proposition minimisation

{ TODO: probably lose this. I increasingly think that, whatever the internal representation of the proposition within the advocate or knowledge base, the proposition as passed around must always be minimised. This is, in any case, very much an implementation detail. }

How are the values of :subject, :object and so on to be passed? If we pass rich knowledge structures around, then we lose the insight that different advocates may know different things about given objects. Thus, while internally within each advocate’s knowledge base objects may be stored with rich data, when they’re passed around in propositions they should be minimised - that is to say, the value should just be a unique identifier, such that, for every object in the domain, if an advocate knows anything at all about that object, it knows its unique identifier and knows the object by that unique identifier.

Thus the unique identifier has something of the nature of a ‘true name’, in the magical sense. A given true name, a given unique identifier, refers to precisely one thing in the world, and provided that two advocates both know the same true name, they can debats propositions which refer to the object with that true name.

Generally, a true name shall be a Clojure keyword. That keyword, passed to any advocate in the game, shall identify either nil (the advocate knows nothing of the object), or a map representing everything the advocate knows about the object, and within that map, the value of the key :id shall be that true name.

But in saying ‘the advocate knows’, actually, the advocate knows nothing. The advocate has access to a knowledge base, and it is in the knowledge base that the knowledge is stored. It may be an individual knowledge base, in which case we can implement that idea that different advocates may have the different knowledge about the same object, or it may be a shared consensual knowledge base.

A proposition is represented as a map. So to minimise a proposition, for every value in that map, if the value is itself a map it shall be replaced by the value of the key :id in that map.

This means that every implementation of the wildwood.knowledge-accessor/Accessor protocol must transduce whatever token its backing store uses as the primary key for an object to :id when it performs a fetch operation.

Thoughts on the shape of a knowledge base

The object of building Bialowieza as a library is that we should not constrain how applications which use the library store their knowledge. Rather, knowledge accessors must transduce between the representation used by the particular storage implementation and that defined in wildwood.schema. However, what we’ve described above suggests that a hierarchical database would be a very natural fit for knowlege base data - more natural, in this case, than a relational database.

Prejudice, and defaults

In Arboretum and later in KnacqTools, default values of features were determined by the ‘knowledge engineer’, normally by asking the domain expert, and were fixed for the knowledge base at all times. But these two programs each reasoned about one case at a time, and did not store knowledge about multiple cases.

These systems could thus be said to be prejudiced, to the extent that knowledge of the world acquired over time did not change their default judgements. Wildwood holds knowledge on potentially very many objects, and that knowledge may change dynamically over time, both as the world changes and as new things which already existed in the world become known.

Suppose we wish to decide the truth value of the proposition

{:verb :is :subject :brutus :object :honourable}

Suppose we have no rule for this, so we want to use a default. Suppose we scan all the propositions in the knowledge base which match the pattern

{:verb :is :object :honourable}

and divide them into two sets, those which assert true and those which assert false.

If the arity of the true set is greater than the arity of the false set, then the default is true (and vice versa). But we can derive more than this: we can derive a confidence score, based on the ratio of true instances to false instances.

The problem is that this is computationally expensive. So we need to cache default values. Different advocates may use different caching strategies, with different ‘time to live’. The longer the time to live of a cached default, the more prejudiced - the less agile in learning - the advocate will be; but the faster it will be able to produce decisions.