Mental Events and Mental Objects

Chapter 10 – Section 4

Vocabulary

Logical Omniscience – to create an agent with infallible logic.

Knowledge Preconditions – Something which requires other knowledge to perform. Such as knowing someone’s phone number or having it saved before calling them.

Knowledge Effects – Knowledge that allows you to perform an action, such as knowing someone’s number has the effect of enabling you to call said person.

Knowledge about knowledge

In order for us to use inference in the best way possible we must construct a knowledge base about our knowledge base.

This may seem redundant, but if you know that you need a map in order to know where things are and do not have one, you know that the first step is to acquire a map, as opposed to attempting to calculate the distance based on no knowledge of the given geography what-so-ever, or simply saying that it’s unknown. This way we have a plan on what actions are needed and why certain data is important. (Knowledge Precondition that having a map has a desired Knowledge Effect)

Belief vs Knowledge

Knowledge; in terms of artificial intelligence is something which is always true.

Belief on the other hand deals more with probability. The same somewhat applies to life, without getting too abstract,

a simple example is that we know that eating food is necessary for living, so we eat. We do what we know is beneficial, we also do things which we believe are beneficial, such as attempting to gain money. One example of belief in society is gambling, we don’t know that we’ll win, but we know that there’s a probability that we’ll win, and we’ll place a bet if we believe we will win.

Belief is also something which can change over time, for example, Lois believes Superman flies today. T(Believes(Lois,”Flies(Superman)”),Today).

The same will not be true in 100 years when Superman’s died of old age.

Referential Transparency

Referential Transparency – One term can be interchanged with another term.

ie. Clark = Superman .·. Flies(Clark) = Flies(Superman)

Referentially Opaque

Referentially Opaque – The opposite of Referential Transparency, meaning that you cannot swap two equal terms.

Why this matters…

Just because Lois believes Superman can fly, doesn’t mean she believes that Clark can fly. By making the Flies(Superman) opaque, we can then say Believes(Lois,Flies(Superman)), without saying Believes(Lois,Flies(Clark)).

Modal Logic

Modal Logic simply defines Believes and Knows as opaque, and therefore no terms in the sentence are exchanged.

Syntactic Theory

Mental objects are represented by strings.

Even if Clark = Superman, “Clark” != “Superman.

.·. The objects are treated separately, while still maintaining equality (Separate but equal).

Unique String Axiom

For us to be able to link Superman to Clark, we’re going to have to do better than saying Clark = Superman, this model of thinking might exchange data that’s not meant for the other, such as which one wears glasses.

We can link them together instead by saying that they’re both equal to a unique ID. Let’s create an ID with Name, and assign the values with Den (like a cougar den).

ie. Name(ManOfSteel) = ID1234567

Den(“Clark”) = ManOfSteel ^ Den(Superman) = ManOfSteel

Defining Syntax

We must create the rules of syntax handling.

ie. If Lois ever found out Clark was Superman… Let p be Superman can fly

Let q be Clark can fly

Person(L) ^ Believes(L,p) ^ Believes(L,”pq”) Believes(L,q)

Remember the string problem though? Let’s fix that with Concat() Person(L) ^ Believes(L,p) ^ Believes(L,Concat(p,””,q)) Believes(L,q)

Das Ende

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