As an exercise in logic programming in
GDL.
Let's look at the outputs of the rules
that we
just saw at various points during an
instance of the game.
To start, we can use the rule set to
compute the roles of the game.
This is simple in the case of
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contained explicitly in the rule set.
now the indicating portions of the rule
set, in the boxes
at the tops of these slides, and, and the
results below them.
Similarly, we can compute the possible
propositions of the game.
Remember that this gives a list of all
such propositions only
a subset are true, will be true at any
particular state.
Can
also compute the relevant actions of the
game for each player.
Extension of the input relation in this
case consists of the 20 sentences shown
here.
The first step in playing or simulating a
game is to compute the initial state.
Now we can do this by computing the init
relation.
As with rolls, this is really easy, since
the initial conditions are
explicitly listed in the program, though
that may not always be the case.
Once we have these conditions, we can turn
them into a state description for
the first step of the game, by asserting
that each initial condition is true.
Taking this input data and the logic
program, we can
check whether the state is terminal, in
this case it's not.
There are cells containing B which means
it's open and there's no line.
We can also compute the goal values of the
state.
And since the state is non-terminal
there's not much point in doing this.
But the description does give values for
the state, namely 50 for both white
and black since there's neither a line of
x's or a line of o's.
More interestingly, using the state
description and logic program,
we can compute the legal actions for the
state.
The white player has nine possible
actions, marking actions for each of
the blank cells, and the black player has
just one action, namely, noop.
let's suppose that the white player
chooses the first legal action.
Mark one, one and the bike player chooses
its sole legal action
noop, this gives us little data set like
the one shown here.
Now combining this data set with the state
description, and the logic
program, we can compute what must be true
in the next state.
For example, using the first update rule
and
the first does fact, we can conclude the
first
fact about the next state.
Namely that there will be an x in cell one
one.
In similar manner we can compute the
various other propositions that must be
true.
In the successive state.
Alright.
Now to produce a description for the
resulting state from next, we
substitute true for next in each of these
sentences and repeat the process.
And this continues until we encounter a
state that's terminal, at which
point we can compute the goals of the
players in a similar manner.
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