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As an exercise in logic programming in
GDL.

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Let's look at the outputs of the rules
that we

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just saw at various points during an
instance of the game.

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To start, we can use the rule set to
compute the roles of the game.

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This is simple in the case of

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[INAUDIBLE]

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contained explicitly in the rule set.

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now the indicating portions of the rule
set, in the boxes

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at the tops of these slides, and, and the
results below them.

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Similarly, we can compute the possible
propositions of the game.

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Remember that this gives a list of all
such propositions only

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a subset are true, will be true at any
particular state.

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Can

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also compute the relevant actions of the
game for each player.

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Extension of the input relation in this

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case consists of the 20 sentences shown
here.

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The first step in playing or simulating a
game is to compute the initial state.

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Now we can do this by computing the init
relation.

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As with rolls, this is really easy, since
the initial conditions are

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explicitly listed in the program, though
that may not always be the case.

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Once we have these conditions, we can turn
them into a state description for

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the first step of the game, by asserting
that each initial condition is true.

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Taking this input data and the logic
program, we can

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check whether the state is terminal, in
this case it's not.

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There are cells containing B which means
it's open and there's no line.

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We can also compute the goal values of the
state.

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And since the state is non-terminal
there's not much point in doing this.

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But the description does give values for
the state, namely 50 for both white

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and black since there's neither a line of
x's or a line of o's.

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More interestingly, using the state
description and logic program,

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we can compute the legal actions for the
state.

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The white player has nine possible
actions, marking actions for each of

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the blank cells, and the black player has
just one action, namely, noop.

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let's suppose that the white player
chooses the first legal action.

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Mark one, one and the bike player chooses
its sole legal action

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noop, this gives us little data set like
the one shown here.

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Now combining this data set with the state
description, and the logic

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program, we can compute what must be true
in the next state.

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For example, using the first update rule
and

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the first does fact, we can conclude the
first

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fact about the next state.

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Namely that there will be an x in cell one
one.

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In similar manner we can compute the

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various other propositions that must be
true.

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In the successive state.

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Alright.

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Now to produce a description for the
resulting state from next, we

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substitute true for next in each of these
sentences and repeat the process.

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And this continues until we encounter a
state that's terminal, at which

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point we can compute the goals of the
players in a similar manner.

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[BLANK_AUDIO]