![](bg8.png)
and the action C has a utility of 3. Therefore, player 1
thinks that player 2 will perform this action, which
means we obtain the property p with frequency of 1.
If the world M
1
is the actual world, the three actions
D, P and C have a utility of 1. For player 1, player 2
will perform one of these three actions equiprobably.
The property is not true after performing actions D or
P, whereas it is true with a frequency of 1 after per-
forming action C. Thus, this universe value is:
1
1
+
1
3
2
.
The same reasoning is used for U
M
1
|C
which, in this
example, has the same computations as U
M
0
|C
. By cal-
culating the average value of these two universes, the
value of the action ”give a clue” is:
v
Clue
(U
M
0
,A, u, 1, p,2) =
1
1
+
1
3
2
+
1
1
+
1
3
2
2
=
2
3
Similarly, v
Discard
(U
M
0
,A, u, 1, p,2) =
1
3
and
v
Place
(U
M
0
,A, u, 1, p,2) =
2
3
. Hence, the best actions
are giving a clue and placing a card. Consequently,
the player intended to get the property ”I know my
card, and player 2 did not discard his” after two turns.
5 CONCLUSION
We defined here a modelling of intention. This is
not the first work integrating intention and epistemic
logic. Lorini and Herzig (Lorini and Herzig, 2008)
model intention via operators of successful or failed
attempts. However, their logic models time linearly
(i.e. there is only one possible future). It is therefore
much less natural to capture game semantics.
Note that, in our approach, the more a formula is
specific to a target universe, the more certain it is that
the actions will be considered intentional. Therefore,
a more general formula would, a priori, result in a bet-
ter characterization of intention. We intend, in future
contributions, to define the generality of a fomrmula
within a set of universes.
Also note that worlds are considered here as
equiprobable. It might be interesting, in a future
work, to integrate weighted logics such as the one pre-
sented by Legastelois (Legastelois, 2017).
Our modelling takes into account players able to
imagine all the possible worlds and all the universes
that would result from them following the actions they
think most relevant. If a machine already has limited
resources, this same job for a human is even more
difficult. One of the ways to take this limitation into
account would be to consider an action as one of the
best when its value exceeds a given threshold (for ex-
ample, 80% of the real maximum value).
Finally, a multi-valued logic such as the one in
(Yang et al., 2019) could be used to reduce the size
of epistemic models. Integration of this in our work
seems feasible.
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