tends it with epistemic capabilities enabling reason-
ing about a wide range of commonsense phenom-
ena, such as temporal and delayed knowledge ef-
fects, knowledge ramifications, concurrency, non-
determinism and others. It is a many-sorted first-order
language, where events indicate changes in the envi-
ronment, fluents denote time-varying properties and
a timepoint sort implements a linear time structure.
The Event Calculus defines predicates for expressing,
among others, which fluents hold when (HoldsAt),
what events happen (Happens) and which their ef-
fects are (Initiates, Terminates).
The theory employs the discrete time Event Calcu-
lus axiomatization described in (Mueller, 2006). It as-
sumes agents acting in dynamic environments, having
accurate but potentially incomplete knowledge and
able to perform knowledge-producing actions and ac-
tions with context-dependent effects. Knowledge is
treated as a fluent, namely the Knows fluent, which
expresses knowledge about fluents and fluent formu-
lae, obtained either from direct effects of actions or
indirectly through ramifications modeled as state con-
straints. For technical reasons, for direct effects the
auxiliary KP fluent (for ”knows persistently”) is used
that is related with the Knows fluent by the axiom
1
:
(KT2) HoldsAt(KP( f),t) ⇒ HoldsAt(Knows( f),t)
DECKT augments a domain axiomatization with a set
of meta-axioms describing epistemic derivations. For
instance, for positive effect axioms that specify un-
der what conditions action e initiates fluent f, i.e.,
V
i
HoldsAt( f
i
,t) ⇒ Initiates(e, f,t), DECKT intro-
duces the (KT3) set of axioms expressing that if the
conjunction of preconditions C = {
~
f
i
} is known then
after e the effect will be known to be true, such as:
(KT3.1)
V
f
i
∈C
HoldsAt(Knows( f
i
),t)∧
Happens(e,t) ⇒ Initiates(e, KP( f ),t)
In a similar fashion, the (KT5) axiom set cap-
tures the fact that if some precondition is un-
known while none is known to be false, then af-
ter e knowledge about the effect is lost. The ap-
proach proceeds analogously for negative effect ax-
ioms
V
i
HoldsAt( f
i
,t) ⇒ Terminates(e, f,t) and re-
lease axioms
V
i
HoldsAt( f
i
,t) ⇒ Releases(e, f,t).
The latter model non-deterministic effects, therefore
they result in loss of knowledge about the effect.
Knowledge-producing (sense) actions provide in-
formation about the truth value of fluents and, by def-
inition, cause no effect to the environment, instead
only affect the mental state of the agent:
(KT4) Initiates(sense( f), KPw( f),t)
1
Free variables are implicitly universally quantified.
Kw is an abbreviation for whether a fluent is
known (similarly for KPw): HoldsAt(Kw( f),t) ≡
HoldsAt(Knows( f),t) ∨ HoldsAt(Knows(¬ f),t)
Furthermore, the theory also axiomatizes so called
hidden causal dependencies (HCDs). HCDs are
created when executing actions with unknown
preconditions and capture the fact that in certain
cases, although knowledge about the effect is lost, it
becomes contingent on the preconditions; obtaining
knowledge about the latter through sensing can
provide information about whether the effect has
actually occurred. Consider the positive effect axiom
HoldsAt( f
′
,t) ⇒ Initiates(e, f,t), where fluent f
′
is unknown to the agent and f known to be false
at T (f may denote that a door is open, f
′
that a
robot stands in front of that door and e the action
of pushing forward gently). If e happens at T, f
becomes unknown at T + 1, as dictated by (KT5),
still a dependency between f
′
and f must be created
to declare that if we later sense any of them we can
infer information about the other, as long as no event
alters them in the meantime (either the robot was
standing in front of the door and opened it or the door
remained closed).
DECKT introduces the (KT6) set of axioms
that specify when HCDs are created or destroyed
and what knowledge is preserved when an HCD is
destroyed. For instance, for positive effect axioms
(KT6.1.1) below creates an appropriate implication
relation:
(KT6.1.1) ¬HoldsAt(Knows( f),t)∧
¬HoldsAt(Knows(
W
f
i
∈C
¬ f
i
),t)∧
W
f
i
∈C
[¬HoldsAt(Kw( f
i
),t)] ⇒
Initiates(e,KP( f ∨
W
f
j
∈C(t)
−
¬ f
j
),t)
where C(t)
−
denotes those precondition fluents that
are unknown to the agent at timepoint t. In a nut-
shell, DECKT augments the mental state of an agent
with a disjunctive knowledge formula, equivalent to
HoldsAt(Knows(
V
f
j
∈C(t)
−
f
j
⇒ f),t + 1), that en-
codes a notion of epistemic causality in the sense that
if future knowledge brings about (
V
f
j
∈C(t)
−
f
j
) it also
brings about f.
DECKT adopts an alternative representation for
knowledge that does not employ the possible worlds
semantics, which are computationally intensive and
not appropriate for practical implementations. In-
stead, its efficiency stems from the fact that HCDs,
which are based on a provably sound and complete
translation of possible worlds into implication rules,
are treated as ordinary fluents.
EPISTEMIC REASONING FOR AMBIENT INTELLIGENCE
243