Behavior change support agents are most efective when they are personalized to the user's goals and motivations. To achieve this the agent should be able to create a user model based on limited initial inputs from the user. We demonstrate how autoepistemic logic can be used to build a model which combines direct input from the user with assumptions about the user's reasoning. These beliefs can be used when reasoning about the user's motivations, but they may also be rejected when presented with conflicting information. This results in a user model in which both knowledge and beliefs about the user are included but still clearly separated. We illustrate our ideas using an example of a behavior support agent which assists the user in exercising more.
ple who are in the process of changing their behavior or There is various technology that aims to support peo- is being used, which initial theory that information is adopting new habits [1]. In order for these behavior sup- agents output. This is also in line with a growing desire port agents to efectively support the user, especially over a longer period of time, they need to be able to adapt to their user’s goals, capabilities and preferences [2]. In this paper we use values to refer to the underlying reasons for choosing certain goals or actions [3]. This approach has been used in several systems [4], [5], especially because values are easily generalizable and tend to be relatively stable over time [6]. We take values to be the motivation for the goals that the user has set for themselves. Each action is connected to the goals it contributes towards or against and can either promote or demote a value. The values, goals and actions are each ordered by a priority relation which states how important they are to the user.
We see the agent and the user as a team and interpret the motivations of the user as a system which the agent and the user aim to optimize to achieve the goals of the user as much as possible. As described in [7], these teams can work together most efectively when they have a shared mental model of the system that is relevant to the task at hand. By representing the knowledge and the htp:/ceur-ws.org ISN1613-073
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reasoning of the user model explicitly, we make it possible
for the agent to explain to the user which information
based on and which efects the information has on the
to ensure that artificial agents are designed responsibly
and the user remains in control of how they use the
technology [8]. An explainable agent can help the user
understand and trust its suggestions [9], [
If the user model is inaccurate, the user should be able to change the relevant information and adapt the agent to their needs. This may be the case because the reasoning of the agent was diferent than the users, information was missing or the user motivations change over time.
Ideally, the agent is also able to recognize a conflict or gap in its knowledge base and ask the user for additional input to solve this. While the most accurate user model could theoretically be achieved by asking the user to input all details themselves, this would create a tedious user experience and deter people from engaging with the agent. Instead, the agent should be able to build a rich user model based of a few initial inputs by the user.
Human motivations can be incredibly complex since there are many diferent factors to consider when making a choice. The decision of whether someone wants to exercise can depend on the type of exercise, the time of day, the weather, and more. Additionally, there are many details which humans usually do not need to actively consider because they are not relevant. For example, it may be common to have few favorite sports but not to have a clear preference ranking of every sport. For these reasons, an agent’s model of the user’s motivations is unlikely to be perfectly accurate, especially considering the user’s of focusing exclusively on the accuracy of the model, (DK), (DB) Consistency Axiom: we emphasize the need for flexibility. Non-monotonic reasoning allows us to achieve this by making it easy to discard assumptions when new information contradicts them. We choose autoepistemic logic of knowledge and beliefs in particular because this allows us to treat the knowledge and the beliefs of the agent separately, which makes it easier to retrace where the information in the user model originates. This is especially useful when beliefs and knowledge contradict each other and we need to resolve the conflict. Additionally, by reasoning about the knowledge of the agent we can also express when something is not known and use this information to ask the user for additional input to build our model.
¬ ⊥, ¬ℬ⊥ (KK), (KB) Normality Axiom: for any sentences , ∈ ℒ , ( → ) → ( → ), ℬ( → ) → (ℬ → ℬ) Knowledge and Belief Necessitation Inference Rule: for any sentence ∈ ℒ , , ℬ
The Consistency Axioms state that falsity is neither known nor believed. The Normality Axioms state that if implies is known (or believed) and is known (or believed) then
must also be known (or believed).
The Necessitation Rule expresses that everything that is We now sketch how autoepistemic logic of knowledge provable in our logic is also known and believed. and beliefs can be used to build a flexible user model based on a few initial inputs from the user and assumptions
In [12] the intended meaning of the belief operator is given by the condition that is believed in an expansion by the agent. We separate these types of information by if is non-monotonically derivable from : reasoning about both the agents knowledge and its beliefs and we base our framework on the autoepistemic logic of knowledge and belief developed in [12]. However, since we want to reason about diferent types of objects such as goals and values and the relations between them, we need to include first-order reasoning. We therefore use a ifrst-order logic of knowledge an belief ( FOALKB).
The language of FOALKB is a first-order modal language ℒ,
with logical connectives ∨, ∧, →, ¬, ⊥, quantifiers ∀, ∃, variables , equality =, a set of predicate sym- tion bols , a set of constants and modal operators ℬ called knowledge and belief operators respectively. and We allow arbitrary nestings of knowledge and belief operators, although they are not necessarily relevant to our application purposes. However, we do not allow the modal operators to be applied to formulas with open variables. Additionally, we restrict the quantifiers to formulas which do not contain any knowledge or belief operators. We are using constant domain semantics, which means we take our domain to be fixed in all expansions of our theory, so we can interpret a sentence of the form ℬ∀ ()
to represent the set of sentences ℬ where is the proposition that expresses the truth value of () and ranges over all elements in our domain. Using this, we can translate all sentences from FOALKB into formulas of the propositional autoepsitemic logic of knowledge and beliefs introduced in [12]. For notation purposes we write our sentences in the language ℒ , , but we use the propositional results obtained in [12].
We assume the following axioms and inference rules to describe the properties of knowledge atoms and belief atoms respectively.
⊨ ℬ if ⊨ , where ⊨
denotes a specific non-monotonic inference relation. We will continue with the notion of minimal entailment which is also used in [12] which means that a sentence is believed to be true if it is true in all minimal models of the theory. A more in depth explanation can be found in [12].
we use the interpreta ⊨
if ⊨ , which means that is known in an expansion if and only if is derivable from .
When given an a FOALKB theory , we are interested in the possible extensions. In our application, contains the initial inputs and the expansions of this theory will constitute our enriched user model. We want these expansions to be closed towards further reasoning which is referred to as a static autoepistemic expansion in [12].
∗( ) as the closure of , the smallest set which contains the theory , all substitution instances of the axioms DK, KK, DB and KB and is closed under the necessitation rules and first-order logic.
A static autoepistemic expansion is a theory ∗ which satisfies the following fixed-point equation: ∗ = ∗( ∪ { ∣ ∗ ⊨ } ∪ {¬ ∣
∗ ⊭ } ∪ {ℬ ∣ ∗ ⊨min }) where ranges over all sentences in ℒ, . In particular we are interested in the zero, one or several consistent static autoepistemic expansions of a theory. The information in this model can be separated into can see that this framework provides us opportunities to three categories. The objective statements are are state- infer additional assumptions which would normally not ments which are independent from the user, such as defibe included in the expansions of our theory. nitions of the objects and relations of the model. In our If we take to be the set of all objective sentences and example we define the unary predicates Goal( ), Value( ) the knowledge sentence (2), we observe that Comfort ≤ and Action( ) to express that is a goal, a value or an Health ∉ action respectively, ≤ (, ) , ≤ (, ) and ≤
(, ) denote priorities between goals, values and actions re- static expansion ∗ would even contain ℬ¬(Comfort ≤ spectively, motiv(, ) a goal , adv(, )
to denote that a value motivates to denote that an action contributes
Health) if we use minimal entailment to interpret the belief operator. This would obviously not be useful for to the relation between Comfort and Health. In fact, the ∗( ) since we have no information about to achieving a goals , prom(, ) tion positively relates to a value , dem(, ) that an action negatively relates to a value and their respective properties.
to denote that an ac
our user model. We could have avoided this situation to denote
by asking the user to provide a full ranking of the val ( Goal(GoForRun)) This states that going for a run is a goal of the user.
( Comfort ≤ Social ∧ Social ≤ Health)
(2) This expresses that the user prioritizes Health over Social
( prom(GymFriend, Health) ∧ prom(GymFriend, Social) ∧ prom(Party, Social)) This expresses that going to the gym with a friend promotes the values Health and Social and going to a party promotes Social.
The beliefs of the agent are based on assumptions which the agent uses in its reasoning process. These assumptions may have been explicitly included during chological research, or they may be formulated during use of the agent based on current data regarding the user.
We give some examples of beliefs which we may want to incorporate in our example agent.
ℬ (∀, , ∶ ( ≤
∧ ≤ ) → ≤ ) This expresses that the priorities the user has between values are transitive.
ℬ (∀, ∶
Action() ∧ Value( ) ∧ ¬
prom(, ) → dem(, )) This expresses that if we do not know that an action promotes a value, then we assume that the action demotes the value instead. All these belief sentences express plausible assumptions in the context of our exercise support agent. While these are relatively simple examples, we (3) (4) (5) The knowledge of the agent comes from the direct more complex scenarios this is no longer feasible. No-one inputs of the user. These sentences could take many wants to provide an ordered list of their top 100 activities forms but we give a few examples below. the design of the agent, based on previous data or psy- By using FOALKB we can build an enriched user model ues, which would have been acceptable in this simplified scenario with only three diferent values. However, in but they will probably be willing to provide their favorite or decide between two options. By including belief sen(1) tences such as (4) the expansion ∗ will now contain the belief sentence ℬ(Comfort ≤ Health), just as intended.
Next, we take to be the set of all objective sentences and knowledge sentences, but omit the belief sentences.
how diferent actions relate to the values we have. Since we have no information about any actions demoting values, the static expansion ∗ would not only contain ¬ dem(GymFriend, Comfort) but also ℬ¬dem(GymFriend, Comfort). This may be warranted if we assume that the user would tell us if an action afects a value in any way and we accept that the value Comfort is not afected by going to the gym with a friend. However, if we include belief sentence (5), then we clearly see that ℬdem(GymFriend, Comfort) ∈ ∗.
based on incomplete initial inputs from the user and assumptions which the agent has about the user model. In the created model we can easily distinguish between information which is based directly on knowledge about the user and information which the agent has infered based on other assumptions. In future work we will explore how this afects the understandability and trustworthiness of the agent. Additionally, we want the agent to allow for additional inputs from the user in case their motivations change or the model is inaccurate. We will explore how we can best incorporate knowledge and belief revision into our framework to make this possible. Lastly, we will explore which additional challenges arise when implementing the framework into a suitable logic programming language. This includes looking into the computational complexity and possibly placing additional restrictions on the logic.