1. The VSK logic for Intelligent Agents
Michael Wooldridge and Alessio Lomuscio
“Multi-Agent VSK Logic”
Proceedings of the 17th European Workshop on Logics in AI, 2000

2. Outline Introduction A Semantic framework Visibility Perception
Knowledge
A Case study: vacuum world

3. Agents
An agent is anything that can be viewed as perceiving its environment through sensors and acting upon that environment through actuators.

4. Agency Autonomy Reactivity Proavtivity Social Ability
acting independently.
Reactivity
reacting to changes that occur in the environment.
Proavtivity
taking the initiative.
Social Ability
interacting with other agents via communication.

5. Environments Accessible vs. inaccessible
An accessible environment is one in which the agent can obtain complete, accurate, up-to-date information about the environment’s state.
Most moderately complex environments (including, for example, the everyday physical world and the Internet) are inaccessible.
The more accessible an environment is, the simpler it is to build agents to operate in it.

6. Environments Deterministic vs. non-deterministic
A deterministic environment is one in which any action has a single guaranteed effect — there is no uncertainty about the state that will result from performing an action.
Non-deterministic environments present greater problems for the agent designer.

7. Environments Episodic vs. sequential
In an episodic environment, the performance of an agent is dependent on a number of discrete episodes, with no link between the performance of an agent in different scenarios.

8. Environments Static vs. dynamic
A static environment is one that can be assumed to remain unchanged except by the performance of actions by the agent.
A dynamic environment is one that has other processes operating on it, and which hence changes in ways beyond the agent’s control.

9. Environments Discrete vs. continuous
An environment is discrete if there are a fixed, finite number of actions and percepts in it.
Continuous environments have a certain level of mismatch with computer systems

10. Multi-Agent Systems

11. Goals
When designing a multi-agent system to carry out a task in environment, it is necessary to:
Reason about the information properties of the agent and its environment.
The information should be accessible, otherwise agents won’t be able to carry out the desired task.
Agents’ sensor must be capable of perceiving the information.
Agents should have abilities to store and reason about the information of the environment.

12. VSK Logic
VSK logic is a multi-model logic, containing modalities “V”, “S”, and “K”
V means that the information  is accessible in the current environment state.
S means that the agent perceives (senses) .
K means that the agent knows .

13. A Semantic Framework

14. Environments An environment Env is a tuple
Env = <E, vis1, …, visn, e, e0>, where
E = {e1, e2, …} is a set of instantaneous local states for the environment
visi : E2E is the visibility function of agent i.
The idea is that if the environment is actually in state e, then it is impossible for agent i in the environment to distinguish between e and any member of visi(e).
visi is transparent if visi(e)=e.
e : E  Act1  …  Actn  E is a total state transform function for the environment.
e0 is the initial state of Env.

15. Agent An agent Agi is a tuple
Agi = <Li, Acti, seei, doi, i, łi>, where:
Li = {li1, li2,…} is a set of instantaneous local states for agent i.
Acti = {i1, i2, …} is a set of actions for agent i.
seei : 2E  Perci is the perception function for agent i.
doi : Li  Acti is the action selection function for agent i, mapping local states to actions available to agent i.
i : Li  Perci  Li is the state transformer function for agent i.
łi is the initial state for agent i.

16. A VSK system
A multi-agent VSK system is a structure M = <Env, Ag1, …, Agn>.
The global states G = {g, g’, …} of a multi-agent VSK system are a subset of E  L1 …  Ln.

17. A run
A run of a multi-agent VSK system is a sequence of global states.
A sequence (g0, g1, …) over G represents a run of a system <Env, Ag1, …, Agn> iff
G0 = (e0, 1 (ł1, see1(vis1(e0))), …,
n (łn, seen(visn(e0)))), and
For all u, if gu = (e, l1, …, ln) and gu+1 = (e’, l’1, …, l’n) then:
e’  e (e, 1, …,n) where i = doi(li) and
l’i = i(li, seei(visi(e’)))

18. Visibility
Interpretation of the formula V is true in some state g  G.
The property  is visible of the environment when it is in state g, not only is  true of the environment, but any agent equipped with suitable sensor would be able to perceive the information .
If V were true in some state, then no agent, no matter how good its sensor was, would be able to perceive .

19. Sense Interpretation of the formula S is true in some state g  G.
Something is visible does not mean that an agent actually sees it.
S represents the information that an agent sees.
SV

20. Knowledge
Interpretation of the formula K is true in some state g  G.
K represents the fact that an agent has knowledge of the formula represented by .
SK if an agent’s next state function is complete.
KS means the agent is local.

21. A case study: vacuum world
A robot agent occupies an environment with two rooms, room 1 and room 2.
The rooms are connected by a single door, which may be open or closed.
Initially, the robot is in room 1.
There may be dirt on the floor in either or both of these rooms.
The robot can detect:
Whether the door is open or closed
Whether it is in the same room as some dirt

22. A case study: vacuum world (cont.)
It has a vacuum cleaner which will suck dirt from one room to the other.
It is also capable of opening the door and moving from one room to the other.
When the door is closed, it is impossible to tell whether there is dirt in the other room. However, when the door is open, an agent could detect dirt in the other room.

23. Possible states of the vacuum world

24. Visibility function of the vacuum world
vis(ei)=
{e0, e1} if ei=e0 or ei=e1
{e4, e5} if ei=e4 or ei=e5
{e8, e12} if ei=e8 or ei=e12
{e9, e13} if ei=e9 or ei=e13
{ei} otherwise

25. Perception of the vacuum world
p0: door ((ag1  d1)(ag2  d2))
p1: door ((ag1  d1)(ag2  d2))
p2: door ((ag1  d1)(ag2  d2))
p3: door ((ag1  d1)(ag2  d2))

26. “see” function of the vacuum world
see(X) =
p0 if X = {e0,e1} or X = {e8,e12}
p1 if X = {e4,e5} or X = {e9,e13}
p2 if X {e2,e3,e10,e14}
p3 if X  {e6,e7,e11,e15}

27. “next state” function of the vacuum world
L = {ł, l0, l1, l2, l3}, where:
ł is the initial state
l0 is the state coding door being closed, and no dirt being present
l1 is the state coding door being closed, and dirt being present
l2 is the state coding door being open, no dirt being present
l3 is the state coding door being open, dirt being present
(li, pj)=
l0 if pj=p0; l1 if pj=p1; l2 if pj=p2; l3 if pj=p3

28. do function of the vacuum world
do(l)=
null if l=ł
open if l=l0
move if l=l2
suck if l=l1 or l=l3
The history of the vacuum world
<e5,l1>suck<e1,l0>open<e3,l2>move<e11,l3>suck<e10,l2>move<e2,l2>move…..