Chitta Baral
Professor, School of Computing, Informatics & DSE
Key faculty, Center for Evolutionary Medicine & Inform.
Arizona State University
Tempe, AZ 85287
1

Action, Change and Evolution: importance to KR & R
 Historical importance
 Applicability to various domains
 Various knowledge representation aspects
 Various kinds of reasoning
2

- interpreted by Plato in Cratylus
" No man ever steps in the same river twice, for it is not the same river and he is not the same man.
“
Panta rei kai ouden menei
Panta rei kai ouden menei
All things are in motion and nothing at rest.
3




… different waters flow in rivers staying the same.
In other words, though the waters are always changing, the rivers stay the same.
Indeed, it must be precisely because the waters are always changing that there are rivers at all, rather than lakes or ponds.
 The message is that rivers can stay the same over time even though, or indeed because, the waters change. The point, then, is not that everything is changing, but that the fact that some things change makes possible the continued existence of other things.
4

5

Where does that line of thought lead us?
 Change is ubiquitous
 But one can shape the change in a desired way
 Some emerging KR issues



How to specify change
How to specify our desires/goals regarding the change
How to construct/verify ways to control the change
6

“Action and Change” is encountered often in Computing as well as other fields

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Robots and Agents
Updates to a database
 Becomes more interesting when updates trigger active rules
Distributed Systems
Computer programs
…
Modeling cell behavior
 Ligand coming in contact with a receptor
Construction Engineering
…
7

 Need for non-monotonicity
 Probabilistic reasoning
 Modal logics
 Open and closed domains
 Causality
 Hybrid reasoning
8

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Prediction
Plan verification; control verification
Narratives
Counterfactuals
Causal reasoning
Planning; control generation
Explanation
Diagnosis
Hypothesis generation
9

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
Motivation: How to specify transition between states of the world due to actions?
 A state transition table would be too space consuming!
Assume by default that properties of the world normally do not change and specify the exceptions of what changes .
 How to precisely state the above?
 Many finer issues!
 To be elaborate upon as we proceed further.
10



Leibniz, c.1679
 "everything is presumed to remain in the state in which it is"
Newton, 1687
( Philosophiae Naturalis
Principia Mathematica )
 An object will remain at rest, or continue to move at a constant velocity, unless a resultant force acts on it.
11

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1959 McCarthy (Programs with common sense),
1969 McCarthy and Hayes 1969 (Some philosophical problems from the standpoint of AI) – origin of the
“frame problem” in AI.
1971 Raphael – The frame problem in problem-solving systems (Defines the frame problem nicely)
1972 Sandewall – An approach to the frame problem
1972 Hewitt – PLANNER
1973 Hayes – The Frame problem and related problems in AI
1977 Hayes – The logic of frames
1978 Reiter – On reasoning by default
12

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In the last section of part 3, in proving that one person could get into conversation with another, we were obliged to add the hypothesis that if a person has a telephone he still has it after looking up a number in the telephone book. If we had a number of actions to be performed in sequence we would have quite a number of conditions to write down that certain actions do not change the values of certain fluents. In fact with n actions and m fluents we might have to write down mn such conditions.
We see two ways out of this difficulty. The rest is to introduce the notion of frame, like the state vector in McCarthy (1962). A number of fluents are declared as attached to the frame and the effect of an action is described by telling which fluents are changed, all others being presumed unchanged.
13

 Action and Change is an important topic in
KR & R





Its historical basis goes back to pre Plato and
Aristotle days
In AI it goes back to the founding days of AI
It has a wide applicability
It involves various kind of KR aspects
It involves various kinds of reasoning
14

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Highlights of some important results and turning points in describing the world and how actions change the world (physical as well as mental)
Other aspects of action and change: here we will talk about mostly our work
 Specifying Goals
 Agent architecture
 Applications
A future direction
 Interesting issues with multiple agents 15

The Yale Shooting Problem: Hanks &
McDermott (AAAI 1986)
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Nonmonotonic formal systems have been proposed as an extension to classical first-order logic that will capture the process of human “default reasoning” or
“plausible inference” through their inference mechanisms, just as modus ponens provides a model for deductive reasoning. …
We provide axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning, thus presumably amenable to representation in nonmonotonic logic. Upon examining the resulting nonmonotonic theories, however, we find that the inferences permitted by the logics are not those we had intended when we wrote the axioms, and in fact are much weaker. This problem is shown to be independent of the logic used; nor does it depend on any particular temporal representation.
Upon analyzing the failure we find that the nonmonotonic logics we considered are inherently incapable of representing this kind of default reasoning.
16

Reiter 1991: A simple solution (sometimes) to the frame problem
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Combines earlier proposal by Schubert (1990) and Pednault
(1989) together with a suitable closure assumption.
Intermediate point:


Poss(a,s)
 pre
R
+ (a,s)

R(do(a,s) )
Poss(a,s)
 pre
R
(a,s)

~R(do(a,s) )
Poss(a,s)

[ R(do(a,s) )
 pre
R
+ (a,s)

R(s)

~ pre
R
(a,s) ) ]
17

Lin & Shoham 1991:
Provably correct theories of actions

“… argued that a useful way to tackle the frame problem is to consider a monotonic theory with explicit frame axioms first, and then to show that a succinct and provably equivalent representation using, for example, nonmonotonic logics, captures the frame axioms concisely”
18

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1991/1994 Book ; IJCAI 1993; 1994 JLC: The range of applicability of some non-monotonic logics for strict inertia
Propose a systematic methodology to analyze a proposed theory in terms of its selection function
When

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Y is a scenario description (expressed using logical formulae),

(Y) is the set of intended models of Y
S(Y) is the set of models of Y selected by the selection function S
Validation of S means showing


S(Y) =

(Y) for an interesting and sufficient large class of Y.
Range of applicability is the set Z: Y

Z

S(Y) =

(Y)
19

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1992. Gelfond & Lifschitz. Representing actions in extended logic programs. Journal of Logic Programming version in 1993.
Syntax
 Value proposition


 F after A1; …; Am initially F
Effect proposition
 A causes F if P1, …, Pm
Domain Description: a set of propositions
Semantics


Entailment between Domain Descriptions & Value Propositions
Entailment defined by models of domain descriptions
 Models defined in terms of initial states and transition between states due to actions
20
Sound translation to logic programs

Kartha 93: Soundness and Completeness of three formalizations of actions
 Used A as the base language
 Proposed translations to

Pednault’s scheme

Reiter’s scheme
 A circumscriptive schemed based on a method by
Baker
 Proved the soundness and completeness of the translations.
21

 1990: I first learn about Frame problem from
Don Perlis
 1991-92: Learn more about it from Michael
Gelfond
22

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Initial frame problem
 Succinctly specifying state transition due to an action
What if we allow actions to be executed in parallel?
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
Do we explicitly specify effects of each possible subsets of actions executed in parallel?
 Too many
Do we just add their effects?
 May not match reality
 l_lift causes spilled r_lift causes spilled
{l_lift, r_lift} causes ~spilled if
~spilled
{l_lift, r_lift} causes lifted
 initially ~spilled, ~lifted paint causes painted
23

 Inherit from subsets under normal circumstances; and
 use specified exceptions when necessary.
 High level language: syntax and semantics
 Logic programming formulation
 Correctness theorem
 Similar work by Lin and Shoham in 1992.
24

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Execution of an action a in a state s causes a fluent literal f if

 a immediately causes f (defined as: there is a proposition a causes f if p
1
, …, p n such that p
1
, …, p n hold in s
) a inherits the effect f from its subsets in s
. (i.e. there is a b
 a , such that execution of b in s immediately causes f and there is no c such that b
 c  a and execution of c in s immediately causes ~ f .)
E + ( a , s) = { f : f is a fluent and execution of a in s causes f }
E ( a , s) = { f : f is a fluent and execution of a in s causes ~ f }
F( a, s) = s 
E + ( a , s)
\ E ( a , s).
25

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Inertia
 holds(F, res(A,S))
 holds(F,S), not may_i_cause(A, F’,S), atomic(A), not undefined(A,S).
Translating “a causes f if p1, …, pn”

 may_i_cause(a,f,S)
 not h’(p1,S), …, not h’(pn,S).
cause(a,f,S)
 h(p1,S), …, h(pn,S).
Effect axioms

 holds(F, res(A,S))
 cause(A,F,S), not undefined(A,S).
undefined(A,S)
 may_i_cause(A, F,S), may_i_cause(A, F’,S).
Inheritance axioms
 holds(F, res(A,S))  subset(B,A), holds(F, res(B,S)), not noninh(F,A,S),


 not undefined (A,S).
cancels(X,Y,F,S)
 subset(X,Z), subseeq(Z,Y), cause(Z,F’,S).
noninh(F,A,S)
 subseeq(U,A), may_i_cause(U, F’,S), not cancels(U,A,F’,S).
undefined(A,S)  noninh(F,A,S), noninh(F’,A,S).
26

Effect of actions in presence of specifications relating fluents in the world
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Examples of “state constraints”:

 dead iff ~alive.
at(X)
 at(Y)

X = Y.
Winslett 1988: s ’  F
(a, s
) if
 s ’ satisfies the direct effect (E) of an action plus state
 constraints (C) and
There is no other state s ” that satisfies E and C and that is closer (defined using symmetric difference) to s than s ’.
But?
27

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Lin’s Suitcase example (Lin - IJCAI 95)
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 flip1 causes up1 filp2 causes up2
State Constraint: up1
 up2
 open initially up1, ~up2, ~open.
What happens if we do flip2?
 But up1
 up2  open is equivalent to ~open
 up2  ~up1
Marrying and moving (me - IJCAI 95)

 at(X)
 at(Y)

X = Y.
married_to(X)
 married_to(Y)

X = Y.
 Ramification vs. Qualification.
28


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We Suggested in IJCAI 95 that a causal specification (in particular: Marek and Truszczynski’s Revision programs) be used to specify “state constraints”

 out(at_B)  in(at_A). out(at_A)  in(at_B).
 in(married_to_A), in(married_to_B).
Presented a way to translate it to logic programs.
 Thus a logic programming solution to the frame problem in presence of “state constraints” that can express causality and that distinguished between ramification and qualification.
 We proved soundness and completeness theorems.
McCain and Turner presented a conditional logic based solution in the same IJCAI. (1995)
Lin 1995: Embracing causality in specifying indirect effects of actions
Thielscher 1996
Used in RCS-Advisor system developed at Texas Tech university.
29


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Moore 1979, 1984 for any two possible worlds w1 and w2 such that w2 is the result of the execution of a in w1 the worlds that are compatible with what the agent knows in w2 are exactly the worlds that are the result of executing a in some world that is compatible with what the agent knows in w1
Suppose sense f is an action that the agent can perform to know if f is true or not. Then for any world represented by w1 and w2 such that w2 is the result of sense f happening in w1 the world that is compatible with what the agent knows in w2 are exactly those worlds that are the result of sense f happening in some world that is compatible with what the agent knows in w1 and in which f has the same truth value as in w2.
30 Scherl & Levesque 1993

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Effect Specifications
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 push_door causes open if ~locked, ~jammed push_door causes jammed if locked flip_lock causes locked if ~ locked
 flip_lock causes ~ locked if locked initially ~ jammed, ~ open
Goal: To make open true
P1: If ~locked then push_door else flip_lock; push_door
P2: sense_locked
If ~locked then push_door else flip_lock; push_door
31

Formalizing sensing actions: a transition function based approach (with Son AIJ 2001) s1 s1, s2, s3, s4, … s1‘, s2’, s3’, … sense f s1 s1, s2, s3, s4, …
32

Combining narratives with hypothetical reasoning: planning from the current situation
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With Gelfond & Provetti JLP1997 – The language L
Besides effect axioms of the type
 a causes f if p
1
, …, p n
We have occurrence and precedence facts of the form


 f at s i a occurs_at s i s i preceeds s j
33


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 rent causes has_car hit causes ~has_car drive causes at_airport if has_car drive causes ~at_home if has_car pack causes packed if at_home
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 at_home at s0
~at_airport at s0 has_car at s0
PLAN
EXECUTE s0 preceeds s1 pack occurs_at s1
OBSERVE s1 preceeds s2
~has_car at s2
Needs to make a new PLAN from the CURRENT situation
34

From sensing and narratives to dynamic diagnosis: basic ideas (With McIlraith, Son: KR2000)

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Diagnosis: Reiter defined diagnosis to be a fault assignment to the various component of the system that is consistent with (or explains) the observations; Thielscher extended it to dynamic diagnosis.
Dynamic diagnosis using L and sensing:


Necessity of Diagnosis: When observation is inconsistent with the assumption that all components were initially fine and no action that can break one of those component occurred. I.e., (SD \ SD ab
, OBS

OK
0
) does not have a model
Diagnostic model M: is a model of the narrative (SD, OBS

OK
0
)
Narratives


OBS: s
0
< s
1
< s
2
~light_on at s
0
< s
3 light_on at s
1
~light_on at s
2 turn_on occurs_at s
0 turn_on occurs_between s turn_off occurs_at s
1
2
, s
3
OK
0
: ~ab(bulb) at s
0
.
~light_on at s
3
Diagnostic plan: A conditional plan with sensing actions which when executed gives sufficient information to reach a unique diagnosis.
35

Golog: JLP1997 (Levesque, Reiter,
Lesperance, Lin, Scherl)
 A logic based language to program robots/agents
 Allows programs to reason about the state of the world and consider effects of various possible course of actions before committing to a particular behavior
 I.e., it will unfold to an executable sequence of actions
 Based on theories of action and extended version of Situation calculus
36

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Primitive actions
Test actions (fluent formulas to be test in a situation)
Sequence
Non-deterministic choice of two actions
Non-deterministic choice of action arguments
Non-deterministic iteration (conditionals and while loops can be defined using it)
Procedures
37

 Work at Toronto
 Work at York
 Work at Aachen
 Etc.
38

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Non-deterministic effect of actions
Probabilistic effect of actions with causal relationships; counterfactual reasoning
Defeasible specification of effects
Presence of triggers
Characterizing active databases
Actions with durations
Hybrid effects of actions
Thielschers’ fluent calculus
Event calculus
Modular action description
Learning action models
…
39

 Mostly about describing how actions may change the world
40




Highlights of some important results and turning points in describing the world and how actions change the world (physical as well as mental)
Other aspects of action and change: mostly presenting our work
 Specifying Goals and directives
 Agent architecture
 Applications
A future direction
 Interesting issues with multiple agents 41

42


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


Always f , also written as □ f
 too strong for many kind of maintainability (eg. maintain the room clean)
Always Eventually f, also written as □ ◊ f.


Weak in the sense it does not give an estimate on when f will be made true.
May not be achievable in presence of continuous interference by belligerent agents.
□ f
□ ◊
3
-----------------□ ◊ k f --------------------------
□ ◊ f f is a shorthand for
□ ( f V O f V OO f V OOO f )
But if an external agent keeps interfering how is one supposed to guarantee □ ◊
3 f .
43

Definition of k-maintainability: AAAI 00


Given
 A system A
= ( S , A , Ф ), where

S is the set of system states


A is the union of agent actions A ag
, and environmental actions A env
Ф : S x A → 2
S
 A set of initial states S, a set of maintenance states E, parameter k, a function exo : S → 2
A env about exogenous action occurrence we say that a control K k-maintains S with respect to E, if
 for each state s reachable from S via K and exo, and each sequence σ
= s , s
1
, . . . , s r
(r <=k) that unfolds within k steps by executing K, we have
{ s , s
1
, . . . , s r
} ∩ E ≠ { }.
44

No 3-maintainable policy for S = {b} with respect to E = {h} b a a’ a c e f e a g d a h
45

3-maintainable policy for S = {b} with respect to E = {h}
Do a in b, c and d.
e a c a d a a a’ f b h e g
46

Finding k-maintainable policies (if exists) : an overview (joint work with T. Eiter): ICAPS 04



Encoding the problem in SAT whose models, if exists, encode the k-maintainable policies.
This SAT encoding can be recasted as a Horn logic program whose least model encodes the maximal control.
(Maintainability is almost similar to Dijkstra’s selfstabilization in distributed systems.)
47

a
7 a
7 a
1
~p , q,~r,~s s
2 a
5 a
2 a
5 a
6
~p , q, r,~s s
1 a
1
~p , ~q,~r,~s s
5 a
4 a
3 a
3 p ,s s
4
~p , ~q,r,~s s
3
48

p
1 a
7 a
7
~p s
2 a
2 a
1 a
5 a
5 a
6
~p s
1 a
1 a
4
~p a
3 s
5 a
3 p s
4
~p s
3
49

p
 LTL: Next, Always, Eventually, Until
 For plans that are action sequences


CTL*: exists path, all paths
 For plans that are action sequences p
-CTL*: exists path following the policy under consideration, all paths following the policy under construction. (ECAI 04)
 For policies (mapping states to actions)
50


 p
-CTL* not powerful enough! (AAAI 06)
In
F
2 doing a
2 in s
1 is trying your best but not in
F
1
.
 How to make that distinction while specifying our goal?
p
-CTL* is not able to make such a distinction.



Consider the policy p
: where p
(s
1
) = p
(s
2
) = a
2 p is a “try your best” policy for
F
2 but not for
F
1
.
But all p
-CTL* formulas have the same truth value with respect to both
F
2 and
F
1 given s
1
, and p.
, s
1 a
2
~p s
1
~p a
2 a
1
F
1 a
2 s
2 p s
2 p a
2 a
2
F
2 a
2
51



P-CTL*: exists policy and for all policies
A representation of “Try your best” in P-CTL*



A: Strong policy: all paths eventually lead to the goal state.
B: Strong cyclic policy: in all paths, in all states, there is a path that eventually leads to the goal state
C: Weak policy: exists a path that eventually leads to the goal state.
 P-CTL* goal:



If exists a strong policy then agent should take that
Elseif exists a strong cyclic policy then agent should take that
Elseif exists a weak policy then agent should take that.
52






Motivation


Initial goal: Please get a cup of coffee.
Weakening: In case the coffee machine is broken; a cup of tea would be fine.


Exception to Exception: Get a cup of tea only if the coffee machine can not be easily fixed.
Revising: If bringing tea, make sure it is hot.
Past work on non-monotonic temporal logics
 Fujiwara and Honiden, 1991: A nonomotonic temporal logic and its Kripke
Semantics.
 Saeki 1987: Non-monotonic temporal logic and its application to formal specifications (in Japneese)
Proposed a non-monotonic temporal logic in IJCAI 07
Currently working to develop a better language.
Started working on natural language semantics to go from discourses in
English to a non-monotonic logical language.
53





Complexity of planning with LTL and CTL* goals:
IJCAI 01.
The approach to find k-maintainable policies also leads to novel algorithms for planning with respect to other temporal goals expressed in p
-CTL*:
AAAI 05.
Diagnostic and repair goals (KR 00)
 Specifies that a unique diagnosis is reached, with certain literals protected, certain literals restored, and certain literals fixed.
Knowledge temporal goals (IJCAI 01)
54




Highlights of some important results and turning points in describing the world and how actions change the world (physical as well as mental)
Other aspects of action and change: our work
 Specifying Goals


Agent architecture
Applications
A future direction
 Interesting issues with multiple agents
55

56



Reactive, Deliberative and Hybrid



Fully reactive: sense-match-act cycle.
Completely deliberative: sense-plan/replan-act a bit
Hybrid: Reactive at low level; deliberative at high levels.
Our view of hybrid architecture (ETAI 98, Agent 98)



Reactive for the most common, most critical, etc.
Fully deliberative for rare cases.
Between reactive and deliberative for the rest.
57



(Condition, Reasoning program) pairs
Different kinds of reasoning programs
 Logic program based (Kowalski, Sadri, Pereira)


Agent programming language (VS et al.)
Planning using domain dependent knowledge




Temporal (Bacchus and Kabanza)
Partial Order, hierarchical (HTN), SHOP?
Procedural (GOLOG, Congolog)
A combination of the above (ATAL99, AAAI04,ACM TOCL06)
58

rd
59




AAAI 96: Robots were given a topological map and required to start from a director’s office, find if conference room 1 was empty, if not then find if conference room 2 was empty. If either was empty then inform prof1 and prof2 and the director about a meeting in that room, otherwise inform the professors and the director that the meeting would be at the director’s office, and finally return to the director’s office.
 Do the above avoiding obstacles and without changing the availability status of the conference rooms.
 We were third with 285 out of a total of 295 points.
AAAI 97: First place in the event “Tidy Up” of the home vacuum contest.
 Goal was to maintain several areas in an office environment clean.
For both we used our notion of correctness of reactive control and had proved the correctness of our control.
60

 Correctness of reactive programs (ETAI98)
 Automatic policy generation algorithms


For maintainability goals (ICAPS 04)
For specific types of goals in p
-CTL* (AAAI05)
61




Highlights of some important results and turning points in describing the world and how actions change the world (physical as well as mental)
Other aspects of action and change: our work
 Specifying Goals


Agent architecture
Applications
A future direction
 Interesting issues with multiple agents
62

Robots; Active Databases; Workflows;
Modeling cells; Question answering; CBioC
63




Discussed our robot in AAAI 96 and 97 contests.
Took a break for a few years.
A recent ONR MURI project involving Indiana
University (lead – Matthias Scheutz), Notre Dame
(Kathy M. Eberhard), Stanford (Stanley Peters) and
ASU (myself, Rao Kambhampati, Pat Langley and
Mike McBeath)
 Effective Human Robot Interaction under Time Pressure through Natural Language Dialogue and Dynamic
Autonomy
64

 Formal characterization of active databases
(LIDS 96, DOOD 97, CL 00)
 Formalizing and reasoning about the specification of workflows
 Coopis 2000
65

 Biosignet-RR (ISMB 04, KR 04, AAAI05)



Hypothetical Reasoning : side effect of drugs
Planning: therapy design
Explanation of observations: figuring out what is wrong
 Biosignet-RRH (ECCB 05)
 Hypothesis generation
66

k




Binding of TNFa with
TNFR1 leads to TRADD binding with one or more of TRAF2, FADD, RIP.
TRADD binding with
TRAF2 leads to overexpression of FLIP provided NIK is phosphorylated on the way.
TRADD binding with RIP inhibits phosphorylation of
NIK.
TRADD binding with
FADD in the absence of
FLIP leads to cell death.
67


 bind(TNFa
,TNFR1) causes trimerized(TNFR1) trimerized(TNFR1) triggers bind(TNFR1,TRADD)
68





 e causes f if f
1
; …; f k g
1
; … ; g k h
1
; … ; h m k
1
; … ; k l causes r
1
; … ; r l inhibits e g n_triggers triggers e e
 e is an event (also referred to as an action) and the rest are fluents (properties of the cell)
 For metabolic interactions: e converts g
1
; … ; g k to f
1
; …; f k if h
1
; … ; h m 69

 Observation part of queries

 f at t a occurs_at t
 Given the Network N and observation O



Predict if a temporal expression holds.
Explain a set of observations .
Plan to achieve a goal.
70

 Given some initial conditions and observations, to predict how the world would evolve or predict the outcome of (hypothetical) interventions.
71





Binding of TNFa with
TNFR1 leads to TRADD binding with one or more of TRAF2, FADD, RIP.
TRADD binding with
TRAF2 leads to overexpression of FLIP provided NIK is phosphorylated on the way.
TRADD binding with RIP inhibits phosphorylation of
NIK.
TRADD binding with
FADD in the absence of
FLIP leads to cell death.




Initial Condition
 bind(TNF-α,TNF-R1)
occurs at t0
Observation

TRADD’s binding with
TRAF2, FADD, RIP
Query
 predict eventually apoptosis
Answer: Yes!
72

 Given initial condition and observations, to explain why final outcome does not match expectation.
73





Binding of TNFa with
TNFR1 leads to TRADD binding with one or more of TRAF2, FADD, RIP.
TRADD binding with
TRAF2 leads to overexpression of FLIP provided NIK is phosphorylated on the way.
TRADD binding with RIP inhibits phosphorylation of
NIK.
TRADD binding with
FADD in the absence of
FLIP leads to cell death.




Initial condition:
 bound(TNFa
,TNFR1) at t0
Observation:
 bound(TRADD, TRAF2)
at t1
Query : Explain apoptosis
One explanation:


Binding of TRADD with
RIP
Binding of TRADD with
FADD
74





Planning interventions
Generating Hypothesis





Our observations can not be explained by our existing knowledge OR the explanations given by our existing knowledge are invalidated by experiments?
Conclusion: Our knowledge needs to be augmented or revised!
How?
Can we use a reasoning system to predict some hypothesis that one can verify through experimentation?
Automate the reasoning in the minds of a biologist, especially helpful when the background knowledge is humongous.
Constructing pathways
Studying drug-drug interactions
75




Highlights of some important results and turning points in describing the world and how actions change the world (physical as well as mental)
Other aspects of action and change: our work
 Specifying Goals


Agent architecture
Applications
A future direction
 Interesting issues with multiple agents
76

77

 Two agents need to lift a table
 Particular agents can do particular actions
 Different agents may be located in different places – depending on where the action is occurring only the agents present there can execute the action
78

Multi-agent action scenarios: Reasoning about each others’ knowledge (Muddy Children problem)









Three children playing in the mud.
Common Knowledge: They can see each other’s forehead but not their own
Father says: One of you have mud in your forehead
Father asks: Do you know if you have mud in your forehead?
All Answer: No
Father again asks: Do you know if you have mud in your forehead?
All Answer: No
Father again asks: : Do you know if you have mud in your forehead?
All answer: Yes
79

 States are Kripke models
 Actions considered in the past:
Announcement actions
 Actions of interest: Ask and faithfully answer
 AAMAS talk tomorrow by co-author Greg
Gelfond.
80

A, B, C in a room and have no clue if the gun is loaded – this is common knowledge a,b,c s
1 l h a,b,c a,b,c s
2
~l




On the left is a Kripke
Model M
S
1 and S
2 are two possible real worlds
(S
1,
M) entails ~K a l,
~K a
~l, ~K b l, ~K b
~l,
~K c l, ~K c
~l, Ka ~K b l,
Ka ~K b
~l, …
(S
2,
M) also entail the same …

A peeks and finds out l; B sees A peeking; C has no clue a,b,c a,b,c l h a,b c l l c a,b,c b a,b,c c
~l a,b
~l
~l c







Ka l - A knows l
~Kb l - B does not know l
~Kb~l - B does not know ~l
Kb (Ka l or Ka ~l)
B knows that A knows the value of l.
~Kc l, ~Kc ~l: C does not know the value of l.
Bc (~Ka l and ~Ka ~l)
Bc Bb (~Ka l and ~Ka ~l):
C has no clue a,b,c a,b,c

A peeks and finds out l; B sees A peeking; C has no clue a,b,c a,b,c l h a,b c l l a,b,c c a,b,c b a,b,c c
~l a,b
~l
~l c a,b,c




C has no clue: As far as C is concerned the old Kripke model is still the structure.
Thus we make a copy of the old
Kripke model. (bottom)
B sees A peeking: So the edge labeled “a” is removed in the top part.
A and B know C has no clue:
So c-edges are intrduced between the top part and bottom part and c-edges are removed in the top part.

Multi-agent scenarios: An action language


Initially: (We allow only restricted knowledge about the initial state)
 initially

 initially C

 initially C(K i

V K i
~

)
Actions and effects

 executable a if
 a causes
 if

 a determines f

 a may_determine f a announces

84

Multi-agent scenarios: An action language (cont.)


Agent roles
 agent observes a if

 agent partially_observes a if

An example
 peek(X) determines l
 X observes peek(X)




Y partially_observes peek(X) if looking(Y) distract(X,Y) causes ~looking(Y) signal(X,Y) causes looking(Y)
The plan: signal(a,b); distract(c); peek(a) will result in a knowing the value of l, b knowing that a knows that value and c having no clue.
85

 A can do an action to distract C so that when he peaks C has no clue.
 Similarly, A can do an action to make B attentive towards what A is doing.
 A can even do action to confuse C
 In a battle field friendly agents need to


Share knowledge as needed, and
Work together to take steps so that foes have no clue or confuse or misinform them towards a strategic goal.

87

Our Conclusions




Action, Change and evolution are important issues that crop up at times in Computer Science.
 They are an important domain for KR & R
Early focus on this had been on the frame problem – succinctly specifying what changes and what does not change due to actions
Over the years we have worked on that aspect as well as other important aspects such as:


Goal specification
Control specification and architecture


Various kinds of reasoning
Various applications
We are facing some interesting challenges in the multi-agent domain – past work in Dynamic epistemic logic is helping us.
88



Current support
 NSF


IARPA
ONR
Past
 NSF



NASA
United Space Alliance
ARDA/DTO
89

(Special thanks to all the collaborators and colleagues, many of whom are here, who at different times and in different ways motivated us.)
90