Upload
vivek-parmar
View
239
Download
0
Embed Size (px)
Citation preview
7/28/2019 Sitcalc Sli
1/21
SITUATION CALCULUS WITH ACTIONS A
OTHER EVENTS
John McCarthy
Computer Science DepartmentStanford University
http://www-formal.stanford.edu/jmc/
2005 Nov 17
A slogan for AI: Whatever a person can do, he shable to make a computer do for him.
Almost all of my papers are on the above-mention
page.
This lecture proposes Events Primary Sequential sicalculus, EPS sitcalc for short.
7/28/2019 Sitcalc Sli
2/21
SITUATION CALCULUS
Proposed 1963 for formalizing effects of actions
Improved 2002 to include occurrence axioms.
http://www-formal.stanford.edu/jmc/sitcalc.htm
7/28/2019 Sitcalc Sli
3/21
ACTIONS ARE EVENTS
In EPS situation calculus, events are primary and
by actors are a kind of event. EPS is sequential.
The logic is first order logic without causal ope
Second order formulas are used for circumscriptio
An event e has some effect axioms formalizing
Holds(f luent, Result(e, s))
An internal event e also has an occurrence axio
Occurs(e, s),
and an axiom for the next situation
Occurs(e, s) Next(s) = Result(e, s).
7/28/2019 Sitcalc Sli
4/21
Some phenomena previously axiomatized with
constraints are often more accurately and conve
axiomatized by using internal events. When bot
are blocked the room becomes stuffy.
We minimize change a situation at a time.
becoming blocked and the room becoming stuffy
in different situations.
When the theory is used for projection of the
quences of sequences of events, the nonmonoton
soning is done one situation at a time.
When an event e is not governed by an occ
axiom, we have branching time, i.e. non-determ
When Occurs(e, s) holds, we have linear time.
7/28/2019 Sitcalc Sli
5/21
Processes that dont settle down cannot be
with state constraints. The buzzer is an examp
the stuffy room elaborated to buzz is another.
7/28/2019 Sitcalc Sli
6/21
Result, N ext, N ext
Result(e, s) gives the situation resulting from
ter the events formalized to occur have happeneexample, if vent1 is closed, then Result(Block
Result(Getstuf f y, Result(Block2, s)).
When what occurs in a situation is determined,
a next situation satisfying
Occurs(e, s) Next(s) = Result(e, s).
When other actions are asserted to occur Nex
sometimes wanted. Result and Next are undefine
the system doesnt settle down as in the buzzer
buzzing stuffy room.
7/28/2019 Sitcalc Sli
7/21
A BUZZER1
A simple buzzer consists of a relay operating a
switch. When the relay isnt energized, current cthrough the switch operating the relay. When
lay operates it opens the switch, cutting off the
through the relay. The system then oscillates, i.e.
The buzzer has only internal eventsfour of them
ating and releasing the relay, and operating and re
the switch.
7/28/2019 Sitcalc Sli
8/21
A BUZZER2
Effect axioms:
Holds(On(R), Result(Onn(R), s))Holds(On(R), Result(Offf(R), s))Holds(On(Sw), Result(Onn(Sw), s)Holds(On(Sw), Result(Offf(Sw), s)).
Occurrence axioms:
Holds(On(Sw), s) Holds(On(R), s) Occurs(Offf(R), s)
Holds(On(Sw), s) Holds(On(R), s) Occurs(Onn(R), s))
Holds(On(R), s) Holds(On(Sw), s) Occurs(Offf(Sw), s)
Holds(On(R), s) Holds(On(Sw), s) Occurs(Onn(Sw), s)
7/28/2019 Sitcalc Sli
9/21
THE STUFFY ROOM
A room has two vents, vent1 and vent2. The ve
be opened or closed. When both vents are closroom is, or becomes stuffy. Matt Ginsberg propos
scenario in 1988 to show that simply minimizing
gives an unintended model, namely a model in whic
one vent is closed, the other opens, which avoids ch
the stuffiness of the room.
We formalize this using the internal events of th
becoming stuffy or unstuffy.
We then elaborate the scenario to express that w
room is stuffy, Pat then opens a vent.
7/28/2019 Sitcalc Sli
10/21
THE STUFFY ROOMsimple
Effect axioms:Holds(Blocked1, Result(Block1, s))
Holds(Blocked2, Result(Block2, s))Holds(Blocked1, Result(Unblock1, s))Holds(Blocked2, Result(Unblock2, s))Holds(Stuf f y, Result(Getstuff y, s))Holds(Stuf f y, Result(U ngetstuf f y, s))
Occurrence axioms:
Holds(Blocked1, s) Holds(Blocked2, s)Holds(Stuffy,s)
Occurs(Getstuf f y, s)and
(Holds(Blocked1, s) Holds(Blocked2, s))Holds(Stuff y, s)
Occurs(U ngetstuf f y, s)
7/28/2019 Sitcalc Sli
11/21
ELABORATING THE STUFFY ROOM
The first elaboration says that when Pat finds th
stuffy he unblocks vent2. We have
Holds(Stuffy,s) Occurs(Does(P at, U nblock2),
A second elaboration in which Mike finds the roo
when there is an unblocked vent and blocks vent
pressed by
Holds(U nstuf f y, s) Occurs(Does(M ike, Block2
With both elaborations, we get an oscillation; P
blocks vent2 and Mike blocks it again.
7/28/2019 Sitcalc Sli
12/21
NONMONOTONIC REASONING IN SITCA
Projection is the easy case of nonmonotonic rea
about the effects of events.
When we project, we can circumscribe in each
tion successively. It gives the same results as Sh
chronological minimization but is much simpler
cally. It doesnt suit the stolen car scenario in w
fact about the future is given.
We minimize the predicates Occurs, Prevents, C
etc. Strictly speaking, we circumscribe (e)Occu
and (f e)Prevents(f , e , s), (e f)Changes(e , f , s).
7/28/2019 Sitcalc Sli
13/21
NONMONOTONIC REASONING2
F oo s F oo (vars)(F oo(vars, s) F oo(vars(F oo
7/28/2019 Sitcalc Sli
14/21
Axiom(F oo, vars) (f oo vars)(Axiom(f oo, vars) ((vars)(f oo(vars, s)
F oo(vars, s)) (vars)(F oo(vars, s) f oo(vars, s)))).
Call this formula Circ(Axiom; F oo; vars; s).
The general frame axioms are
Changes(e,p,s) (Holds(p, Result(e, s)) Holds
for propositional fluents and
Changes(e , f , s) V alue(f, Result(e, s)) = V alue
for general fluents.
7/28/2019 Sitcalc Sli
15/21
NARRATIVES
A narrative is a set of situations, event, and ass
about situations and maybe assertions about even
A simple narrative consists of two sequences (S1and (E1, E2, . . .), where Si+1 = Result(Ei, Si) for e
Unfortunately, real narratives, whether historicational, are rarely if ever simple.
7/28/2019 Sitcalc Sli
16/21
SOME PHILOSOPHY
Assume a deterministic worldif you like with s
tic processes and quantum processes. That doesfree will.
Some entities, including people and chess promake choices.
Making a choice involves considering the conseq
of alternative actions, e.g. using a non-deterministlike situation calculus. This is minimal free will.
Thus deterministic entities use non-deterministries.
Do the philosophy as you like, but this is how AIbe done.
7/28/2019 Sitcalc Sli
17/21
FREE WILL IN A DETERMINIST WORLD
We can make our theory of a process more dete
by adding occurrence axioms. We can do it if wmore or adopt rules for deciding on actions.
Human free will may consist of using a non-dete
theory to decide deterministically on an action.
Heres a minimal example of using a non-determin
ory within a determinist rule.
Occurs(Does(John,if Prefers(John, Result(Does(J ohn, a1), s),
Result(Does(J ohn, a2), s))then a1else a2
), s).
7/28/2019 Sitcalc Sli
18/21
Here Prefers(J ohn, s1, s2) is to be understood as
ing that John prefers situation s1 to s2.
Do animals, even apes, make decisions based o
paring anticipated consequences? If not, can a
trained to do it? Chess programs do. Accord
Dan Dennett, some recent experiments suggest th
sometimes consider the consequences of altern
tions.
We envisage an extended theory of free will th
treat whether an action was done freely and wh
merits blame or praise.
7/28/2019 Sitcalc Sli
19/21
CONCLUSIONS AND REMARKS
This formalism is preliminary. It needs to be ela
to allow concurrent and continuous events.
Sequential processes, as treated in EPS, are wort
rate formalization, because most common sense na
and planning fit within the sequential case.
The eventual formalism must permit elaboratinquential theory by adding a few or many concur
continuous processes. On the other hand, specia
to the sequential case also needs to be a simple op
on a theory allowing concurrent events.
For the future: It would be more Newton-likethat a proccess continues until something interrup
7/28/2019 Sitcalc Sli
20/21
OTHER WORK
Events that are not actions have been previously us
least by Fangzhen Lin, Sheila McIlraith, and Javie
Occurrence axioms are even more important in th
ment of concurrent events in situation calculus
the subject of another article.
http://www-formal.stanford.edu/jmc/freewill2.ht
these ideas to formalizing simple deterministic fre
This work benefited from discussions with Eya
Tom Costello, Ron Fadel, Hector Levesque, Vladim
chitz, Fangzhen Lin, Sheila McIlraith, Leora Morge
Aarati Parmar, Raymond Reiter, and Tran Son a
comments of three anonymous referees.
7/28/2019 Sitcalc Sli
21/21
This research was partly supported by SRI Subc
No. 34-000144 under SPAWAR Prime Contract No
00-C-8018.