sitcalc sli

7/28/2019 Sitcalc Sli

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SITUATION CALCULUS WITH ACTIONS A

OTHER EVENTS

John McCarthy

Computer Science DepartmentStanford University

[email protected]

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.


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SITUATION CALCULUS

Proposed 1963 for formalizing effects of actions

Improved 2002 to include occurrence axioms.

http://www-formal.stanford.edu/jmc/sitcalc.htm


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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).


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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.


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Processes that dont settle down cannot be

with state constraints. The buzzer is an examp

the stuffy room elaborated to buzz is another.


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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.


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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.


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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)


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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.


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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)


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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.


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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).


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NONMONOTONIC REASONING2

F oo s F oo (vars)(F oo(vars, s) F oo(vars(F oo


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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.


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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.


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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.


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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).


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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.


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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


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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.


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This research was partly supported by SRI Subc

No. 34-000144 under SPAWAR Prime Contract No

00-C-8018.

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