Important:
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This is the last time that the ETAI-DRU newsletter will be sent
to unsubscribed people. For those which have not yet subscribed, please
send the following information by email (to benferhat@irit.fr,
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Last and first name, affiliation, email address, personal web-page
in order to continue receiving Newsletters and News Journals.
This newsletter contains:
1. Call for contributions
2. Discussions regarding the submitted paper of David Poole
3. New books
4. Table of Contents for International Journal of Approximate Reasoning
Volume 19, Issue 1-2, 01-July-1998
5. Table of Contents for International Journal of Uncertainty, Fuzziness
and Knowledge-Based Systems
August 1998 (Volume 6, Number 4)
6. Table of Contents for International Journal of Intelligent Systems
Volume 13, Issue 9 (1998)
Volume 13, Issue 10-11 (1998)
7. Table of contents for Statistics and Computing Journal
Volume 8, Issue 1, 1998
8. Details of the discussions regarding the submitted paper of David Poole
==========================================================================
1. Call for contributions
==========================================================================
Researchers on decision and reasoning under uncertainty are invited
to submit their papers to ETAI Journal. The call for papers
is available at : http://www.ida.liu.se/ext/etai/dru/index.html.
Besides, please send emails to benferhat@irit or prade@irit.fr for
announcing Conferences, Books, Journal issues, PhD thesis and technical
reports, Career Opportunities and Training, and softwares dealing
with uncertainty.
Books reviews are also welcome.
==========================================================================
2. Discussions regarding the submitted paper by David Poole
==========================================================================
The discussions concerning David Poole's paper have started. We got questions
and comments from Uffe Kjærulff and from R. Reiter. Please, consult the web-page
http://www.ida.liu.se/ext/etai/ra/rac/008/.
At the end of this newsletter, the detail of these discussions is given.
To contribute, please send your question or comment as an E-mail message.
to benferhat@irit.fr or prade@irit.fr or erisa@ida.liu.se.
Title: Decision Theory, the Situation Calculus and Conditional Plans.
Authors: David Poole
Poscript file: http://www.ep.liu.se/ea/cis/1998/008/cis98008.ps
==========================================================================
3. New books
==========================================================================
3.1.
Handbook of Defeasible Reasoning and Uncertainty
Management Systems
editors: Dov M. Gabbay and Philippe Smets
Volume 1 : Quantified Representation of
Uncertainty and Imprecision
edited by : Philippe Smets
Kluwer Academic Publishers, Dordrecht
* Hardbound, ISBN 0-7923-5100-2
July 1998, 484 pp.
NLG 399.00 / USD 215.00 / GBP 135.00
Prepublication price is valid until December 1, 1998
Table of contents
P. Smets
Probability, possibility, beliefs: which and where? 1
G. Panti
Multi-valued logics 25
V. Novak
Fuzzy logic 75
C. Howson
The bayesian approach 111
D. Gilles
Confirmation theory 135
D. Dubois and H. Prade
Possibility theory: qualitative and quantitative aspects 169
H. E. Kyburg, JR.
Families of probabilities 227
N. Sahlin and W. Rabinowicz
The evidentiary value model 247
P. Smets
The transferable belief model for quantified belief
representation 267
S. Benferhat
Infinitesimal theories of uncertainty for plausible
reasoning 303
A. W. F. Edwards
Statistical inference 357
J. Pearl
Graphical models for probabilistic and causal reasoning 367
B. Skyrms and P. Vanderschraaf
Game theory 391
G. Gigerenzer
Psychologoical challenges for normative models 441
3.2.
Handbook of Defeasible Reasoning and Uncertainty
Management Systems
editors: Dov M. Gabbay and Philippe Smets
Volume 3 : Belief Change
edited by : Didier Dubois and Henri Prade
Kluwer Academic Publishers, Dordrecht
* Hardbound, ISBN 0-7923-5162-2
August 1998, 458 pp.
NLG 380.00 / USD 199.00 / GBP 129.00
Prepublication price is valid until December 1, 1998
Table of Contents
. Introduction: revising, updating and combining knowledge
(D. Dubois, H. Prade)
. SYMBOLIC APPROACHES
a. Semantic approaches to the revision of propositional knowledge bases
(S.O. Hansson)
b. How hard is it to revise a belief base?
(B. Nebel)
c. Conditionals and the Ramsey test
(S. Lindstrom, W. Rabinowicz)
e. Logics for belief base updating
( A.Herzig)
f. The combination of knowledge bases
( L. Cholvy)
. NUMERICAL APPROACHES
a. Numerical representations of uncertainty
(P. Smets )
b.Belief change rules in ordinal and numerical uncertainty theories
(D. Dubois, S. Moral, H. Prade
c. Parallel combination of information sources
(R. Kruse & J. Gebhardt)
3.3.
Possibility Theory with Applications to Data Analysis
O.WOLKENHAUER,
Control Systems Centre, UMIST, UK
http://www.csc.umist.ac.uk/
Set theory and logic are the basic theoretical tools for modelling and
reasoning. Their application to real-world problems induces various types of
uncertainty related to the observation of processes, the measurement of
signals and the mismatch between mathematical models and the real world in
general. Possibility theory provides a framework in which all forms of
uncertainty can be represented. This book reviews, extends and applies
possibility theory in an integrated approach that combines probability
theory, statistical analysis and fuzzy mathematics.
Special features of the book include:
* An up-to-date introduction to possibility theory.
* An integrated view on uncertainty techniques based on multi-valued
mappings, fuzzy relations and random sets.
* Adoption of concepts into a temporal environment characterised by
signal or data processing.
* Illustration of the application of possibility theory to data analysis
in process and supervisory control systems with examples taken from the
area of condition monitoring.
CONTENTS: Motivation and Methodology. Uncertainties in Control Systems.
Uncertainty Techniques. Possibility Theory. Possibilistic Change Detection.
Fuzzy Data Analysis. Conclusions and Perspectives. Probability Theory.
Evidence Theory. Fuzzy Systems. Selected Topics. Glossary. Bibliography.
Index.
READERSHIP: Postgraduate Students interested in cutting edge topics related
to Fuzzy Systems; Researchers and Research Engineers in Control Engineering
- specifically in the area of data analysis for condition monitoring and
process control - data mining and data fusion applied to engineering
problems.
RSP SERIES: UMIST Control Systems Centre Series, No. 5
SERIES EDITORS: Dr M.B. Zarrop and Professor P.E. Wellstead, UMIST, UK
086380 229 X £55.00 January 1998 290pp
3.4.
Fuzzy Logic in Data Modeling
Semantics, Constraints, and Database Design
by
Guoqing Chen
Tsinghua University, Beijing, PR of China
THE KLUWER INTERNATIONAL SERIES ON ADVANCES IN
DATABASE SYSTEMS Volume 15
Kluwer Academic Publishers, Boston
hardbound, ISBN 0-7923-8253-6
August 1998, 240 pp.
NLG 260.00 / USD 115.00 / GBP 78.25
<<Fuzzy Lugic in Data Modeling: Semantics, Constraints and Database
Design>> addresses fundamental and important issues of fuzzy
data modeling, such as fuzzy data representation, fuzzy integrity
constraints, fuzzy conceptual modeling, and fuzzy database design.
The purpose of introducing fuzzy logic in data modeling is to
enhance the classical models such that uncertain and
imprecise information can be represented and manipulated.
Fuzzy data representation reflects how, where and to what extent
fuzziness is incorporated into classical models. Fuzzy integrity
constraints are a sort of fuzziness-involved business rules and
semantic restrictions that need to be specified and enforced.
Fuzzy conceptual modeling describes and treats high-level data
concepts and related semantics in a fuzzy context, allowing
the model to tolerate imprecision at different degrees. Fuzzy
database design provides guidelines for how relation schemes of
fuzzy databases should be formed and develops remedies to possible problems
of data redundancy and update anomalies.
Fuzzy Logic in Data Modeling£ºSemantics, Constraints and Database
Design is intended to be used as a text for a graduate-level
course on fuzzy databases, or as a reference for researchers and
practitioners in industry.
Contents:
Preface.
PART I: Basic Concepts
1. The Relational Data Model
2. Conceptual Modeling with the Entity-Relationship Model
3. Fuzzy Logic
PART II: Fuzzy Conceptual Modeling
4. Fuzzy ER Concepts
5. Fuzzy EER Concepts
PART III: Representation of Data and Constraints
6. Fuzzy Data Representation
7. Fuzzy Functional Dependencies as Integrity Constraints
8. A FFD Inference System
PART IV: Fuzzy Database Design and Information Maintenance
9. Scheme Decomposition and Information Maintenance
10.Design of Fuzzy Databases to Avoid Update Anomalies
Bibliography
Appendix
3.5.
J.E. Yukich , Lehigh University, Bethlehem, PA, USA
Probability Theory of Classical Euclidean Optimization Problems
This monograph describes the stochastic behavior of the solutions to
the classic problems of Euclidean combinatorial optimization,
computational geometry, and operations research. Using two-sided
additivity and isoperimetry, it formulates general methods
describing the total edge length of random graphs in Euclidean
space. The approach furnishes strong laws of large numbers, large
deviations, and rates of convergence for solutions to the random
versions of various classic optimization problems, including the
traveling salesman, minimal spanning tree, minimal matching, minimal
triangulation, two-factor, and k-median problems. Essentially
self-contained, this monograph may be read by probabilists,
combinatorialists, graph theorists, and theoretical computer
scientists.
Keywords: Euclidean optimization, subadditivity, limit
theorems.
For graduate students and researchers interested in probability,
operations research, statistical physics, combinatorics,
optimization, etc.
Table of Contents : Introduction.- Subadditivity and Superadditivity.-
Subadditive and Superaddititive Euclidean Functionals.- Asymptotics
for Euclidean Functionals: The Uniform Case.- Rates of Convergence
and Heuristics.- Isoperimetry and Concentration Inequalities.-
Umbrella Theorems for Euclidean Functionals.- Applications and
Examples.- Minimal Triangulations.- Geometrics Location Problems.-
Worst Case Growth Rates.- Bibliography.- Index.
1998 . X, 152 pp.
ISBN 3-540-63666-8
Brosch.
DM 45,-
==========================================================================
4. Table of Contents for International Journal of Approximate Reasoning
Volume 19, Issue 1-2, 01-July-1998
==========================================================================
Wolfgang Slany, Special issue on approximate reasoning in scheduling --
Preface, International Journal Of Approximate Reasoning (19)1-2 (1998) pp.
1-3
M.P. Fanti, B. Maione, D. Naso, B. Turchiano, Genetic multi-criteria
approach to flexible line scheduling, International Journal Of Approximate
Reasoning (19)1-2 (1998) pp. 5-21
Klaudia Dussa-Zieger, Markus Schwehm, Scheduling of parallel programs on
configurable multiprocessors by genetic algorithms, International Journal Of
Approximate Reasoning (19)1-2 (1998) pp. 23-38
David Sinclair, The GST load balancing algorithm for parallel and
distributed systems, International Journal Of Approximate Reasoning (19)1-2
(1998) pp. 39-56
Teik Guan Tan, Wynne Hsu, Approximating scheduling for multimedia
applications under overload conditions, International Journal Of Approximate
Reasoning (19)1-2 (1998) pp. 57-71
Claudia Leopold, Arranging program statements for locality on the basis of
neighbourhood preferences, International Journal Of Approximate Reasoning
(19)1-2 (1998) pp. 73-90
Thomas Wagner, Alan Garvey, Victor Lesser, Criteria-directed task
scheduling, International Journal Of Approximate Reasoning (19)1-2 (1998)
pp. 91-118
I.B. Türksen, M.H. Fazel Zarandi, Fuzzy system models for aggregate
scheduling analysis, International Journal Of Approximate Reasoning (19)1-2
(1998) pp. 119-143
Jürgen Sauer, Gerd Suelmann, Hans-Jürgen Appelrath, Multi-site scheduling
with fuzzy concepts, International Journal Of Approximate Reasoning (19)1-2
(1998) pp. 145-160
Andreas Raggl, Wolfgang Slany, A reusable iterative optimization software
library to solve combinatorial problems with approximate reasoning,
International Journal Of Approximate Reasoning (19)1-2 (1998) pp. 161-191
==========================================================================
5. Table of Contents for International Journal of Uncertainty, Fuzziness
and Knowledge-Based Systems
August 1998 (Volume 6, Number 4)
==========================================================================
Decomposable Financial Laws and Profitability
S. C. Rambaud and A. G. S. Ventre (page 329)
Canonical Hierarchical Decomposition of Choquet Integral Over Finite Set
with Respect to Null Additive Fuzzy Measure
K. Fujimoto, T. Murofushi and M. Sugeno (page 345)
Possibilistic Residuated Implication Logics with Applications
C.-J. Liau (page 365)
Ordinal Explanation of the Periodic System of Chemical Elements
E. R. Scerri, V. Kreinovich, P. Wojciechowski and R. R. Yager (page 387)
LSLNCF: A Hybrid Uncertain Reasoning Model Based on Probability
X. Luo and C. Zhang (page 401)
Interval Methods in Knowledge Representation (Abstracts of Recent Papers)
V. Kreinovich (page 423)
==========================================================================
6. Table of Contents for International Journal of Intelligent Systems
Volume 13, Issue 9 (1998)
Volume 13, Issue 10-11 (1998)
==========================================================================
785-799 Stratification for default logic variants
Grigoris Antoniou
801-820 From ordered beliefs to numbers: How to elicit numbers without
asking for them (doable but computationally difficult)
Brian Cloteaux, Christoph Eick, Bernadette Bouchon-Meunier,
Vladik Kreinovich
821-840 Logical inference of clauses based on Petri net models
Chuang Lin, Samuel T. Chanson
841-858 Reasoning with incomplete information in a multivalued multiway
causal tree using the maximum entropy formalism
Dawn E. Holmes, Paul C. Rhodes
859-886 Some neural net realizations of fuzzy reasoning
Kuhu Pal, Nikhil Pal, James Keller
887-890 Introduction: Genetic fuzzy systems
Francisco Herrera, Luis Magdalena
891-903 Genetic-based on-line learning for fuzzy process control
Juan R. Velasco
905-927 Artificial evolution of fuzzy rule bases which represent time:
A temporal fuzzy classifier system
Brian Carse, Terence C. Fogarty, Alistair Munro
929-948 Context adaptation in fuzzy processing and genetic algorithms
Ricardo Gudwin, Fernando Gomide, Witold Pedrycz
949-974 Learning fuzzy control by evolutionary and advantage
reinforcements
Munir-ul M. Chowdhury, Yun Li
975-991 Fuzzy clustering with evolutionary algorithms
Frank Klawonn, Annette Keller
993-1010 Crossing unordered sets of rules in evolutionary fuzzy
controllers
Luis Magdalena
1011-1023 Multistage control of a stochastic system in a fuzzy
environment using a genetic algorithm
Janusz Kacprzyk
1025-1053 Genetic learning of fuzzy rule-based classification systems
cooperating with fuzzy reasoning methods
Oscar Cordón, María José del Jesus, Francisco Herrera
==========================================================================
7. Table of contents for Statistics and Computing Journal
Volume 8, Issue 1, 1998
==========================================================================
* Probabilistic ’generalization‘ of functions and
dimension-based uniform convergence results
MARTIN ANTHONY
pp. 5-14
* Interpolation models with multiple hyperparameters
DAVID J. C. MACKAY , RYO TAKEUCHI
pp. 15-23
* Coaching variables for regression and classification
ROBERT TIBSHIRANI , GEOFFREY HINTON
pp. 25-33
* Some results concerning off-training-set and IID
error for the Gibbs and the Bayes optimal
generalizers
DAVID H. WOLPERT , EMANUEL KNILL , TAL GROSSMAN
pp. 35-54
* Statistical mechanical analysis of the dynamics of
learning in perceptrons
C. W. H. MACE , A. C. C. COOLEN
pp. 55-88
================================================================
8. Details of the discussions concerning Poole's paper
=================================================================
Q1. Uffe Kjærulff:
The focus of the paper seems to be on representational issues, which is
fine. But, being a Bayesian-network person, I'm would find it interesting to
see how computations of expected utilities of plans are performed in the ICL
framework. This issue is only touched upon very briefly in the paper,
mentioning that it involves enumerating all possible cases. In my
understanding that amounts to constructing the corresponding decision tree
(which may be huge), and then computing the probability and utility for each
leaf of the tree.
So, my question boils down to: Is there an efficient computational scheme
for ICL?
Uffe Kjærulff
Dept. of Computer Science, Aalborg University, Denmark
A1. David Poole:
The focus of the paper seems to be on representational issues,
which is fine. But, being a Bayesian-network person, I would find
it interesting to see how computations of expected utilities of
plans are performed in the ICL framework. This issue is only
touched upon very briefly in the paper, mentioning that it
involves enumerating all possible cases. In my understanding that
amounts to constructing the corresponding decision tree (which may
be huge), and then computing the probability and utility for each
leaf of the tree.
So, my question boils down to: Is there an efficient computational
scheme for ICL?
Thanks for the question! First, ICL theories can be seen as representations
of Bayesian networks; there is a local translation between groundings of the
ICL theories and Bayesian networks. ICL theories (with only choices by
nature) can be seen as first-order rule-based representations of Bayesian
networks. Thus any Bayesian network algorithms can, in principle, be used
for the ICL. There are two main computational advantages of the ICL
approach. The first is that they can exploit logic-based reasoning
techniques for probabilistic reasoning (although it turns out that once the
link is realized, it isn't restricted to ICL theories). Secondly they give
us an opportunity to exploit, not only the graphical independence of a
Bayesian network, but also the contextual independence that i natural in the
rule based representations. I will expand briefly on each of these here.
The ICL (with only choices by nature) can be seen as a way to write
first-order Bayesian networks as rules. There is a local translation between
ICL theories and Bayesian networks. Note that a Bayesian network has nothing
to say about how a node depends on its parents. The ICL lets us write the
conditional probabilities as a set of rules. (This is often a more compact
representation than conditional probability tables when there are contextual
independencies).
To translate an ICL theory into a Bayesian network: ground the theory
(substituting ground terms for the free variables); the ground atoms are the
nodes of the Bayesian network; the atoms in the bodes of the rules that
imply a become the parents of a. There is a lot more structure that can be
expressed by the rules than in the network (in particular the contextual
independencies). Note that the acyclicity of the logic program ensures that
the resulting network is acyclic and (even when the resulting network is
infinite) there are only finitely many ancestors for any node (which means
you only need a finite subset of the graph to answer any conditional
probability statement).
To translate a Bayesian network to an ICL theory, you write as rules how the
parents of a influence a. The atomic choices are introduced as extra
conditions on the rules to let us interpret the rules logically. For more
details see (Poole 1993).
The first way that the ICL can be used computationally is adapting the
logic-based algorithms for probabilistic reasoning. In particular, the
algorithms for consistency-based diagnosis (such as the focusing algorithms
of de Kleer), based on the notions of conflicts, can be adapted to compute
posterior probabilities in the ICL (and so for Bayesian networks). This
works well when there are skewed probability distributions. This has been
explored in (Poole 1996).
Another approach is to exploit the structure that can be expressed in a
Bayesian network as well as the rule structure of the ICL. This is ongoing
work with Nevin Zhang. I'll first sketch how the efficient structured
Bayesian network algorithms (such as clique-tree propagation and more
query-oriented algorithms such as D'Ambrosio's SPI, Zhang and Poole's VE or
Dechter's bucket elimination) can be seen as ways to exploit the
factorization of the joint probability distribution. The basic operation is
to sum out a (non-observed, non-query) variable. Algorithms such as
clique-tree propagation are efficient because they can compile this
operation into an secondary structure (the clique tree or join tree) that
works by message passing in the join tree so that the posterior distribution
for all variables can be obtained in twice the time it takes to compute the
posterior on one. The basic operation of the message passing from one clique
to another is to sum out the variable that appears in one clique that
doesn't appear in the other.
It turns out that you can carry out a similar operation on the rule base
directly. We have been working on a rule-based variation of the
query-oriented algorithms I call probabilistic partial evaluation (Poole
1997). Eliminating a variable turns out to be like resolution. When the
rules give no structure beyond that of the Bayesian network (i.e., there is
no contextual independence, and there is a rule for each assignment of
variables to a parent), the algorithm reduces to the standard query-oriented
Bayesian network algorithms. But when there is contextual independence (as
there is in many ICL theories) the algorithm lets us exploit that. This also
seems to be very promising for approximation, where different approximations
can be used in different contexts (Poole 1998).
Aside: One main difference between clique tree propagation and the
query-oriented algorithms is that clique tree propagation acts on marginal
distributions (each clique represents the marginal distribution of the
variables in the clique), whereas the query-oriented algorithms act on
conditional probabilities. Probabilistic partial evaluation relies on
manipulating conditional probabilities. The contextual independencies get
lost quickly when you reason with marginal distributions.
Finally, there is also a promise of structured dynamic programming using the
rules. The most comment methods for solving sequential decision problems is
to do dynamic programming. Traditional dynamic programming explicitly
reasons over state space.s and thus suffers from what Bellman calls the
"curse of dimensionality". We should be able to do much better by reasoning
in terms of the variables (or propositions) that define the state space and
exploiting the rule-structure in dynamic programming. In the ICL, dynamic
programming looks much like regression planning. We can either do this in
POMDPs where we regress values through conditional plans (Boutilier and
Poole 1996) or where we are building plans conditional on history (as in
influence diagrams), and we can use the rule structure to determine states
that all have the same utility (Poole 1995).
Thus in answer to your question, this is an active area of research by
myself and others who are looking at exploiting contextual independence for
probabilistic inference and sequential decision making. One of the reasons I
am optimistic that this will work is that it promises nice methods of
approximation, where we can approximate differently in different contexts.
We will have to see if we can deliver on this promise.
References
The following are references to some of my papers that give more details:
* C. Boutilier and D. Poole, ``Computing Optimal Policies for Partially
Observable Decision Processes using Compact Representations'', Proc.
Thirteenth National Conference on Artificial Intelligence (AAAI-96),
Portland, Oregon, August 1996.
* D. Poole, ``Probabilistic Horn abduction and Bayesian networks'',
Artificial Intelligence, 64(1), 81-129, 1993.
* D. Poole, ``Exploiting the Rule Structure for Decision Making within
the Independent Choice Logic'', Proceedings of the Eleventh Conference
on Uncertainty in AI, Montreal, August 1995, 454-463.
* D. Poole, ``Probabilistic conflicts in a search algorithm for
estimating posterior probabilities in Bayesian networks'', Artificial
Intelligence, 88, 69-100, 1996.
* D. Poole, ``Probabilistic Partial Evaluation: Exploiting rule structure
in probabilistic inference'', Proc. Fifteenth International Joint
Conference on Artificial Intelligence (IJCAI-97), Nagoya, Japan, August
1997, pp. 1284-1291.
* D. Poole, ``Context-specific approximation in probabilistic
inference'', Proc. Fourteenth Conference on Uncertainty in Artificial
Intelligence (UAI-98), Madison, Wisconsin, July 1998.
* N.L. Zhang and D. Poole, ``Exploiting Causal Independence in Bayesian
Network Inference'', Journal of Artificial Intelligence Research, 5,
301-328, 1996.
----------------------------------------------------------------------------
Q2. Ray Reiter :
David,
I enjoyed reading your paper, and learned a lot from it. I agree with you
that axiomatic action theories need an account of probability/decision
theory, although I do not share your reservations about being able to do so
in the sitcalc (see below). My comments and questions concern only the
probabilistic (as opposed to the decision theoretic) components of your
paper.
Technical issues
1. Examples 2.8 and 2.9.
The predicate pickup_succeeds(S) in the first clause.
(a) It is not parameterized by the thing -- in this case key -- being picked
up. It should be pickup_succeeds(key, S) . Presumably, you need one of
these predicates for each action type, e.g. putdown_succeeds ,
goto_succeeds , etc. Therefore, why not introduce a generic predicate
succeeds(action, S) , in which case, you can write
succeeds(pickup(key), S) , succeeds(goto(loc), S) , etc? Similarly, you can
have a relation fails(action, S) . Now, C0 contains
union(succeeds(pickup(key), S), fails(pickup(key), S)) , where the union is
over all ground instances of these atoms. Incidentally, your specifications
of what sets are in C0 , e.g. bottom p. 13, is an abuse of notation, since
it looks like an object level sentence, when in fact it is a metalevel
statement for which universal quantification over situations is not defined.
(b) In axiomatizing at on p. 20, you do not include a goto_succeeds atom
in the clause body. Does the atom would_not_fall_down_stairs(S) play this
role?
2. In the conditional plan of p. 21, don't you want at(key, r101) instead
of at_key ?
3. Consider the axiom of Example 2.9 and your comment "Note that this
implies that putting down the key always succeeds". Suppose not. Then is it
the case that the axiom should be modified by replacing the atom
A =/ putdown(key) by something like
¬ (A = putdown(key) ^ putdown-succeeds(key, S))
If so, perhaps this should be pointed out. (See my call below for a guide
for the perplexed.)
4. In the axiom of Example 2.9, you include a choice
keeps_carrying(key, S) , which you introduce because "there may be a
probability that the agent will drop the key". You then axiomatize this with
P0(keeps_carrying(key, S)) = .95 But I can't think of any realistic way to
axiomatize this probability when only the parameter S is available.
Basically, you want to describe the probability that the robot doesn't lose
the key during the interval between the occurrence of the last action in
S , when carrying(key, S) was true, and the occurrence of the next action
A . In other words, you want to describe the probability that the robot is
still carrying the key at situation do(A, S) given it is carrying it in
situation S . But that depends, at the very least, on WHEN this next action
A occurs. Now on one account of adding time to the sitcalc (Reiter, Proc
KR'96), an action can take an additional temporal argument denoting that
action's occurrence time, for example, openDoor(t) . Then one expects that
P0(keeps_carrying(key, S)) given that openDoor(10) is the next action
should be greater than this probability given that openDoor(1000) is the
next action. So as far as I can tell, the choice keeps_carrying(key, S)
should take another argument, namely A , or perhaps simply time(A) , where
time(A) is the occurrence time of the next action A .
The need for action preconditions
On p. 8, you claim "None of our representations assume that actions have
preconditions; all actions can be attempted at any time." I'm sceptical of
this claim. Consider your example domain, where you adopt the axioms
P0(pickup_succeeds(S)) = .88 Just prior to this, you say
" P0(pickup_succeeds(S)) reflects how likely it is that the agent succeeds
in carrying the key given that it was at the same position as the key and
attempted to pick it up". So you can't seriously write
P0(pickup_succeeds(S)) = .88 because here S is any situation, including
one in which the agent is 1000 kms from the key. I take it that what you
intended to write was something like
at(key, Pos, S) ^ at(robot, Pos, S) ·-> P0(pickup_succeeds(S)) = .88
(*)
If this is the case, then it is exactly here where you are using action
preconditions, namely, in characterizing those situations in which an action
has a high probability of succeeding. It also appears that you are appealing
to action preconditions in the axiom of Example 2.8 (namely,
at(robot, Pos, S) ^ at(key, Pos, S) ). Probably, these atoms should be
omitted because their effects are realized in the above axiom (*).
Finally, you often talk about actions being "attempted", as in the above
quotation. I found this particularly confusing since nothing in your
ontology deals with action "attempts". Actions simply realize their effects
with certain probabilities. You do not, for example, have an action
try_pickup , as do other authors (e.g. James Allan) who do try to axiomatize
action attempts . In this connection, I had a hard time making sense of
footnote 9, since it motivates the axiom of Example 2.9 in terms of talk
about "trying" to pick up the key. In fact, even after reading this material
several times, I couldn't figure out footnote 9 until, much later, I began
to think about how your approach compares with Bacchus, Halpern and
Levesque. See my comments below on BHL.
Section 3.3
I must confess that I couldn't make much sense of the discussion in Section
3.3, especially your arguments that the sitcalc is inherently unsuitable for
modeling multiple, possibly reactive agents. It's true that Golog lacks the
right control structures for doing this, but your comments on p. 26 and p.
27 (p. 26 "In order for a situation calculus program to ... and does the
appropriate concurrent actions." p. 27 "When there are multiple agents ...
or complex actions.") suggest to me that you are not aware of more recent
work by De Giacomo, Lesperance and Levesque on Congolog that addresses
precisely these issues (Proc. IJCAI 97). Congolog provides reactive rules
(interrupts) and interleaving concurrency in a semantically clean way, all
formulated within the sitcalc. I believe that Congolog addresses all your
criticisms of the sitcalc, except, of course, it does not (yet) incorporate
utilities.
Comparison with Bacchus, Halpern and Levesque
So far as I know, there have only been two proposals for augmenting the
sitcalc with probabilities, yours and BHL. As I indicate below, these two
approaches are considerably different, and therefore I believe it is
important to elaborate on these differences more than you do (top p. 25)
especially the substantial ontological differences.
For BHL, there is no action_succeeds and action_fails fluents. Instead,
an action whose outcome depend on nature is represented by the
nondeterministic choice of simpler, deterministic actions corresponding to
each different outcome. For example, the nondeterministic action flipaCoin
is represented as the complex action
flipaCoin = flipHeads|flipTails
where | is GOLOG's operator for nondeterministically choosing between the
two actions flipHeads and flipTails . For your ongoing example,
pickup(key) would be represented by
pickup(key) = pickup_succeeds(key)|pickup_fails(key)
When an agent executes the action pickup(key) in situation S , nature
steps in and selects which of the two actions pickup_succeeds(key) and
pickup_fails(key) actually occurs, and it does so with frequencies
determined by an axiom of the form:
P0(pickup_succeeds(key), S) = p <-> (suitable
conditions on S and p)
In other words, your atomic choice of bottom p 13, and your axiom for P0
top of p 14 are represented by BHL in the way I have indicated above. These
are very different ontological and representational commitments than yours,
and I think they deserve a deeper analysis than your discussion provides.
Here are a few important differences these commitments lead to:
1. Primitive actions for BHL are entirely different than yours. BHL
primitive actions would be things like pickup_succeeds(key) , flipHeads
etc, i.e. they consist of the deterministic actions that nature can perform,
together with those deterministic actions (if any) that the agent can
perform. For you, primitive actions are typically nondeterministic, and
correspond to those actions that the agent can perform (but with
nondeterministic outcomes chosen by nature), e.g. pickup(key) ,
flipaCoin .
2. Therefore, for BHL, situation terms describe the "actual" history
selected by nature in response to the agent performed actions, e.g.
do(pickup_fails(key), do(flipHeads, S0)).
For you, situations denote the history of agent performed actions, e.g.
do(pickup(key), do(flipaCoin, S0)).
The BHL axioms all refer to the former situations. In your ontology, only
the latter are allowed.
3. In BHL, all primitive actions ( pickup_succeeds(key) , flipHeads ) are
deterministic and successor state axioms (the causal laws + solution to the
frame problem) are formulated only wrt these. For you, the causal axioms are
formulated wrt the (nondeterministic) agent's actions ( pickup(key) ,
flipaCoin ); hence the need for your fluents pickup_succeeds(S) and
pickup_fails(S) . These function as random variables that determine the
effects of the nondeterministic action pickup(key) . O ne consequence of
this difference is that for BHL, successor state axioms are perfectly
straightforward, whereas for you, because of these random variables, the
causal laws become, at least conceptually, somewhat opaque (e.g. footnote
9). Moreover, BHL use "classical" action precondition axioms, in contrast to
you (see above about action preconditions).
4. For BHL, your nondeterministic agent actions like pickup(key) , are not
part of the language of the sitcalc. Rather, they are nondeterministic GOLOG
programs. Since you also introduce a notion of a program (Sections 2.8,
2.10), there are some natural comparisons to be made. The obvious (and
perhaps only) important difference is in the nature of the primitive program
actions. For BHL programs, the primitives are the deterministic actions
described above (e.g. pickup_succeeds(key) , flipHeads ) whereas for you,
they are the agent actions like pickup(key) .
Suggestion: A Guide for the Perplexed
Your paper uses a single, ongoing example to illustrate the axiomatization
style required by your approach. Personally, I couldn't abstract, from the
example, a set of guidelines by which I could invent my own axiomatization
for a different example of my choosing. I think it would considerably
enhance the paper if you provided such guidelines. For example, for each
action, tell the reader what axioms need to be specified. What choice of
fluents needs to be made? (For example, there seem to be at least two
categories of fluents -- "normal" fluents like carrying(X, S) , and atomic
choice fluents. How does one decide on the latter, when given the primitive
actions and "normal" fluents of an application domain?) Similarly, for each
fluent, what axioms need to be specified? Also, what needs to be axiomatized
about the initial situation? Finally, what do all these axioms look like
syntactically? In connection with this last question, notice that on p. 20,
the clause with head at(X, P, S) resembles neither an effect axiom (as in
Example 2.8) nor a frame axiom (as in Example 2.9).
A2. David Poole:
Ray,
Thanks for your comments. I will try to explain everything so that it makes
sense, and try to explain why I am doing what I am doing. I'll answer the
questions in order, although it may help to read the guide to the perplexed
first.
Technical issues
1. Examples 2.8 and 2.9.
The predicate pickup_succeeds(S) in the first clause.
(a) It is not parameterized by the thing -- in this case key --
being picked up. It should be pickup_succeeds(key, S) .
What it says now is that the probability that picking up something (in this
case a key) actually achieves the agent carrying the object doesn't depend
on what is being picked up (nor does it depend on the position, as long as
the robot and key are at the same position). You are right in that this
probably isn't what you want. [This would really only make a difference if
the key term was a variable.] As it stands now, pickup_succeeds(key, S)
should probably be
pickup_succeeds_in_carrying_key_when_robot_and_key_are_at_same_position(S) .
Presumably, you need one of these predicates for each action type,
e.g. putdown_succeeds , goto_succeeds , etc. Therefore, why not
introduce a generic predicate succeeds(action, S) , in which
case, you can write succeeds(pickup(key), S) ,
succeeds(goto(loc), S) , etc? Similarly, you can have a relation
fails(action, S) .
In this case succeeds would not only be a function of the action and the
situation, but also a function of the condition being achieved (in this case
that the key is being carried), and a context (in this case that the robot
and the key are at the same position). But this is all that the rules say.
The rules should be seen as axioms of conditional effects (see below).
Now, C0 contains
union(succeeds(pickup(key), S), fails(pickup(key), S)) , where the
union is over all ground instances of these atoms.
I am not sure what you mean by the union, but C0 would contain infinitely
many 2-element sets. (See the answer to the next point.)
Incidentally, your specifications of what sets are in C0 , e.g.
bottom p. 13, is an abuse of notation, since it looks like an
object level sentence, when in fact it is a metalevel statement
for which universal quantification over situations is not defined.
Yes. I mean for each situation term S the set {pickup_succeeds(S),
pickup_fails(S)} is in C0 . That is, I am quantifying over terms in the
language.
Here C0 is a set of 2-element sets of ground terms. In this case C0 is
infinite but countable. I could have made it a set of open formulae, in
which case it could be finite, but this would have complicated the
presentation for no obvious gain.
(b) In axiomatizing at on p. 20, you do not include a
goto_succeeds atom in the clause body. Does the atom
would_not_fall_down_stairs(S) play this role?
Yes.
2. In the conditional plan of p. 21, don't you want
at(key, r101) instead of at_key ?
No. at_key is the sensor defined in Example 2.11 that (noisily) senses
whether the robot is at the same position as the key. The robot can only
condition on its sensed values. The robot doesn't know if the key is at room
r101; it only knows what its sensors tell it. [You could also imagine that a
robot could also condition on internal state variables, and what can be
computed from internal state variables, which is hinted at in Section 2.10.]
3. Consider the axiom of Example 2.9 and your comment "Note that
this implies that putting down the key always succeeds". Suppose
not. Then is it the case that the axiom should be modified by
replacing the atom A =/ putdown(key) by something like
¬ (A = putdown(key) ^ putdown-succeeds(key, S))
If so, perhaps this should be pointed out. (See my call below for
a guide for the perplexed.)
This is sort of correct, but it doesn't get the probabilities right. I would
expect that the probability of keeping the key to be independent of of the
other two cases. There are three free parameters to be assigned
probabilities, so we need three choice alternatives (when we only have
binary alternatives). See the guide for the perplexed below; I do this
example in more detail.
4. In the axiom of Example 2.9, you include a choice
keeps_carrying(key, S) , which you introduce because "there may be
a probability that the agent will drop the key". You then
axiomatize this with P0(keeps_carrying(key, S)) = .95 But I
can't think of any realistic way to axiomatize this probability
when only the parameter S is available.
Basically, you want to describe the probability that the robot
doesn't lose the key during the interval between the occurrence of
the last action in S , when carrying(key, S) was true, and the
occurrence of the next action A . In other words, you want to
describe the probability that the robot is still carrying the key
at situation do(A, S) given it is carrying it in situation S .
But that depends, at the very least, on WHEN this next action A
occurs. Now on one account of adding time to the sitcalc (Reiter,
Proc KR'96), an action can take an additional temporal argument
denoting that action's occurrence time, for example,
openDoor(t) . Then one expects that P0(keeps_carrying(key, S))
given that openDoor(10) is the next action should be greater
than this probability given that openDoor(1000) is the next
action. So as far as I can tell, the choice
keeps_carrying(key, S) should take another argument, namely A ,
or perhaps simply time(A) , where time(A) is the occurrence
time of the next action A .
Yes. That is right. If the agent could drop the key at any time, we need to
model (or learn) how the agent may drop the key as a function of time.
Presumably this would be modelled as a Poisson process (assuming it is
equally probable that the agent can drop the key at any time). As outlined
on page 1, I haven't dealt here explicitly with time.
The axiomatization I gave assumes that the agent can hold on to the key
tightly enough so whether it drops the key isn't a function of time ;^}
The need for action preconditions
On p. 8, you claim "None of our representations assume that
actions have preconditions; all actions can be attempted at any
time." I'm skeptical of this claim. Consider your example domain,
where you adopt the axioms P0(pickup_succeeds(S)) = .88 Just
prior to this, you say " P0(pickup_succeeds(S)) reflects how
likely it is that the agent succeeds in carrying the key given
that it was at the same position as the key and attempted to pick
it up". So you can't seriously write
P0(pickup_succeeds(S)) = .88 because here S is any situation,
including one in which the agent is 1000 kms from the key. I take
it that what you intended to write was something like
at(key, Pos, S) ^ at(robot, Pos, S) ·-> P0(pickup_succeeds(S)) = .88
(*)
If this is the case, then it is exactly here where you are using
action preconditions, namely, in characterizing those situations
in which an action has a high probability of succeeding. It also
appears that you are appealing to action preconditions in the
axiom of Example 2.8 (namely,
at(robot, Pos, S) ^ at(key, Pos, S) ). Probably, these atoms
should be omitted because their effects are realized in the above
axiom (*).
There are two separate issues here, first the meaning of preconditions, and
secondly how the atomic choices act in contexts where they aren't
applicable.
There are three things that could be meant by a precondition of an action:
* A condition under which the action can be done.
* A condition under which some effect follows from the action.
* A condition under which the action should be done.
It is only the second, which are often called conditional effects, that I
represent. The first is what I meant as "preconditions", which I don't have.
(These correspond to your Poss predicate, if I am not mistaken). This
shouldn't really be seen as a feature, but as a necessary evil. It means
that I have to axiomatize the effect of an action under all conditions
(including the conditions under which you may say the action is not
possible). I do this because, in general, an agent may carry out an action
even if it doesn't know that the action is "possible" (in the normal sense).
The third point, where the action should be done, is obtained because I want
to build sensible agent that maximize utility, but I also want to be able to
evaluate how good arbitrary agents are, not just good ones.
The second issue is a bit more subtle. Let's assume that the choice
alternatives are all binary (non-binary alternatives are useful when a
relation is functional). In this case, there are the same number of
alternatives as there are free parameters (conditional probabilities that
can be independently assigned) in the probability model. For example, when
converting a Bayesian network to an ICL theory, there are the same number of
alternatives as there are numbers to be assigned in the Bayesian network.
You typically have, for each effect e, rules of the form:
e <- context1 ^ ac1
..
e <- contextk ^ ack
where the contexti's are disjoint and covering. In this case we can assign
the probabilities of the atomic choice aci as the conditional probability:
P0(aci) =P(e|contexti)
Your question on conditions for P0 could be recast as: What happens to the
aci in the context when the corresponding rule is not applicable? Basically
it gets marginalized out. We don't have to worry about it. The abductive
characterization of the ICL shows that we only need to worry about the
atomic choices that are needed to prove a goal (in our case the utility and
the observations).
This should be seen in the context of an overriding theme of this work. We
are not trying to see how much we can put into a formalism, but how little
we can get away with. We don't need conditions on the probabilities of the
atomic choices, so we don't have them.
Finally, you often talk about actions being "attempted", as in the
above quotation. I found this particularly confusing since nothing
in your ontology deals with action "attempts". Actions simply
realize their effects with certain probabilities. You do not, for
example, have an action try_pickup , as do other authors (e.g.
James Allan) who do try to axiomatize action attempts . In this
connection, I had a hard time making sense of footnote 9, since it
motivates the axiom of Example 2.9 in terms of talk about "trying"
to pick up the key. In fact, even after reading this material
several times, I couldn't figure out footnote 9 until, much later,
I began to think about how your approach compares with Bacchus,
Halpern and Levesque. See my comments below on BHL.
Perhaps the term "attempted" is misleading. What I mean is that the robot
sends the motor control for the action, irrespectively of whether the robot
can do it (in this sense it is attempting the action). By the pickup(key)
action I mean a particular motor control (the one that would achieve
carrying the key if it is at the same position as the key and the pickup
succeeded). This action can be carried out in any context; it just doesn't
achieve carrying the key in these contexts.
Section 3.3
I must confess that I couldn't make much sense of the discussion
in Section 3.3, especially your arguments that the sitcalc is
inherently unsuitable for modeling multiple, possibly reactive
agents. It's true that Golog lacks the right control structures
for doing this, but your comments on p. 26 and p. 27 (p. 26 "In
order for a situation calculus program to ... and does the
appropriate concurrent actions." p. 27 "When there are multiple
agents ... or complex actions.") suggest to me that you are not
aware of more recent work by De Giacomo, Lesperance and Levesque
on Congolog that addresses precisely these issues (Proc. IJCAI
97). Congolog provides reactive rules (interrupts) and
interleaving concurrency in a semantically clean way, all
formulated within the sitcalc. I believe that Congolog addresses
all your criticisms of the sitcalc, except, of course, it does not
(yet) incorporate utilities.
"It's true that Golog lacks the right control structures for doing this..."
I am quite happy with the agent having simple control structures. I am
concerned about modelling asynchronous external actions or events (by other
agents or by nature).
It is not clear to me that Congolog addresses this, in the sense that all of
the concurrency in the language is internal to the agent. It doesn't model
exogenous actions (they generated externally). This would seem to mean that
external events are restricted to occur at the situations defined by the
primitive events. [I am looking forward to being told I am wrong.]
Moreover, with respect to the mix of the situation calculus and time, it is
clear now that we can do what we want when we have both the situation
calculus and time. But when you have statements saying when an event
occurred, you don't need situations. Thus parsimony would suggest that we do
away with situations. [I would expect that this should form a different
thread.]
Comparison with Bacchus, Halpern and Levesque
So far as I know, there have only been two proposals for
augmenting the sitcalc with probabilities, yours and BHL. As I
indicate below, these two approaches are considerably different,
and therefore I believe it is important to elaborate on these
differences more than you do (top p. 25) especially the
substantial ontological differences.
Yes, I do need to discuss this further (that is the joy of ETAI discussion
of papers; we can retrospectively expand those parts that are of most
interest).
First let me say that I am not claiming that mine is better than theirs, nor
that it is different just for the sake of being different. We start from
very different perspectives. In their introduction, they explicitly contrast
their work with the work starting from Bayesian networks. In particular,
they claim "...they [Bayesian networks] have difficulties in dealing with
features like disjunction ...". I take a Bayesian perspective that
disjunction is not a feature we want! What defines a Bayesian is that
probability is a measure of belief, that any proposition can have a
probability (both of which BHL would agree with) and that all uncertainty
should be measured by probability. Thus you need to keep in mind that the
different design choices could stem from this different perspective.
For BHL, there is no action_succeeds and action_fails fluents.
Instead, an action whose outcome depend on nature is represented
by the nondeterministic choice of simpler, deterministic actions
corresponding to each different outcome. For example, the
nondeterministic action flipaCoin is represented as the complex
action
flipaCoin = flipHeads|flipTails
where | is GOLOG's operator for nondeterministically choosing
between the two actions flipHeads and flipTails . For your
ongoing example, pickup(key) would be represented by
pickup(key) = pickup_succeeds(key)|pickup_fails(key)
When an agent executes the action pickup(key) in situation S ,
nature steps in and selects which of the two actions
pickup_succeeds(key) and pickup_fails(key) actually occurs, and
it does so with frequencies determined by an axiom of the form:
P0(pickup_succeeds(key), S) = p <-> (suitable
conditions on S and p)
In other words, your atomic choice of bottom p 13, and your axiom
for P0 top of p 14 are represented by BHL in the way I have
indicated above.
Except that BHL don't model probabilistic actions (in their IJCAI-95 paper,
which is the only one I had seen) although I believe they could. All of
their probabilities are within the agent, so such axioms would have to be
part of the formula for updating belief. [I just found a new paper,
Reasoning about Noisy Sensors and Effectors in the Situation Calculus, 1998,
at Faheim Bacchus's web site that does this. I'll call this BHL98.]
One other important point to note is that the probabilistic part of the ICL
is a restricted form of Bacchus's and Halpern's logics of probability as
belief. The translation is that each atom that isn't an atomic choice is
defined by Clark's completion of the rules defining that atom. We need
statements that the elements of an alternative are exclusive and covering
and that the atomic choices that aren't in the same alternative are
probabilistically independent. Thus the translation doesn't require
"suitable conditions on S and p".
A general framework for probability and action is intuitively
straightforward (see Halpern and Tuttle (1993) for a general semantic
framework). You can think about forward simulating the system.
Nondeterministic/stochastic actions split the worlds and impose a
probability over the resulting worlds. In the ICL we handle splitting the
worlds using one simple mechanism: independent choice alternatives. I treat
actions by the agent and other stochastic mechanisms (e.g., the
ramifications of actions) in exactly the same way. BHL-98 split the worlds
by nondeterministic actions (as you outline). They would then need a
different mechanism for stochastic ramifications.
These are very different ontological and representational
commitments than yours, and I think they deserve a deeper analysis
than your discussion provides. Here are a few important
differences these commitments lead to:
1. Primitive actions for BHL are entirely different than yours.
BHL primitive actions would be things like pickup_succeeds(key) ,
flipHeads etc, i.e. they consist of the deterministic actions
that nature can perform, together with those deterministic actions
(if any) that the agent can perform. For you, primitive actions
are typically nondeterministic, and correspond to those actions
that the agent can perform (but with nondeterministic outcomes
chosen by nature), e.g. pickup(key) , flipaCoin .
Yes.
2. Therefore, for BHL, situation terms describe the "actual"
history selected by nature in response to the agent performed
actions, e.g.
do(pickup_fails(key), do(flipHeads, S0)).
For you, situations denote the history of agent performed actions,
e.g.
do(pickup(key), do(flipaCoin, S0)).
The BHL axioms all refer to the former situations. In your
ontology, only the latter are allowed.
Yes. I tried to be explicit about both of these points.
3. In BHL, all primitive actions ( pickup_succeeds(key) ,
flipHeads ) are deterministic and successor state axioms (the
causal laws + solution to the frame problem) are formulated only
wrt these. For you, the causal axioms are formulated wrt the
(nondeterministic) agent's actions ( pickup(key) , flipaCoin );
hence the need for your fluents pickup_succeeds(S) and
pickup_fails(S) . These function as random variables that
determine the effects of the nondeterministic action
pickup(key) . One consequence of this difference is that for BHL,
successor state axioms are perfectly straightforward, whereas for
you, because of these random variables, the causal laws become, at
least conceptually, somewhat opaque (e.g. footnote 9).
Except I would think that my successor state axioms are perfectly
straightforward. I get by with just Clark's completion, in much the same way
as other logic programming representations of action. Frame and ramification
axioms are treated the same (in fact I don't even think of them as
different, and the paper doesn't distinguish them). I get by with Clark's
completion because it is defined with respect to each world, where I just
have a simple acyclic logic program. Maybe the guide to the perplexed below
will help.
Moreover, BHL use "classical" action precondition axioms, in
contrast to you (see above about action preconditions).
So what happens if the agent doesn't know if the precondition holds, but
still wants to do the action? This is important because, with noisy sensors,
agents know the actual truth values of virtually nothing outside of their
internal state, and most preconditions of actions are properties of the
world, not properties of the agent's beliefs.
4. For BHL, your nondeterministic agent actions like
pickup(key) , are not part of the language of the sitcalc. Rather,
they are nondeterministic GOLOG programs. Since you also introduce
a notion of a program (Sections 2.8, 2.10), there are some natural
comparisons to be made. The obvious (and perhaps only) important
difference is in the nature of the primitive program actions. For
BHL programs, the primitives are the deterministic actions
described above (e.g. pickup_succeeds(key) , flipHeads ) whereas
for you, they are the agent actions like pickup(key) .
One major difference is that in BHL, it is the agent who does probabilistic
reasoning. In my framework, the agent doesn't (have to) do probabilistic
reasoning, it only has to do the right thing (to borrow the title from
Russell and Wefald's book). The role of the utility is to compare agents.
This is important when we consider what Good calls type 2 rationality and
Russell calls bounded rationality (see the work by I.J. Good, Eric Horvitz,
and Stuart Russell for example), where we must take into account the time of
the computation done by the agent in order to compute utility. I would
expect that optimal agents wouldn't do (exact) probabilistic reasoning at
all, because it is too hard! That is why we want a language that lets us
model agents and their environment, and defines the expected utility of an
agent in an environment. One of the reasons I didn't want to just add "time"
into the framework is that I want a way to take into account the computation
time of the agent (the thinking time as well as the acting time), and that
makes it much more complicated (I wanted to get the foundations debugged
first).
Suggestion: A Guide for the Perplexed
Your paper uses a single, ongoing example to illustrate the
axiomatization style required by your approach. Personally, I
couldn't abstract, from the example, a set of guidelines by which
I could invent my own axiomatization for a different example of my
choosing. I think it would considerably enhance the paper if you
provided such guidelines. For example, for each action, tell the
reader what axioms need to be specified. What choice of fluents
needs to be made? (For example, there seem to be at least two
categories of fluents - "normal" fluents like carrying(X, S) ,
and atomic choice fluents. How does one decide on the latter, when
given the primitive actions and "normal" fluents of an application
domain?) Similarly, for each fluent, what axioms need to be
specified? Also, what needs to be axiomatized about the initial
situation? Finally, what do all these axioms look like
syntactically?
Thanks for the suggestion. The following is a paraphrase of how we tell
people to represent knowledge in Bayesian networks, translated into the
language of the ICL.
First I'll do the propositional (ground) case. We totally order the
propositions. The idea is that we will define each proposition in terms of
its predecessors in the total ordering. For each proposition e, a parent
context is a conjunction of literals made up of the predecessors of e, such
that the other predecessors are conditionally independent of e given the
context. We find a set of mutually exclusive and covering set
{context1,...,contextk} of parent contexts. (The atoms appearing in one of
the parent contexts are the parents of e in the corresponding Bayesian
network). If e is always true when contexti is true, we write the rule:
e <- contexti
If P(e | contexti) isn't 0 or 1, we create a rule:
e <- contexti ^ aci
and create an alternative {aci,naci} (where these are both atoms that don't
appear anywhere else), with the probability:
P0(aci) =P(e|contexti)
If the context is empty ( e doesn't depend on any of its predecessors) we
don't need to create a rule; we can just make e an atomic choice.
When the probability given the context is 0, we don't write any rules.
The case for the ICL with the situation calculus is similar. Intuitively, we
make the total ordering of the propositions respect the temporal ordering of
situations. We write how a fluent at one situation depends on fluents (lower
in the ordering) at that situation and on fluents at previous situations.
Note that this rule automatically handles ramifications as well as frame
axioms. The total ordering of the fluents guarantees the acyclicity of the
rule base and that we don't have circular definitions. The initial situation
is handled as any other, but the predecessors in the total ordering are only
initial values of fluents (and perhaps atoms that don't depend on the
situation).
The only thing peculiar about this is that we often have fluents that depend
on values at the current as well as the previous situation. This is
important when there are correlated effects of an action; we can't just
define each fluent in terms of fluents at the previous situation. But this
also means that we don't treat frame axioms and ramification axioms
differently.
Let's look at how we would do Examples 2.8 & 2.9, with putting-down the key
possibly failing. Lets consider when carrying would be true. Suppose
carrying doesn't depend on anything at the same time, so we can ask what are
the contexts on which carrying(O,do(A,S)) depends. It would seem there are
three such contexts:
* A=pickup(O)), and the robot and O are at the same position.
* The action isn't pickup(O)), the robot was carrying O in situation
S, and the action wasn't to put down O.
* The robot was carrying O in situation S, and the action was to put
down O.
In no other cases would the robot be carrying O.
The robot would be carrying O in the first context if the pickup succeeds
(hence the name of the atomic choice in Example 2.8). This results in the
rule:
carrying(O,do(pickup(O),S)) <-
at(robot,Pos,S) &
at(O,Pos,S) &
pickup_succeeds(O,S).
The robot would be carrying O in the second context if it keeps carrying
the key (hence the name of the atomic choice in Example 2.9). This results
in the rule:
carrying(O,do(A,S)) <-
carrying(O,S) &
A \= putdown(O) &
A \= pickup(O) &
pickup_succeeds(O,S).
The robot would be carrying O in the third context if the putdown failed.
Thus, to account for the chance that the putdown failed, we would write the
extra clause:
carrying(O,do(putdown(O),S)) <-
carrying(O,S) &
putdown_fails(O,S).
where putdown_fails(O,S) is an atomic choice, with P0(putdown_fails(O,S))
the conditional probability that the robot is still carrying O after it has
carries out the putdown(O) action.
Note that putdown may succeed in doing other things, it just fails in
stopping the robot from carrying O. So maybe putdown_fails should be
something more like putdown_fails_to_stop_the_robot_from_carrying.
Footnote 9 is there to try to explain what the rules mean if the rule bodies
aren't disjoint. We can interpret what these rules mean, but it usually
isn't what you want (for the cases where both rules are applicable). When we
write these rules, having non-disjoint rules is usually a bug (the
implementation available from my web page warns when it finds non-disjoint
rules.)
In connection with this last question, notice that on p. 20, the
clause with head at(X, P, S) resembles neither an effect axiom
(as in Example 2.8) nor a frame axiom (as in Example 2.9).
It is a ramification of the robot moving. The above methodology handles
these ramifications in the same way it handles frame axioms (and any other
axioms).
Thanks for your comments and questions. I hope this made the paper clearer.
I would be happy to answer any other questions you may have (or engage in
debate about the usefulness of this).
David
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