Abstract
A very influential work on belief change is based on the seminal paper “On the Logic of Theory Change: Partial Meet Contractions and Revision Functions”. In this paper Alchourron, Gärdenfors, and Makinson investigate the properties that such a method should have in order to be intuitively appealing. The result was a set of postulates (named AGM postulates after the initials of the authors) that every belief change operator should satisfy. The “AGM Theory” had a major influence in most subsequent works on belief change. In special, the constructive approach given there was adopted in Artificial Intelligence (AI) as the (almost) universal model for the specification of the updates of Knowledge Bases as it usually involves a new belief that may be inconsistent with the old ones. From that moment, the references to the original paper within the field of AI have increased drastically. In this chapter we intend to explain why AGM receive such swift acceptance from the AI community. We will show that the AGM theory came out at a critical time for AI. In particular, the question of how to actualize the knowledge bases in the face of inputs that are possible inconsistent with the previous corpus, was an unresolved, problematic issue. This is why, when AGM appears, it combines with various attempts under development that synchronize perfectly with them, as is the case with the pioneering work we will be discussing in this chapter. The high level of abstraction of the new approach was what a lot of researchers in AI were seeking.
This chapter also contains a description of the genesis of AGM theory, a historical analysis of the circumstances in which the theory was introduced to AI, and a qualitative and quantitative evaluation of the impact of the AGM theory in AI research.
In memory of Carlos E. Alchourrón
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- 1.
Another important line of research was developped in theoric foundations of economic sciences. In particular, we can call it “epistemic foundations of equilibria in games”. Cristina Bicchieri was the first researcher to introduce an application of AGM to game theory see Bicchieri, Cristina (1988a). She also attended the TARK’88 Conference. We thanks Horacio Arló Costa for this observation.
- 2.
Jon Doyle (1979).
- 3.
Jon Doyle and Philip London (1980).
- 4.
Ronald Fagin et al. (1983).
- 5.
- 6.
Harper, W. (1977).
- 7.
C. Alchourrón et al. (1985).
- 8.
Alan Newell (1981).
- 9.
M. Vardi (1988).
- 10.
J. Halpern (1986).
- 11.
“Carlos made some very penetrating remarks that made me feel quite ashamed – there was I, talking about deontic logic to people who I had assumed knew nothing about it, and this guy in front of me evidently had a clearer picture of what is involved than I did”. D. Makinson, Personal communication.
- 12.
This problem began to get the attention of Alchourrón and his colleague Eugenio Bulygin early in the 1970s.
- 13.
D. Makinson. Personal communication to the authors.
- 14.
C. Alchourrón and D. Makinson (1981).
- 15.
“Groping painfully towards ideas that would later became formulated as maxichoice contraction and safe contraction”. David Makinson (1996).
- 16.
The term “contraction” does not appear in the text, only “derogation” is used.
- 17.
Let A be the set of regulations; \(B,\;C \subseteq A\), and let F1 and F2 be sets of facts. The stated situation is that of \(B \cup {\textrm{F}}1 \Rightarrow x\); \(C \cup {\textrm{F}}2 \Rightarrow \neg x\).
- 18.
In the general case of an inconsistent code A, the proposal was to make a derogation of A by \(x \wedge \neg x\).
- 19.
In the last years of his life, Alchourrón published a series of articles on the logic of defeasible conditional. In these papers he proposed a philosophical elucidation of the notion of defeasiblity and applied it to clarify deontic concepts such as that of prima facie duty.
- 20.
One of these examples of possible applications of delivery was the case of a computational information system that, because of some “accident”, had included inconsistent information during a process and had to be kept in operation, in a secure way, while the cause of the error was being repaired. In those years the “TMS” systems were being developed in AI, but the authors, far from suspecting their future involvements, only made reference to conventional systems, which is obvious because the system of the example was conceived as acquiring inconsistent information through an error that later a support team would have to repair.
- 21.
C. Alchourrón and D. Makinson (1982).
- 22.
Carlos Alchourrón. Presentation of his research work included in the application for the competition for full professor of Logic in the Faculty of Philosophy and Literature of the University of Buenos Aires, in 1985. The application was kindly given to the authors by Gladys Palau.
- 23.
In the case of full meet, the revision derived from it by Levi’s identity produces as result only the consequences of the “new belief ”, losing all the previous background. In the case of maxichoice, if a non complete theory is contracted, the generated revision generated by Levi produces a complete theory; the agent becomes omniscient. This result is counterintuitive, except in the case where the set of starting beliefs is already complete. Both problems are resolved with “partial meet contraction”.
- 24.
- 25.
C. Alchourrón and D. Makinson (1982). The major part of the references in this paper are to Gärdenfors’ papers, to whom they express their gratitude for having put them at their disposal, even those that were being typed.
- 26.
Peter Gärdenfors (1980).
- 27.
In fact, when, in 1977, Gärdenfors presents, in Helsinki, one of his first papers in this area, “Conditional and Change of Belief”, he has an extensive and fruitful interchange of ideas with both researchers.
- 28.
This idea of a connection between Belief revision and the Ramsey Test for conditionals was abandoned later because it was shown to be impossible (Gärdenfors reported this result in Peter Gärdenfors (1986).
- 29.
Peter Gärdenfors (1979).
- 30.
Peter Gärdenfors (1981).
- 31.
Peter Gärdenfors (1982).
- 32.
D. Makinson. Personal communication to the authors.
- 33.
- 34.
“This approach has never had much echo among computer scientists – perhaps because of the place where it was published – but I have always had a particular affection for it. I think that Carlos quite liked it too, although I would describe myself as the father and he as an uncle”. D. Makinson. Personal communication to the authors.
- 35.
There is consensus in locating the “birth” of AI in the Dartmouth Conference of 1956.
- 36.
American Association for Artificial Intelligence Conference (Stanford, 8/19/80). Newell was, at that moment, the President of AAAI.
- 37.
This point of view was framed inside the leibnitzian tradition.
- 38.
Special Issue on Knowledge Representation. SIGART Newsletter. February 1980 (70).
- 39.
In the work of that time, “knowledge” and “belief” are two terms used indistinctively, even in those cases in which the authors acknowledge their philosophical differences. In the context of AI, “knowledge” would be all that it is assumed to be represented in the data structures of the system.
- 40.
This “level” refers to a previous notion of level or tier in a computational system. The lowest is the device level, the next one the circuit level and so on up to the level of programs or symbolic systems (SL). Each level is not an “abstraction” of the lower ones, neither a simple “point of view”. It has a real existence, even independent of the multiple possible ways in which it may be realized or supported by the lower level. Each level or tier is a specialization of the class of systems capable of being described in the next level. Thus, it is a priori an open question which is the physical realization of a level in the lower structure in the agent at the knowledge level; the determination of behavior by a global principle and the failure to determine behavior uniquely, running counter to the common feature at all levels that a system is a determinate machine…Yet, radical incompleteness characterizes the knowledge level. As Newell said “…Sometimes behavior can be predicted by the knowledge level description; often it cannot. The incompleteness is not just a failure in certain special situations or in some small departures. The term radical is used to indicate that entire ranges of behavior may not be describable at the knowledge level, but only in terms systems at a lower level (namely, the symbolic level). However, the necessity of accepting this incompleteness is an essential aspect of this level… .”. Alan Newell (1981).
- 41.
If a system has a data structure from which it can be said that it represents something (object, procedure, or whatever) and it can use it, by means of certain components that interpret the structure, then it is said about the same system that it has knowledge, the knowledge is embodied in that representation of the thing. When we say that “the program knows K”, what we want to say is that there is a certain structure in the program which we “see” as supporting K, and that, also, it selects actions exactly as we would expect that an agent that “knows K” would do, following the rationality principle, that is, the most adequate to reach its goals.
- 42.
A priori, it could be any consequence from K.
- 43.
To reinforce the idea that the problem was “on the table” at that time, we note that some similar (but not identical) considerations had been proposed previously. The main example is McCarthy, in his work McCarthy (1977) where he proposed to divide any problem in AI in two parts: the epistemological (“what information is available to an observer and what conclusions can be drawn from information” and “what rules permit legitimate conclusions to be drawn… ”) and the heuristic (“how to search spaces of possibilities and how to match patterns”), although he left in the epistemological part the question about how the information was represented in the memory of a computer. In fact, this proposal dates back to J. McCarthy and P. Hayes (1969).
- 44.
Brachman, Levesque, Moore, Halpern, Moses, Vardi, Fagin and others. For example, H. Levesque in “Logic and the complexity of Reasoning”, confronting objections of the type “a realistic cognitive activity is much more complex that any type of neat mathematical a priori analysis”, notes that a model is interesting only if it serves to explain the behavior one wishes to model, and also that if that behavior is disorderly or mixed up, the model does not have to be so. The model can be more or less idealized or realistic, but this does not alter “the hard fact that a model that has a mistaken behavior or the correct behavior for mysterious reasons does not have any explanatory power”. H.J. Levesque (1988).
- 45.
Some of these debates were the ones that divided symbolists from the researchers that tried to simulate neural mechanisms. See, for example, Graubard Stephen (1988)
- 46.
“Data-dependencies are explicit records of inferences or computations. These records are examined to determine the set of valid derivations, and hence the current set of beliefs (that is, those statements with valid arguments). In some cases, they are erased along with the beliefs they support when changes lead to removing a belief and its consequences from the database... In other systems, the dependencies are kept permanently. In this latter case, dependency-based revision techniques can use a uniform procedure, sometimes called truth maintenance (Doyle 79a), to mark each database statement as believed or not believed, depending on whether the recorded derivations currently provide a valid argument for the statement. One might view this sort of dependency analysis as analogous to the mark~sweep garbage collection procedures of list-processing systems… ” Jon Doyle and Philip London (1980) page 9.
- 47.
As we remarked in the previous section, this is the same type of problem that Alchourrón and Bulygin had considered a few years before, with respect to the derogation in a legal corpus.
- 48.
Bernhard Nebel (1992).
- 49.
Peter Gärdenfors and Hans Rott (1992).
- 50.
“While the application that we have in mind here is updating databases, we believe that the framework developed here is also relevant to any kind of knowledge base management system. From the point of view of Artificial Intelligence, what we have here is a logic for belief revision, that is, a logic for revising a system of beliefs to reflect perceived changes in the environment or acquisition of new information. The reader who is interested in that aspect is referred to Doyle & London”. Ronald Fagin et al. (1983).
- 51.
Fagin, R. et al. (1986).
- 52.
Borgida A. (1985).
- 53.
Weber, A. (1986).
- 54.
Winslett M. (1988).
- 55.
Winslett M. (1986).
- 56.
For example, in the case of a distributed system, you could assign knowledge to it externally in this way: a processor X “knows” A if in all the global state in which X may be in, A is true.
- 57.
- 58.
P. Gärdenfors and D. Makinson (1988).
- 59.
Of the remaining papers presented at the conference, only one made reference to AGM theory. Its author was Cristina Bicchieri, a researcher on economic subjects and game theory, who, in a personal communication to the present authors, remarked that it was I. Levi who had made her aware of the relevance of AGM for her work. The paper was Bicchieri, Cristina (1988b)
- 60.
Peter Gärdenfors. Personal Communication to the authors.
- 61.
Peter Gärdenfors. Personal Communication to the authors. Gärdenfors started, a short time before, to get acquainted with the problems of revision in databases and AI, starting with the works by Ronald Fagin et al., 1983 and by the interchange – on occasion of a sojourn in Canberra at the end of 1986 – with the group of Norman Foo and Anand Rao in Sydney.
- 62.
In a revised version, published in 1995, of the overview which Halpern used to inaugurate the first TARK in 1986 J. Halpern (1986), he does not speak anymore of BR as a “can of worms”. When he refers to BR, he mentions AGM theory. This author, in the years that followed TARK’88, worked in BR and proposed an alternative model to AGM.
- 63.
H.J. Levesque (1986).
- 64.
Which was identified in AI with systems of the type of the already mentioned “Truth Maintenance Systems” (TMS) by Jon Doyle, and a family of derived systems.
- 65.
Mukesh Dalal (1988).
- 66.
H.J. Levesque (1984).
- 67.
Mukesh Dalal (1988). The sense of this expression by Dalal is already suggested in section 3, in the last of the conclusions that we attributed to Newell’s work. For an external observer, the beliefs of an agent are, in principle, whichever consequences of his KB. Although it may not be realistic to consider that he “knows” them all, it should be expected that he may be able to arrive at any of them through a “goal” driven search and following the rationality principle.
- 68.
Mukesh Dalal. Personal Communication to the authors.
- 69.
Alex Borgida. Personal Communication to the authors.
- 70.
“I certainly did, quite early on – though never in print – notice a connection between the AGM work on belief revision and the work in AI on nonmonotonic reasoning and simply assumed, a little glibly, that the latter could be subsumed within the former – roughly the case dealt with via entrenchment, where some parts of a theory are protected against revision. In terms of abstract consequence relations, that wasn’t a bad guess; but notice that it simply leaves unaddressed the issues of finding the relevant non-monotonic (default) fixed points and that, in the context of various models of extended logic programming, is where much of the interesting action of late has been. So, I’d give myself a B-/C+ for prophecy on this one.”. David Israel. Personal Communication to the authors.
- 71.
Ken Satoh (1988).
- 72.
Ray Reiter (1980).
- 73.
J. McCarthy (1980).
- 74.
Contrary to the AGM model, which only depends on the original ones.
- 75.
The Vacuity postulate says that if the new information is not contradictory with the old one, then revision consists simply of including it directly (without any removal). The additional postulates say that to revise by a disjunction has to be the same as revision by one of the disjuncts or the revision by the other, or the intersection of both.
- 76.
Ken Satoh. Personal communication to the authors.
- 77.
A. S. Rao and N. Foo (1989).
- 78.
It was common to speak about the “frame problem” and the “ramification problem”, and these topics implied presumptive reasoning. Given that, a priori, all the possible consequences of the actions on a given scene are not known, the agent has to assume that it occurred a minimal change within what is expressed by the previous knowledge about the consequences of that actions and go into a new state of belief about the scene in which he is acting which is not “certain”. It is in this point that non monotonic reasoning enters into the problem.
- 79.
Later, Katsuno and Mendelzon developed the idea of “updating” as different from “revision” to distinguish between the consequences over a Knowledge Base of a change in the World from a change in the beliefs about the World.
- 80.
Norman Foo. Personal Communication to the authors
- 81.
Peter Gärdenfors in a personal communication to the authors confirms that “…when I was in Canberra in the fall of 1986 I was contacted by Norman Foo and Annand Rao in Sydney who invited me to give a talk on belief revision…”.
- 82.
Norman Foo. Personal communication to the authors.
- 83.
The tables of references are in Section 5.
- 84.
Bernhard Nebel (1989).
- 85.
Bernhard Nebel (1989). In our opinion, the relativization made by Nebel ("…at least some aspects of belief revision can be subject to a knowledge level analysis…) derives from the "radical incompleteness" that characterizes the knowledge level in Newell’s definition.
- 86.
P. Gärdenfors (1988).
- 87.
The bibliographic references he mentions embrace almost all the publications of the authors of the theory, from the paper about contraction by Alchourrón and Makinson in 1982 to the paper by Gärdenfors on that same year of 1989, including the one presented in TARK’88.
- 88.
When you want to delete a conjunction from a theory, at least one of the conjuncts has to be extracted (if not, given that the result is closed by consequence, you would obtain the conjunction once again). The postulate of conjunctive inclusion expresses that if one of the conjuncts is deleted, you should expect that all the formulas that would have been deleted when making an explicit contraction only of that conjunct are also deleted.
- 89.
Nebel developed his work in the context of an Esprit Project about knowledge management.
- 90.
Bernhard Nebel. Personal Communication to the authors.
- 91.
Bernhard Nebel. Personal Communication to the authors.
- 92.
H. Katsuno and A. Mendelzon (1989).
- 93.
Contrasting with Dalal’s comparison, this review of proposals intended to verify which AGM postulates satisfied each one of the analyzed frameworks.
- 94.
Hirofumi Katsuno. Personal communication to the authors. Regrettably, the distinguished argentine researcher, resident in Canada, Alberto Mendelzon, died prematurely in 2005.
- 95.
Second Workshop on NMR, Grassau, Germany, June 1988.
- 96.
David Makinson (1989).
- 97.
D. Makinson. Personal communication to the authors.
- 98.
“I probably first heard about Theory Revision in a talk given by David Makinson at NMR Workshop 6/88 in Grassau, Germany”. Karl Schlechta. Personal communication to the authors.
- 99.
Karl Schlechta (1989).
- 100.
Workshop on The logic of theory change. Andre Furhmann and Michel Morreau. Konstanz. Germany. October 1989.
- 101.
A. Furhmann and M. Morreau (1990).
- 102.
N. Friedman and J. Halpern (1999).
- 103.
Reliabilism is the principal concern of formal learning theory. See for example K. Kelly, O. Schulte and V. Hendricks 1997.
- 104.
It is possible to access the table in http//:http://www.dc.uba.ar/people/ricardo/referencesAGM.xls
- 105.
It should be noted that, during the first years of the period under analysis, a number of papers were not electronically available for dissemination, nor were they rendered in that format at a later date; for this reason, the cites quoted for those first years are clearly incomplete; a remarkable case is that of Rao and Foo’s work, commented under Section 1.4.
- 106.
Originally, this research meant to honour the memory of Carlos Alchourrón in commemoration of the 10th anniversary of his passing. Hence, we selected this year due to the fact that, at the time, our well established, consolidated data was that of the previous year.
- 107.
Adnan Darwiche and Judea Peral (1997).
- 108.
Hans Rott (1989).
- 109.
M. Pagnucco (1996).
- 110.
In the most recent Belief Revision literature from 2005 to the present there is increased attention to issues of belief merging and judgement aggregation (the latter viewed in comparison with older theory on the aggregation of individual preferences, in economics, and the aggregation of votes in political science). We owe this remark to David Makinson.
- 111.
The work of Cristina Bicchieri (1988b) is one of the precursors for this line of research.
- 112.
Carlos Alchourrón (1986).
- 113.
P. Gärdenfors and D. Makinson (1991).
- 114.
The extralogical factor is not totally eliminated (since the behavior of an agent is not wholly definable in the KL), but the arbitrariness can be restricted. The works on safe contraction as well as the ones on epistemic entrenchment go in depth in this sense.
- 115.
David Makinson and George Kourousias (2006).
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Acknowledgments
We would not be able even to attempt to reconstruct the history of the introduction of the AGM Theory in Artificial Intelligence without invaluable contributions of many of the principle actors of those years’ long, extensive and effervescent discussions. All of them approached our inquiry with enthusiasm and made true efforts to honor us with their emotive memories.
Therefore we want to thank Cristina Bicchieri, Horacio Arló Costa, Alex Borgida, Mukesh Dalal, Norman Foo, Peter Gärdenfors, Joseph Halpern, Gilbert Harman, David Israel, Hirofumi Katsumo, Hector Levesque, Bernhard Nebel, Hans Rott, Ken Satoh, Karl Schlechta for accepting to respond our questions and being our partners this time.
We are very grateful to our friend Eduardo Fermé for his sharp observations that helped us to revise the original Spanish draft of our work.
Also, we are indebted to our colleague and friend José Alvarez who helped us to translate to English our first draft. In addition, during this process, he offered us a lot of helpful and interesting discussions on different parts of this chapter.
We own a very special gratitude to Gladys Palau, Eugenio Bulygin, David Makinson and Antonio Martino who committed themselves in a very personal way to the reconstruction of the history, patiently accepting our repeated inquiries and generously sharing their reminiscences of Carlos Alchourrón.
Thanks all of them to accompany us to honor the memory of Carlos Alchourrón whose disciples and friends we consider ourselves to be.
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Carnota, R., Rodríguez, R. (2010). AGM Theory and Artificial Intelligence. In: Olsson, E., Enqvist, S. (eds) Belief Revision meets Philosophy of Science. Logic, Epistemology, and the Unity of Science, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9609-8_1
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