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Analog Project

Foundations of Analogical Inference and their Applications to Symbolic Reasoning and Learning

PRONTIC 122-93

Josep-Lluis Arcos, Eva Armengol, Beatriz López,
Ramon López de Màntaras, Enric Plaza i Cervera

IIIA - Artificial Intelligence Research Institute (CSIC)

Keywords: Case-based reasoning, Reflective languages, Analogical reasoning, Introspective learning, Multistrategy learning, Cognitive architectures, Artificial Intelligence.

SUMMARY: A theoretical study and implementation of an integrated cognitive architecture (ICA) based on analogical inference is proposed. The theoretical study will improve the understanding, comparison and use of ICAs, specially those integrating reasoning with learning. The theoretical study will be based on the analysis of learning as a kind of introspective reasoning in the ICA. Different learning methods (inductive, chunking, and case-based) will be analysed concerning the self-model the ICA needs to integrate those methods. This approach allows to give a clear semantics to the integration of different reasoning modules in the ICA, and to improve the understanding ICAs foundations. The approach also supports an implementation using introspective languages. The practical proposal is implementing an analogy-based ICA by extending the Noos introspective language developed at IIIA.

Contents of Progress Report
1. The reflective representation language Noos
1.1 Inference and reflection
1.2 Feature terms
1.3 The Noos WWW interface
2. New learning techniques
2.1 Case-based reasoning
2.2 Inductive learning
2.3 Compilative learning
3. Applications

Progress Report

The summary above is the original one in the proposal of the Analog project. The main goal of the Analog Project was to study and implement a computational framework for integration of different machine learning (ML) methods into a problem solving system. We called this computational framework an ICA, integrated cognitive architecture (related architectures are decribed in the Survey of Cognitive and Agent Architectures).The Analog project hypothesis was that ML methods could be integrated if they were viewed as introspective methods in a representation language. That is to say, a learning method is one that knows, based on its past behavior, how to modify the actual contents of a problem solving system in order to improve the future behavior. In order to do this the system needs to be able to inspect its own past behavior (introspection) and create new improved knowledge structures in the language of the problem solving system. The approach taken was to start with the reflective representation language Noos developed at our Institute that integrate analogical reasoning (also called CBR --case-based reasoning) and learning, and then extend Noos as needed for integrating other machine learning methods. Summarizing, the target was a problem solving architecture capable of integrating multistrategy learning. In this progress report we will discuss the current definition and implementation of the Noos language, the integration of different ML methods, the development of new learning techniques and their implementation, and some application systems developed within the project.

1. The reflective representation language Noos

During the project, a new version of Noos was implemented as a result of the study of requirements for new inductive and compilative (EBL) learning techniques, the experience in the implementation of applications systems, and formal studies about Noos as a representation language and about reflection in AI systems --this last aspect was performed in cooperation with the ARREL project, one of which partners was our Institute. We have developed a formal model of the reflective architecture of Noos using Descriptive Dynamic Logic. DDL is a framework for describing reflective systems that was started in cooperation with the ARREL project (TIC 92-579-C02-01) and later continued in this project.

1.1 Inference and reflection

The main extension of Noos expressive power has been providing three new sorts of metalevel inference. It is possible now to ask whether there is any reachable solution for a task (the P provability operator), whether a given solution is currently known (the K epistemic operator), and all the possible solutions to a task that satisfy the current constraints. These types of inference are used on default reasoning and reasoning about preferences. For instance, default reasoning is modelled as follows: if it cannot be proven of an instance to be an exception (using the P operator), the default applies. Reasoning about preferences allows a declarative way to introduce control constructs in the Noos programs. Preferences are modelled as partial orders over sets of alternatives upon which a Noos program is up to make a decision. Reasoning about references allow a declarative specification of case retrieval and selection using domain knowledge in case-based reasoning (CBR). Moreover, higher-level preferences allow meta-level reasoning upon conflicting criteria and have been used to model legal problems that involve non-monotonic reasoning.

1.2 Feature terms

The introduction of ML methods based on induction shed new light on the object-centered basis of Noos. It turned out that the subsumption relation among Noos object descriptions we have already defined was very akin to the those defined in psi-terms (developed by Aït-Kaci to model structured data in Prolog-like languages), and also in feature structures (Carpenter). This lead to the modelling of Noos object descriptions as feature-terms. Consequently, Noos descriptions form a lattice regarding the subsumption relation (the general-to-specific ordering relation among descriptions). Since induction methods can be viewed as a search process among descriptions that generalize (subsume) a set of training examples, it was clear that inductive methods in Noos could be modelled and implemented as methods that perform different strategies in searching the possible Noos descriptions in the subsumption lattice. In fact, the subsumption relation was the main construct used in the first version of Noos to retrieve cases for case-based reasoning (CBR). Because of this, new inductive learning methods could now be integrated seamlessly in the Noos framework with existing case-based learning.

The Noos WWW interface

The current implementation of Noos is an interpreter written in Common Lisp that runs in Apple platforms (using MCL) and Unix platforms (using CMU Lisp). The Apple version has a GUI that lacks the Unix version. However, we have developed WebNoos, a World-Wide-Web interface to Noos. WebNoos allows any user with a web-browser (like Netscape or Mosaic) to interact with a Noos system from anywhere in the Internet. NoosWeb is a new concept of GUI that uses hypertext instead of windows. NoosWeb supports the same functionality as the Apple windowing interface with the advantage of being platform-independent and using an already familiar visualizer system. Since HTTP protocol is stateless and Noos interaction is session-oriented, NoosWeb keeps track of the user interactions to provide stateful computation without any need to modify HTTP protocol, server, client browser. NoosWeb's locator is <url:>.

2. New learning techniques

Although the focus of the project was on a framework for integrating multiple learning methods, there have also been results on developing new learning techniques. In particular the Noos framework currently is able to integrate learning methods based on analogy, induction and compilation. There have been new ML techniques developed in these three areas --we will presently explain them and later we'll explain some application systems that integrate implemented methods based of them.

2.1 Case-based reasoning

Similitude terms is new method for case retrieval in CBR based on a symbolic description of similitude --instead of the classical numerical measure. The basic notion here is antiunification (AU). The AU of two Noos descriptions is the MSG (most specific generalization) description that subsumes both. Intuitively, it captures all that is in common on two descriptions --those aspects in which they are similar and all of them. Thus the AU of the current problem and a case in CBR defines its similitude term. Using the subsumption ordering over similitude terms, we can induce a partial order over the cases in memory from more to less similar cases. Consequently, a CBR system can choose the most similar cases and also explain in what sense they are similar --since it has a symbolic account of similarity. The importance of similitudes is a second CBR technique we have developed in which an entropy-based measure is used to estimate the discrimination power of a similitude term. The set of cases in memory that are subsumed by a similitude term are distributed along a partition of solution classes, and measuring the set entropy we can assess if the aspects involved in the similitude are also discriminant with respect to the solution classes the system is dealing with. The main novelty of both techniques is that they allow to work with structured representations --while classical distance-based similarities can only be defined upon "flat" representations like attribute-value vectors. These two techniques are currently used in the CBR component of the SPIN application.

2.2 Inductive learning

INDIE is an inductive technique also based on AU. In the SPIN application INDIE has been used to build up a hierarchy of concepts to identify marine sponges. INDIE performs an heuristic search for MSG in a series of languages L1, L2, ..., Ln. First, INDIE computes from the examples in a class the MSG description D1 by AU in L1 (that allows only one disjunct). If the description is discriminant (does not subsume any counter example) the method has reached a solution. Otherwise, INDIE uses the heuristic based on the "López de Màntaras distance" to select the most discriminant attribute in D1, Then the examples are divided in k subsets according to which of the k values of D1 has each example. The method now has advanced to the Lk language where a disjunctive description of k disjuncts is allowed. INDIE computes then the MSG for each subset forming a disjunctive generalization for the concept. The process of checking whether these descriptions are discriminants (and moving if need be to a more expressive language Lk+j) is recursive until a discriminant description is found. Optionally, a post-processing method that generalizes the final MSG description to most discriminant generalizations can be applied. DISC is a second, related inductive technique. DISC computes a MGG (most general generalization) description that is discriminant. When a MGG is not discriminant it uses the same heuristic as INDIE to select the most discriminant attribute to be included in a specialized description. DISC works in a constrained language LAU such that only the attributes appearing in the AU of the examples of a concept are considered. When examples have different values for the selected attribute, they are split into subsets accordingly and a disjunction of MGG descriptions is computed. When the disjuncts in the description are discriminant the method stops, and otherwise recursively specializes the non-discriminant ones. The novelty of both techniques regard the way they exploit the properties of the structured representation of feature terms --while rule-based learning exploit the properties of clausal-form representations. The structure in feature terms help in pruning the search space in that when an attribute is elided by the technique all derived attributes can also be elided automatically (and vice versa: until an attribute is considered derived attributes need not be considered).

2.3 Compilative learning

Finally, we have developed PLEC, new analytical learning technique. PLEC is a form of compilative learning (like EBL, explanation-based learning) for learning to specialize and speed-up Noos methods. Because of the reflective capabilities of Noos, methods are also descriptions. Noos methods are composed of subtasks and submethods. PLEC can be seen as a process of generating new methods by unfolding existing Noos methods. The unfolding is biased to consider only those methods used in the subtasks in a particular problem --introspection is used to analyze the proof tree of that probelm. The result of PLEC is generating a new method that is a specialization of the existing one and is assured to solve that problem (and similar ones) more efficiently. The main process of PLEC is subtask elision: the methods used in the proof tree for every subtask are unfolded into the main body of the new method. The speed-up is achieved by pruning the search space: the original method allows alternative methods in subtask while the PLEC-generated method cuts off unused methods in the elided subtasks --only the successful method in each subtask is unfolded. The novelty of this technique lies in the development of an EBL-like technique --originally developed to learn rules-- to methods in an object-centered representation language.

3. Applications

Several applications have been developed during the project that integrate multistrategy learning and problem solving. CHROMA is an application that recommends how to use chromatographic techniques to purify proteins from tissues and cultures. CHROMA can learn to solve protein purification problems by induction and CBR. These two learning methods, and their corresponding problem solving methods are integrated by the reflective capabilities of Noos. A novelty of the system is the use of meta-level reasoning to decide, on a case-by-case basis whether a problem has to be attacked by one problem solving methods or another. It is shown empirically that this approach is better than the usual fixed sequencing of methods until one succeeds. SPIN is an application for identifying species, genus, and family of marine sponges. SPIN also integrates the INDIE inductive method and the similitude terms importance method for CBR. We have also implemented a non-linear planning system that learns from experience using CBR, and during this year the PLEC method, now tested classical EBL problems, will also be integrated.

The permanent location of this article is <url:>


Publications of the Analog Project

Most of these publications are available online. You may consult the
IIIA Publications and the catalog of IIIA Research Reports


Enric Plaza, Ramon López de Mántaras, and Eva Armengol On the Importance of Similitude: An Entropy-based Assessment. EWCBR-96 European Workshop on Case-based Reasoning. Lecture Notes in Artificial Intelligence (to be published), Springer Verlag.

Enric Plaza, Josep Lluís Arcos, and Francisco Martín. Cooperation Modes among Case-Based Reasoning Agents. ECAI-96 Workshop on Learning in DAI Systems.

J. L. Arcos, E. Plaza; Inference and reflection in the object-centered representation language Noos. Journal of Future Generation Computer Systems. Accepted for publication Elsevier Science Publ.

J. L. Arcos, E. Plaza; Reasoning abour preferences in a reflective framework. Research Report.

F. Esteva, L. Godo, R López de Màntaras, E. Plaza, Precedent-based Plausible Reasoning: A similarity-based model of case-based reasoning. Submitted.

B. López, E. Plaza (1995); Case-based learning of plans and goal states in medical diagnosis. Artificial Intelligence in Medicine Journal, Accepted for publication.

C. Sierra, L. Godo, R. López de Màntaras, M. Manzano, Descriptive Dynamic Logic and its application to reflective architectures. Journal of Future Generation Computer Systems. Accepted for publication Elsevier Science Publ.


E. Armengol, E. Plaza; Explanation-based Learning: A Knowledge Level Analysis. AI Review. Vol. 9, pp. 19-35. 1995 Kluwer Academic Publishers

J. L. Arcos, E. Plaza (1995); Reflection in Noos: An object-centered representation language for knowledge modelling. IJCAI'95 Workshop: On Reflection and Meta-Level Architecture and their Applications in AI. Montréal, Canada, August 21, 1995, pp. 1-10.

E. Plaza (1995); Cases as terms: A feature term approach to the structured representation of cases. Lecture Notes in Artficial Intelligence, n. 1010, pp. 265-276. Springer-Verlag, 1995.

E. Plaza (1995); Aprender con Inteligencia Artificial. Arbor, 595, pp. 119-154. CSIC, Julio 1995.

E. Armengol, E. Plaza (1995); Integrating induction in a Case-based Reasoner. Lecture Notes in Artificial Intelligence. n. 984, pp. 3-17, Springer-Verlag.


A. Aamodt, E. Plaza (1994), Case-Based Reasoning: Foundational Issues, Methodological Variations, and System Approaches. AI Communications, Vol. 7, n. 1, pp. 39-59. Ios Pres, March 1994

R. López de Mántaras (1994), Reasoning under Uncertainty and Learning in Knowledge Based Systems: Imitating Human Problem Solving Behavior. En: J.M. Zurada, R.J. Marks II, Ch. J. Robinson (eds.) Computational Intelligence Imitating Life. IEEE Press, New Yorl 1994, pp. 104-115.

E. Plaza, J.L. Arcos (1994) Flexible Integration of Multiple Learning Methods into a Problem Solving Architecture. Lecture Notes in Artificial Intelligence, n. 784. Springer-Verlag 1994, pp.403-406

E. Armengol, E, Plaza (1994), A Knowledge Level Model of Knowledge -Based Reasoning. Lecture Notes in Artificial Intelligence, n. 837. Springer-Verlag 1994, pp.53-64.

J.L. Arcos, E. Plaza (1994), A Reflective Architecture for Integrated Memory-Based Learning and Reasoning. Lecture Notes in Artificial Intelligence, n. 837. Springer-Verlag 1994, pp.289-300.

J.L. Arcos, E. Plaza (1994), Integration of Learning into a Knowledge modelling framework. Lecture Notes in Artificial Intelligence, n. 867. Springer-Verlag 1994, pp.355-373.

E. Armengol, E. Plaza (1994); Integrating induction in a case-based reasoner. Second European Workshop on Case-Based Reasoning. EWCBR-94. Chantilly, Francia 7-10 Nov. 1994. pp. 243-251.


E. Plaza, A Aamodt, A. Ram, W. van de Velde, M. van Someren (1993), Integrated Learning Architectures.En: Machine Learning: ECML-93. P.B. Brazdil, Ed. Lecture Notes in Artificial Intelligence n. 667. Springer-Verlag, pp. 429-441

E. Plaza, J.L. Arcos (1993), Using Reflection Principles in the Integration of Learning and Problem Solving. Proceedings of the ECML-93 Workshop on Integrated Learning Architectures. ILA-93. E. Plaza, Ed. Viena, Austria , Abril 1993

B. López, E. Plaza (1993), Case-based planning for medical diagnosis. In: Methodologies for Intelligent Systems ( J. Komorowski & Z.W. Ras, eds.). Lecture Notes in Artificial Intelligence. n. 689. Springer-Verlag, pp. 96-105.

B. López (1993), Reactive Planning through the integration of a case-base system and a rule-based system. Prospects for Artificial Intelligence. (A. Sloman et al., eds.), IOS Press, 1993, pp. 189-198.

E. Plaza, J.L. Arcos (1993), Reflection and Analogy in Memory-based Learning. MSL-93 Second International Workshop on Multistrategy Learning. Harpers Ferry, USA, Mayo 93, pp. 42-49.