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Survey of Analogy Reasoning

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  • 1. Survey on Analogical Reasoning 2009. 4. 21 Sang-Kyun Kim [email_address]
  • 2. Table of Contents
    • The Analogical Mind
    • Case-Based Reasoning
    • An analogy ontology for integrating analogical processing and first-principles reasoning
  • 3. The Analogical Mind
  • 4. Introduction
    • Analogy in Cognitive Science
      • Topic of analogy has a special place in the field of cognitive science
    • About 1980, several research projects in AI and psychology
      • Complex analogies in reasoning and learning
        • Cased-based reasoning (vs. Rule-based reasoning)
      • Gentner began working on mental model and analogy
        • Key similarities lie in the relations that hold within the domains rather than in features of individual objects
      • Holyoak investigated the role of analogy in complex cognitive tasks
        • Multiconstraint approach to analogy in which similarity, structural parallelism, and pragmatic factors interact to produce an interpretation
      • Others …
  • 5. Introduction
    • Model of analogical thinking
      • Depend on representations that can explicitly express relations
      • All models of analogy have been based on knowledge representations that express the internal structure of propositions, binding values to the arguments of predicates
    • Process of analogical thinking
      • One or more relevant analogs stored in long-term memory must be accessed
      • A familiar analog must be mapped to the target analog
      • The resulting mapping allows analogical inferences to be made about the target analog
      • These inferences need to be evaluated and possibly adapted to fit requirements of the target
      • After reasoning, learning can result in the generation of new instances
  • 6. Exploring Analogy in the Large
    • Structure-mapping theory
      • (Gentner 1983, 1989)
      • Account of comparison processes that is consistent with a growing body of psychological evidence
    • SME (Structure Mapping Engine)
      • (Falkenhainer, Forbus, and Gentner 1989; Forbus, Ferguson, and Gentner 1994)
      • Simulation of the comparison processes
      • SME operated in polynomial time and can also incrementally extend its mappings
  • 7. Exploring Analogy in the Large
    • Input of two structured propositional representations, base and target
      • Attributes : unary predicated indicating features
      • Relations : express connections between entities
      • Higher-order relations : express connections between relations
    • Given a base and target, SME computes a mapping
      • Each mapping contains a set of correspondences that align particular items in the base with items in the target
      • Candidate inferences : statements about the base that are hypothesized to hold in the target by these correspondences
  • 8. Exploring Analogy in the Large
    • MAC/FAC (Many Are Called/Few Are Chosen)
      • (Forbus, Gentner, and Law 1995)
      • Models similarity-based retrieval
      • MAC first uses a simple, nonstructural matcher to filter out a few promising candidates
      • FAC then evaluates these candidates more carefully using SME
        • Correspondences and candidate inferences that indicate how the reminded information may be relevant to the current situation
    • Scalability comes from the simplicity of MAC
  • 9. Integrating Memory and Reasoning in Analogy-Making
    • AMBR (Associative Memory-Based Reasoning)
      • (Kokinov 1988; Kokinov 1998)
      • A model of human reasoning in problem solving, unifying analogy, deduction, and induction
    • AMBR1
      • Integrate memory, mapping, and transfer and simulated analogy-making in a commonsense domain
        • Suppose you are in the forest and you want to heat some water, but you have only a knife, an ax, and a matchbox. You do not have a container of any kind. You can cut a vessel of wood, but it would burn in the fire. How can you heat the water in this wooden vessel?
      • Used in studying some interactions between memory (priming), perception (context effects), and reasoning (problem solving)
  • 10. Integrating Memory and Reasoning in Analogy-Making
    • AMBR2
      • Relies on emergent context-sensitive computations and implements in an even more decentralized way
      • Concepts and objects are represented in the same way as in AMBR1
  • 11. The STAR-2 Model for Mapping Hierarchically Structured Analogs
    • STAR (Structured Tensor Analogical Reasoning)
      • Halford et al. 1994
      • Neural net model
      • Designed to be consistent with human processing capacity limitations
    • Approaches for representation of propositions that comprise the base and target in neural net model
      • Synchronous oscillation model
      • Product operations such as circular convolution or tensor products
  • 12. Toward an Understanding of Analogy within a Biological Symbol System
    • LISA (Learning and Inference with Schemas and Analogies)
      • Hummel and Holyoak 1997; Holyoak and Hummel 2000
      • Neural net model
      • Integrated model of analogical access, mapping, inference, and learning
      • Consider capacity limits of human working memory
      • How complex analogies can be processed within a system with inherent constraints on the capacity of working memory
      • Biological symbol systems – knowledge representations that capture the symbolic nature of human cognition
  • 13. Case-Based Reasoning
  • 14. CBR in Context : The Present and Future
    • Knowledge source in CBR
      • Not generalized rules but a memory of stored cases recording specific prior episodes
    • Reasoning in CBR is based on remembering
      • New solutions are generated not by chaining, but by retrieving the most relevant cases from memory
    • Library of cases
      • Most important component of a case-based reasoning system
  • 15. What is a Case?
    • Definition
      • A case is a contextualized piece of knowledge representing an experience that teaches a lesson fundamental to achieving the goals of the reaoner
    • Content of Cases
      • Content
        • Problem/situation description : state of the world when the episode recorded in the case occurred
        • Solution : stated or derived solution to the problem
        • Outcome : resulting state of the world
      • Indexes
        • Combinations of its important descriptors
        • Ones that distinguish it from other cases
  • 16. A Sketch of the CBR Process
    • Case-based reasoning tasks
      • Interpretation (Interpretive CBR)
        • Use cases for criticism and justification
        • Use prior cases as reference points for classifying or characterizing new situations
        • Form a judgment about or classification of a new situation, by comparing and contrasting it with cases that have already been classified
      • Problem-solving (Problem-solving CBR)
        • Use cases to propose solutions
        • Use prior cases to suggest solutions that might apply to new circumstances
        • Apply a prior solution to generate the solution to a new problem
  • 17. The Process of CBR Retrieve Propose ballpark solution Adapt Justify Criticize Evaluate Store
  • 18. What is the Point of CBR
    • True CBR
      • Not abstract CBR or rule-based reasoning
      • Process of true CBR
        • Partial matching (selection)
          • Don’t find matching case
          • Find the cases that matches best
        • Adaptation (reasoning)
          • Don’t apply a case by filling in the details
          • Have to decide which details to throw away, which to replace, and which to keep
  • 19. Relationship to Analogical Reasoning
    • Analogical reasoning vs. CBR
      • CBR can be viewed as fundamentally analogical
      • There is no clear line between research “on analogy” and “on CBR”
      • Research on analogy
        • More concerned with abstract knowledge and structural similarity
        • Focus on analogical mapping
      • Research on CBR
        • More concerned with forming correspondences between specific episodes based on pragmatic considerations about the usefulness of the result
        • Focus on analogical mapping + related processes that occur both before and after mapping
  • 20. An analogy ontology for integrating analogical processing and first-principles reasoning
  • 21. Introduction
    • Understanding how to integrate analogical processing into AI systems seems crucial to creating more human-like reasoning system
      • Similarity plays at best a minor role in many AI systems
      • Most AI systems operate on a first-principles basis using rules or axioms plus logical inference
    • Few reasoning systems that include analogy tend to treat it as a method of last resort, something to use only when other forms of inference have failed
    • The exceptions are CBR systems, but
      • CBR use only minimal first-principles reasoning
      • Most CBR systems rely on feature-based descriptions that cannot match the expressive power of predicate calculus
  • 22. Introduction
    • Integrate analogical processing and first-principle reasoning
    • Key idea is to use Analogy ontology
      • Formal representation of the contents and results of analogical reasoning
      • Provide the glue between 1 st principles reasoning and analogical processing
      • Semantics is defined by structure-mapping theory
      • Simulation : SME and MAC/FAC
  • 23. Analogy Ontology
    • Cases
      • Functions (task constraints in analogical reasoning)
        • minimal-case-fn ?thing : all of the statements in the KB that directly mention ?thing, where ?thing can be any term
        • case-fn ?thing : union of (minimal-case-fn ?thing)
        • recursive-case-fn ?thing : union of case-fn applied to ?thing and to all of its subparts, recursively
    • Matches
    • Pragmatic constraints
    • Mappings
    • Correspondences
    • Candidate inferences
    • Similarities and differences
  • 24. Integrating 1 st principles and analogical reasoning
    • Analogy Ontology
      • Language for the entities and relationships of structure-mapping
    • Procedural attachment
      • Enforce the semantics of the analogy ontology
      • Two-way communication between the reasoning system and the attached software
    • Reasoning system -> analogy software
      • Recognize predicates with procedural attachments
      • Carry out the appropriate procedure when queries involving them are made
    • Analogy software -> reasoning system
      • Handled by using the reasoner’s query software from within the analogy subsystem
  • 25. Simple example
    • Goal : (match-between ?base ?target ?match)
    • When ?base and ?target are bound, this goal invokes SME to match the value of ?base against the value of ?target
    • When ?base is unbound, this goal invokes MAC/FAC
    • When ?target is unbound, the query is considered to be an error and the goal fails
    • If ?base and ?target are a non-atomic term, further reasoning is invoked to derive the contents of the case
    • Successful match-between query results in
      • Creation of a new term in the reasoning system to represent the match
      • ?match is bound to this new term as part of the bindings produced by the goal
      • New term is linked the analogical processing data structure to support future queries
      • Mappings associated with the match are reified as new terms in the reasoning system, with the appropriate mapping-of, best-mapping
      • Structural evaluation score information asserted
  • 26. References
    • Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science 7:155-170
    • Gentner, D. (1989). The mechanisms of analogical learning. In S. Vosniadou and A. Ortony, Eds., Similarity and analogical reasoning, pp.199-241. London: Cambridge University Press.
    • Falkenhainer, B., Forbus, K., and Gentner, D. (1989). The Structure-mapping engine: Algorithm and examples. Artificial Intelligence 41:1-63
    • Forbus, K., Ferguson, R., and Gentner, D. (1994). Incremental structure-mapping. Proceedings of the sixteenth annual conference of the Cognitive Science Society, pp.313-318
    • Forbus, K., Gentner, D., and Law, K. (1995). MAC/FAC: A model of similarity-based retrieval. Cognitive Science 19(2):141-205
  • 27. References
    • Kokinov, B. (1988). Associative memory-based reasoning: How to represent and retrieve cases. In T.O’Shea and V. Sgurev, Eds., Artificial intelligence III: Methodology, systems, applications, pp.51-58. Amsterdam: Elsevier.
    • Kokinov, B. (1998). Analogy is like cognition: Dynamic, emergent, and context-sensitive. In K. Holyoak, D. Gentner, and B. Kokinov, Eds., Advances in analogy research: Integration of theory and data from the cognitive, computational, and neural sciences, pp.96-105. Sofia: New Bulgarian University Press.
    • Halford, G.S., Wilson, W.H., Guo, J., Gayler, R.W., Wiles, J., and Stewart, J.E.M. (1994). Connectionist implications for processing capacity limitations in analogies. In K.J. Holyoak and J. Barnden, Eds., Advances in connectionist and neural computation theory, vol.2, Analogical connections, pp.363-415. Norwood, NJ: Ablex.
    • Hummel, J.E., and Holyoak, K.J. (1997). Distributed representations of structure: A theory of analogical access and mapping. Psychological Review 104: 427-466
    • Holyoak, K.J., and Hummel, J.E. (2000). The proper treatment of symbols in a connectionist architecture. In E. Dietrich and A. Markman, Eds., Cognitive dynamics: Conceptual change in humans and machines, pp.229-263. Mahwah, NJ: Erlbaum.
  • 28. References
    • Gentner, D., Holyoak, K.J., and Kokinov, B.N. (2001). The Analogical Mind: Perspectives from Cognitive Science. The MIT Press.
    • David B. Leake. (1996). Case-Based Reasoning, The MIT Press.
    • Kenneth D. Forbus, Thomas Mostek, and Ron Ferguson. An analogy ontology for integrating analogical processing and first-principles reasoning, Proc. of IAAI-02 (2002)