Survey of Analogy Reasoning


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Survey of Analogy Reasoning

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