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Daily Research Report: Sunday, November 30, 2008
New Idea
I need a model of matching along with model of mapping. There should be a contest of matching between gestalts of different situations.
In the current implementation, the matching is done on two factors: (1) importance of gestalts and (2) similarity of gestalts. The first idea is based on the heuristic that most salient elements of a situation are mapped onto each other and the second says that, in order to draw an analogy, one should have at least some similarity between gestalts.
However, the details were not well founded so the system lacked a robust matching algorithm. Here I'll try to describe a better one in more details.
Firstly, the importance metric which is calculated during the combination of microelements should be based on a better algorithm. Current algorithm tries to calculate importance when a gestalt is made up of unit figures. Taken superficially this can work but does not. Instead of making this idea to work, the algorithm can calculate "gestalt-production importance" and "gestalt-matching importance" by different means. Because the first is used when combining elements to make gestalts but while this calculation, the algorithm may produce interesting numbers that halts the calculation. (The importance has an upper limit, when the algorithm reaches an important element, it ceases to work.) Second should be relative to other gestalts in a situation, and their positioning etc.
Secondly, the similarity between gestalts are calculated as element-wise similarity. This is not a well-founded approach. Because, for example:
P1P1P1
and
P1 P1 P1
which are described as Obj "P1" `Ex` 3 and Obj "P1" `Ey` 3 are very similar, although their parameters are not. A superficial comparison between these gestalts does not yield a similarity, but a comparison which maps `Ex` also to `Ey` element should be better. However, instead of making such parameter mappings, I'll devise a new similarity metric which compares not only parameters but also values. A 3 in any location of a gestalt description makes it similar to other gestalts which has 3 in them. Normally, a shared parameter value has more similarity points, though this may not be always forced.
Reading
The Time Course of Metaphor Comprehension Δ
Citation: Philip Wolff and Dedre Gentner, Proceedings of the fourteenth annual conference of the Cognitive Science Society, 1992, Hillsdale, NJ, Erlbaum
Key Ideas:
- Glucksberg and Keysar's Category-mapping model
- A map-first model of metaphors based on two basic observations: (1) There should be an intimate relation between metaphor and categorization and (2) the categories explain why metaphors are often directional. (A vacation is a doctor but not A doctor is a vacation)
Abstract in 5 Sentences: There are three types of models of analogy based metaphor comprehension; (1) matching (2) mapping and (3) matching-then-mapping. In matching models, commonalities of two representations are recognized by aligning their parts and structures. In mapping theories, processing begins by accessing or creating from the base term a higher-order category or abstraction which is then used to attribute properties to the target term. In matching-then-mapping theories, first an alignment is discovered between base and target then a mapping is tried to be established. Experiments show that map-first models' prediction that processing begins with base term's categorization found no evidence for novel metaphors, but it may apply well to stock metaphors.
Questions & Answers
- How can Category-mapping view be refined?
Though the paper does not make a detailed account of category-mapping model, its prediction that metaphors are began to be processed by categorization of the base element may be refined by allowing simultaneous categorization of both base and target. Then, instead of map-first view, we can propose a "categorize-first" view, which neither maps nor matches base and target. The base and target are classified first, then these are mapped. (Though I can't fully explain why will this make a difference from match-then-map models.)
Relevant References
Concept Formation by Incremental Analogical Reasoning and Debugging? Derivational Analogy: A Theory of Reconstructive Problem Solving and Expertise Acquisition? The Structure Mapping Engine: Algorithm and Examples? Viewing Metaphor as Analogy? Understanding Metaphorical Comparisons: Beyond Similarity? Abstraction-based Analogical Inference? Purpose-Directed Analogy? Computational Theory of Metaphor? Features of Similarity? Learning and Reasoning by Analogy?
Daily Research Report: Saturday, November 29, 2008
New Idea
Integrating Semantic Information to SITAR
Once the gestalts are created, we need to attach semantics to identified gestalts. In order to do this, we need to have "models" which represent "archetypes" of common ideas. For example, a "line" can be any gestalt where two or more elements are next to each other. However, a "dashed line" is not something like this. Hence there is also an analogy making between these archetypes and gestalts to classify them and assign meaning.
Programming
Reading
Analogy in Creative Writing Δ
Author: Kiran Pandey A Final Report for a Course in a university in India
Key Ideas:
Abstract in 5 Sentences: There are a total of six stages in analogy making; representation building, retrieval, mapping, transfer, evaluation, learning. SMT which defines an analogy as an application of a relational structure in another domain, accomplishes analogy making in three stages; (1) access, given a target situation retrieving a base situation; (2) mapping elements between base and target and (3) evaluating the quality of this match. ACME employs a connectionist approach to match base and target with semantic and pragmatic information taken into hand. Hofstadter and colleagues' HLP takes perception and analogy making inherently related and they use structures called (1) Slipnet as a means to represent LTM, (2) Workspace which is like a blackboard and (3) Coderack which has small functions to run on elements to model this in computer models.
Questions & Answers
- Which systems does the paper tell?
SME, ACME, HLP
- What did I learn from the paper in general?
Almost nothing, these are the things I already know. :)
Relevant References
All references are relevant, but I already read them.
Daily Research Report: Wednesday, November 26, 2008
New Idea
The analogy procedure has three different operations:
- sim
- finds similarity of two gestalts
- dif
- finds difference of two gestalts
- plus
- "adds" a gestalt to another one.
Sim finds the common denominator between two gestalts, for example, if
g1 = Obj "D1D2" `Mx` 2 g2 = Obj "D2D1" `Mx` 3
then g1 `sim` g2 gives
Obj "D_D_" `Mx` 2
since these are common across these elements.
For diff, an inverse operation takes place.
g1 `diff` g2
gives
Obj "_2_1" `Mx` 1
since pattern has these differences and x location is also different by one unit.
The `plus` operation, takes a gestalt and produces another one, like
g1 `plus` (Obj "_2_2" `Mx` 3)
gives
Obj "D2D2" `Mx` 5
as a result.
We can define analogy procedure like follows after these operations:
D = (A `sim` C) `plus` (A `diff` B)
where A, B and C are gestalt groups (situations.)
However, we can also add another twist to this by making sim, diff and plus returning a list of gestalt instead of a single gestalt. Then, we can provide different strategies for similarity, difference and addition for these.
Programming
Reading
Concepts and Consciousness Δ
Citation: Stephen Yablo, Philosophy and Phenomenological Research, Vol LIX, No. 2, June 1999
Key Ideas:
- zombie worlds
- Chalmers's idea, conceivable but impossible worlds.
- presentation of a zombie world
- an aspect of a zombie world, where, e.g. we attribute a single property to a world to understand whole implications
- primary intension
- |E|_1 = the set of worlds that, considered as actual, make E true
- secondary intension
- |E|_2 = the set fo worlds that, considred as counterfactual, E truly describes
Abstract in 5 Sentences: There can be a coherence constraint in existence of zombie worlds, where for example, hydrogen's inexistence leads to water's inexistence.
This paper has no direct relation with my research.
Daily Research Report: Sunday, November 23, 2008
Reading
A Theory of Rerepresentation in Analogical Mapping Δ
Authors: Jin Yan, Kenneth Forbus, Dedre Gentner
Keywords:
- SME
- Structure Mapping Engine, the analogy-making system based on Gentner's SMT
- tiered identicality
- identical relationships (e.g. above, below ...) are required in mapping, if this is not found a looser criteria may be used.
- minimal ascension
- see Analogical Interpretation in Context? for this.
- 1-to-1 constraint
- each item in the base matches at most one item in the target and vice versa
- parallel connectivity constraint
- if a correspondence between two statements is included in the mapping, then so must correspondences between its arguments
Abstract in 5 Sentences:
The are 4 types of rerepresentation opportunity which can be classified w.r.t. identicality constraint, 1-1 constraint and parallel connectivity constraint. These four are holes (roots are aligned, arguments are not), gulches (arguments are aligned, roots are not), rivals (violations of 1:1 constraint) and leftovers (kernels which cannot be mapped altogether). The (possibly endless) rerepresentation strategies are transformation (rewriting predicates with same order of arguments and identical relations), decomposition (writing only an aspect of predicates in identical terms), entity splitting (rewriting an entity with its different roles), entity collecting (combining multiple entities in a single one). Along with these task-independent factors are systematicity to have larger structures and high selectivity to aim tighter selection factors.
Questions & Answers
- Is the rerepresentation automatic?
No, the paper just furnishes general principles of rerepsentation. Principles are not automatically adoptable to computational rerepresentation.
- Is the process domain independent?
The process is domain independent, but rerepresentation task is domain-specific. The paper only suggests some criteria, though criticizes Copycat for being domain-specific, the idea behind this paper cannot be automated without a deep domain knowledge, hence shows how "domain-independent" SME is actually.
Relevant References
- Systematicity as a selection constraint in analogical mapping? by Clement & Gentner, 1991
- Integrating Structure and Meaning: A Distributed Model of Analogical Mapping? Eliasmith & Thagard, 2001
- Analogical Interpretation in Context? Falkenheiner, 1990
- The Structure Mapping Engine? Falkenheiner, Forbus & Gentner, 1986
- The Structure Mapping Engine, Algorithm and examples? Falkenheiner, Forbus & Gentner, 1989
- Exploring analogy in the large? Forbus, 2001
- Incremental Structure-Mapping? Forbus, Ferguson & Gentner, 1994
- An analogy ontology for integrating analogical processing and first-principles reasoning? Forbus, Mostek & Ferguson
- Subtlety of Sameness? French, 1995
- Structure-mapping: A theoretical framework for analogy? Gentner, 1983
- Analogical Reasoning and conceptual change: A case study of Johannes Kepler? Gentner, Brem, Ferguson, Levidow, Wolff, & Forbus (1997)
- The Copycat project: A model of mental fluidity and analogy-making? Hofstadter & Mitchell, 1994
- Analogical mapping by constraint satisfaction? Holyoak & Thagard, 1989
- LISA: A computational model of analogical inference and schema induction? Hummel & Holyoak, 1997
- Incremental analogising: Theory & Model? Keane, 1990
- Case-based reasoning? Kolodner, 1994
- Comparison and categorization in the development of relational similarity? Kotovsky & Gentner, 1996
- Case-Based Reasoning: Experiences, Lessons and Future Directions? Leake, 1996
- Dynamic case creation and expansion for analogical reasoning? Mostek, Forbus & Meverden, 2000
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