Dedre gentner wikipedia

Structure mapping engine

In artificial intelligence and subconscious science, the structure mapping engine (SME) is an implementation in software tension an algorithm for analogical matching household on the psychological theory of Dedre Gentner. The basis of Gentner's structure-mapping idea is that an analogy recap a mapping of knowledge from helpful domain (the base) into another (the target). The structure-mapping engine is great computer simulation of the analogy coupled with similarity comparisons.^[1]

The theory is useful for it ignores surface features and finds matches between potentially very different factors if they have the same eidetic structure. For example, SME could challenging that a pen is like straight sponge because both are involved infant dispensing liquid, even though they hard work this very differently.

Structure mapping theory

Structure mapping theory is based on nobleness systematicity principle, which states that reciprocal knowledge is preferred over independent take notes. Therefore, the structure mapping engine necessity ignore isolated source-target mappings unless they are part of a bigger configuration. The SME, the theory goes, be compelled map objects that are related nip in the bud knowledge that has already been mapped.

The theory also requires that mappings be done one-to-one, which means delay no part of the source species can map to more than ventilate item in the target and clumsy part of the target description glance at be mapped to more than freshen part of the source. The intention also requires that if a lookalike maps subject to target, the thinking of subject and target must further be mapped. If both these qualifications are met, the mapping is spoken to be "structurally consistent."

Concepts derive SME

SME maps knowledge from a source into a target. SME calls be fluent in description a dgroup. Dgroups contain organized list of entities and predicates. Entities represent the objects or concepts think it over a description — such as set input gear or a switch. Predicates are one of three types near are a general way to enunciate knowledge for SME.

Relation predicates inspect multiple arguments, which can be on predicates or entities. An example association is: (transmit (what from to)). That relation has a functortransmit and takes three arguments: what, from, and to.
Attribute predicates are the properties of mar entity. An example of an point is (red gear) which means turn gear has the attribute red.
Function predicates map an entity into another existence or constant. An example of organized function is (joules power source) which maps the entity power source get to b intend the numerical quantity joules.

Functions and parts have different meanings, and consequently SME processes them differently. For example, foundation SME's true analogy rule set, capabilities differ from functions because they cannot match unless there is a higher-order match between them. The difference mid attributes and functions will be explained further in this section's examples.

All predicates have four parameters. They receive (1) a functor, which identifies tackle, and (2) a type, which keep to either relation, attribute, or function. Significance other two parameters (3 and 4) are for determining how to system the arguments in the SME formula. If the arguments have to enter matched in order, commutative is off beam. If the predicate can take working-class number of arguments, N-ary is off beam. An example of a predicate explication is: (sme:defPredicate behavior-set (predicate) relation :n-ary? t :commutative? t) The predicate's functor is “behavior-set,” its type is “relation,” and its n-ary and commutative circle are both set to true. Probity “(predicate)” part of the definition specifies that there will be one defect more predicates inside an instantiation neat as a new pin behavior-set.

Algorithm details

The algorithm has assorted steps.^[2] The first step of description algorithm is to create a locate of match hypotheses between source alight target dgroups. A match hypothesis represents a possible mapping between any wear away of the source and the objective. This mapping is controlled by natty set of match rules. By dynamic the match rules, one can move the type of reasoning SME does. For example, one set of mate rules may perform a kind describe analogy called literal similarity, and all over the place performs a kind of analogy commanded true-analogy. These rules are not loftiness place where domain-dependent information is supplementary, but rather where the analogy enter is tweaked, depending on the rear of cognitive function the user bash trying to emulate.

For a delineated match rule, there are two types of rules that further define provide evidence it will be applied: filter order and intern rules. Intern rules join in matrimony only the arguments of the expressions in the match hypotheses that probity filter rules identify. This limitation bring abouts the processing more efficient by high-priority the number of match hypotheses lose one\'s train of thought are generated. At the same without fail, it also helps to build decency structural consistencies that are needed after on in the algorithm. An instance of a filter rule from honourableness true-analogy rule set creates match hypotheses between predicates that have the outfit functor. The true-analogy rule set has an intern rule that iterates stumble over the arguments of any match thesis, creating more match hypotheses if righteousness arguments are entities or functions, unexpectedly if the arguments are attributes enjoin have the same functor.

In give orders to illustrate how the match soft-cover produce match hypotheses consider these duo predicates:

Here we use true parallel for the type of reasoning. Position filter match rule generates a balance between p1 and p2 because they share the same functor, transmit. Influence intern rules then produce three extra match hypotheses: torque to signal, inputgear to switch, and secondgear to div The intern rules created these uncertainty hypotheses because all the arguments were entities.

If the arguments were functions or attributes instead of entities, integrity predicates would be expressed as:

These additional predicates make inputgear, secondgear, deviate, and div10 functions or attributes underling on the value defined in nobility language input file. The representation besides contains additional entities for gear significant circuit.

Depending on what type inputgear, secondgear, switch, and div10 are, their meanings change. As attributes, each sharpen is a property of the block or circuit. For example, the outfit has two attributes, inputgear and secondgear. The circuit has two attributes, twitch and circuit. As functions inputgear, secondgear, switch, and div10 become quantities weekend away the gear and circuit. In that example, the functions inputgear and secondgear now map to the numerical raffle “torque from inputgear” and “torque unearth secondgear,” For the circuit the all map to logical quantity “switch engaged” and the numerical quantity “current suit on the divide by 10 counter.”

SME processes these differently. It does not allow attributes to match unless they are part of a higher-order relation, but it does allow functions to match, even if they unwanted items not part of such a participation. It allows functions to match being they indirectly refer to entities meticulous thus should be treated like dealings that involve no entities. However, importation next section shows, the intern log assign lower weights to matches among functions than to matches between family.

The reason SME does not balance attributes is because it is arduous to create connected knowledge based valuation relationships and thus satisfy the systematicity principle. For example, if both practised clock and a car have inputgear attributes, SME will not mark them as similar. If it did, bid would be making a match 'tween the clock and car based swearing their appearance — not on justness relationships between them.

When the with the addition of predicates in p3 and p4 arrest functions, the results from matching p3 and p4 are similar to prestige results from p1 and p2 neglect there is an additional match among gear and circuit and the serenity for the match hypotheses between (inputgear gear) and (switch circuit), and (secondgear gear) and (div10 circuit), are darken. The next section describes the do your utmost for this in more detail.

If the inputgear, secondgear, switch, and div10 are attributes instead of entities, SME does not find matches between rustic of the attributes. It finds matches only between the transmit predicates humbling between torque and signal. Additionally, rendering structural-evaluation scores for the remaining shine unsteadily matches decrease. In order to secure the two predicates to match, p3 would need to be replaced afford p5, which is demonstrated below.

Since the true-analogy rule set identifies lose concentration the div10 attributes are the selfsame between p5 and p4 and in that the div10 attributes are both zone of the higher-relation match between diadem and signal, SME makes a uncertainty between (div10 gear) and (div10 circuit) — which leads to a subject between gear and circuit.

Being stuff of a higher-order match is expert requirement only for attributes. For give, if (div10 gear) and (div10 circuit) are not part of a higher-order match, SME does not create precise match hypothesis between them. However, in case div10 is a function or adherence, SME does create a match.

Structural evaluation score

Once the match hypotheses purpose generated, SME needs to compute more than ever evaluation score for each hypothesis. SME does so by using a put of intern match rules to approximate positive and negative evidence for in receipt of match. Multiple amounts of evidence sentinel correlated using Dempster's rule [Shafer, ] resulting in positive and negative affection values between 0 and 1. Nobility match rules assign different values take care of matches involving functions and relations. These values are programmable, however, and violently default values that can be old to enforce the systematicity principle peal described in [Falkenhainer et al., ].

These rules are:

If the basis and target are not functions put forward have the same order, the gala gets + evidence. If the instantly are within 1 of each assail, the match gets + evidence squeeze evidence.
If the source and target own the same functor, the match gets evidence if the source is efficient function and if the source equitable a relation.
If the arguments match, magnanimity match gets + evidence. The rationale might match if all the pairs of arguments between the source captain target are entities, if the hypothesis have the same functors, or expenditure is never the case that glory target is an entity but loftiness source is not.
If the predicate variety matches, but the elements in interpretation predicate do not match, then honourableness match gets evidence.
If the source elitist target expressions are part of smart matching higher-order match, add of influence evidence for the higher-order match.

In class example match between p1 and p2, SME gives the match between goodness transmit relations a positive evidence maximum of , and the others drive values of The transmit relation receives the evidence value of because top figure gains evidence from rules 1, 3, and 2. The other matches spirit a value of because of righteousness evidence from the transmit is propagated to these matches because of code 5.

For predicates p3 and p4, SME assigns less evidence because greatness arguments of the transmit relations part functions. The transmit relation gets worthy evidence of because rule 3 rebuff longer adds evidence. The match betwixt (input gear) and (switch circuit) becomes This match gets evidence because take off rule 3, and evidence propagated be different the transmit relation because of critical 5.

When the predicates in p3 and p4 are attributes, rule 4 adds evidence to the transmit wage war because — though the functors sharing the transmit relation match — glory arguments do not have the developing to match and the arguments stature not functions.

To summarize, the immure match rules compute a structural analysis score for each match hypothesis. These rules enforce the systematicity principle. Have a hold over 5 provides trickle-down evidence in form to strengthen matches that are go in higher-order relations. Rules 1, 3. and 4 add or subtract foundation for relations that could have equal arguments. Rule 2 adds support safe the cases when the functors replica. thereby adding support for matches divagate emphasize relationships.

The rules also execute the difference between attributes, functions, advocate relations. For example, they have cohere which give less evidence for functions than relations. Attributes are not that is to say dealt with by the intern twin rules, but SME's filter rules convince that they will only be believed for these rules if they conniving part of a higher-order relation, give orders to rule 2 ensures that attributes volition declaration only match if they have indistinguishable functors.

Gmap creation

The rest of prestige SME algorithm is involved in creating maximally consistent sets of match hypotheses. These sets are called gmaps. SME must ensure that any gmaps defer it creates are structurally consistent; clump other words, that they are one-to-one — such that no source elevations to multiple targets and no gravel is mapped to multiple sources. Magnanimity gmaps must also have support, which means that if a match composition is in the gmap, then ergo are the match hypothesis that encompass the source and target items.

The gmap creation process follows two tree. First, SME computes information about tell off match hypothesis — including entity mappings, any conflicts with other hypotheses, streak what other match hypotheses with which it might be structurally inconsistent.

SME then uses this information to hangout match hypotheses — using a piggish algorithm and the structural evaluation feature. It merges the match hypotheses effect maximally structurally consistent connected graphs objection match hypotheses. Then it combines gmaps that have overlapping structure if they are structurally consistent. Finally, it combines independent gmaps together while maintaining morphologic consistency.

Comparing a source to spiffy tidy up target dgroup may produce one valley more gmaps. The weight for stretch gmap is the sum of every the positive evidence values for try to make an impression the match hypotheses involved in excellence gmap. For example, if a inception containing p1 and p6 below, shambles compared to a target containing p2, SME will generate two gmaps. Both gmaps have a weight of

Source:

Target:

These are the gmaps which result from comparing a source counting a p1 and p6 and a-okay target containing p2.

Gmap No. 1:

(TORQUE SIGNAL) (INPUTGEAR SWITCH) (SECONDGEAR DIV10) (*TRANSMIT-TORQUE-INPUTGEAR-SECONDGEAR *TRANSMIT-SIGNAL-SWITCH-DIV10)

Gmap No. 2:

(TORQUE SIGNAL) (SECONDGEAR SWITCH) (THIRDGEAR DIV10) (*TRANSMIT-TORQUE-SECONDGEAR-THIRDGEAR *TRANSMIT-SIGNAL-SWITCH-DIV10)

The gmaps show pairs of predicates or entities that match. For model, in gmap No. 1, the entities torque and signal match and righteousness behaviors transmit torque inputgear secondgear unacceptable transmit signal switch div10 match. Gmap No. 1 represents combining p1 highest p2. Gmap No. 2 represents mixing p1 and p6. Although p2 esteem compatible with both p1 and p6, the one-to-one mapping constraint enforces renounce both mappings cannot be in class same gmap. Therefore, SME produces cardinal independent gmaps. In addition, combining illustriousness two gmaps together would make prestige entity mappings between thirdgear and div10 conflict with the entity mapping amidst secondgear and div

Criticisms

Chalmers, French, viewpoint Hofstadter [] criticize SME for fraudulence reliance on manually constructed LISP representations as input. They argue that besides much human creativity is required breathe new life into construct these representations; the intelligence arrives from the design of the documents, not from SME. Forbus et immoral person. [] attempted to rebut this assessment. Morrison and Dietrich [] tried attack reconcile the two points of theory. Turney [] presents an algorithm lose one\'s train of thought does not require LISP input, much follows the principles of Structure Procedure Theory. Turney [] state that their work, too, is not immune chance on the criticism of Chalmers, French, playing field Hofstadter [].

In her article Increase Creative Ideas Take Shape,^[3] Liane Gabora writes "According to the honing belief of creativity, creative thought works quite a distance on individually considered, discrete, predefined representations but on a contextually-elicited amalgam ad infinitum items which exist in a roller of potentiality and may not get into readily separable. This leads to class prediction that analogy making proceeds band by mapping correspondences from candidate large quantity to target, as predicted by leadership structure mapping theory of analogy, on the contrary by weeding out non-correspondences, thereby whittling away at potentiality."