Information and processing from deductive mental models at dyslectics

Summary


Introduction


The lack of good definitions make dyslexia to an interesting and frustrating field of science.
Pegleg is a new contribution to look at eyemovement recordings and logical sentences. The background are that there are not only the eyemovements that are erratic among the dyslectics. Eyemovements implicates more factors like fex. decoding- and probelmsolving more strategies among dyslectics contra normal readers. Pegleg compares the two different reading models: the staircase- and the connective reading modelpattern.

The Language PegLeg


We shall consider a fragment of English called "PegLeg" consisting of the atomic sentences "Peg has a leg" and "Bob is a snob", together with the connectives "and", "or", "not". We also introduce the metalinguistic variables "p", "q" which range over sentences, "A" which range over connectives and "X", "Y" which range over models. Using brackets when necessary, we shall allow the same well-formed-formulas as the propositional calculus over the corresponding connectives. The semantics will however differ. In general, the interpretation of q will not be trith-value, but rather the operation of constructing one of its model. E.G. my interpretation of "peg has a leg" is the construction of a mental picture of Peg and her leg, my interpretation of "Bob is a snob" is the construction of a mental picture of the snobbish Bob. In other words, we have the semantical valuation:
"Peg has a leg":-construction of model of Peg having a leg. "Bob is a snob":- construction of Bob being a snob. "and":- operation of constructing a model embracing an arbitrary pair of models (X,Y). "or":- operation of constructing a model embracing at least one of a pair of models (X,Y). "not":-operation of constructig a model ruling uot an arbitrary model x. We also include an operation we call EVALUATE. Given a binary string "pAq" the evaluate is the operation of supplying (p,q) with a pair of models (X,Y) and feeding these models to the operation associated with "A". The evaluate of "Aq" is to supply q with a model X and apply the operation associated with "A" to X. In other words we sress that the semantical value of a sign is not a model of it, but rather the operation of constructing a model in a given context. The particualr model you get of a sentence depends on which you choose to construct when you evaluate. E.G. EVALUATE "Bob is a snob and Peg has a leg":- the mental picture of Bob snobbishly commenting on Peg's (wooden ) leg. EVALUATE"Not" (Bob is a snob and Peg has a leg)":-(a & b) In the latter case, the interpreatation of the sentence is to construct a paraphrase in propositional calculus. Sentence are made up of physical sign. The semantical value of a sign is an operation, an operation to be performed on objects of consciousness (unconsciousness?) like perception (inkblots) and vizualizations. Finally when you evaluate a sentence the machinery comes to life and hopefully spewes out a model. Thus we distinguish between three ontological levels: syntactical (physical signs), operational (mental acts) object (mental objects).

Reasoning in PegLeg


When the subject has mastered the semantics of PegLeg he is ready to reson about sentences. In general, the subject is presented with a list of sentences to evaluate. E.g. is this proposition contradictary? Peg has a leg and not: Peg has a leg. Does the first proposition imply the second? Peg has a leg and Bob is a snob. Bob is a snob. Are these propositions equivalent? Not:(Bob is a snob and Peg has a leg). (Not: Bob is a snob)or (not: Peg has a leg). The resolution of problems of this type consists in the evaluation of the sentences and comparison of their models in the obvious way. Succes depends upon systematic evaluation. An effective strategy is parametrization. This consists in singling out one or more atomic sentences as parameters, and substitue their negations whenever they occur. If evaluation of a sentence fails for all parametrizations, it is demmed contradictary. If evaluation succeed for all parametrization, the sentence is deemed tautological. If two sentences evaluates for a commen parametrization they are deemed non-contradictary. Etc.

Backmapping and Skolem-models


We say that a sentence is a Skolem-model (in honour to him) if evaluate p:-p. The notion is simple. A sentence, by the operational semantics of its component signs, is an instruction to construct models. These models are constructed out of elements of mind. If these elements comprise the image of the sentence itself, the sentence is a Skolem-model. The sentence thus enters two modes of representation; first, it represents certain operations to be carried out, next, it represents a structure upon which these operation is carried out. When a sentence becomes a Skolem-model, we say the backmapping occurs. This duality may be likened to the fifferent conceptions of meaning in Wittgenstein's "Tractatus and Investigations". In the former, a sentence is regarde as a picture or a diagram, of a state of affairs. Its meaning consists in its use. Hypothetically, backmapping occurs when the sentence is to complex for the subject to form an internal model. He then forms an external model by turning the sentence into a Skolem-model. Thus hypothetically, backmapping occurs when the subjects exceeds his capabilities for internal reasoning. Again hypothtically, if the threshold is reached without the possibility of backmapping, the current process of reasoning terminates.

Two models of reading


We have tried to look if there exsist a more systematic coordinated readingpattern. We have made an index for constructed sytematic patterns. In the traditional systematic or staircasepattern have dyslexics erratic reading pattern. The reader fixate and sweeps his eyes is dependent of the perceptual span. There is a saccade to the next fixation. If the reader looks back we have a regression. Erratic eyemovementpatterns gives a bad informationprocessing (Carpenter, 1991). But it depends if the staircase models is right.
Contributions with the staircase reading-pattern. 1. The eyes moves from word to word because of the lexical processing 2. This model needs a lot of attention 3. This informationprocessing provokes much noise (noise def.= erratic eyemovements which are not attached to a word with higher meaning E.G. the context is a noisefactor that ruins the informationprocessing.
The connective model is an alternative model for eyemovements. A linearlized automatic eyemovement reading pattern will be less effiancy because it will not select out the right information. The connective reading pattern means looking for logical operators to construct your own meaning. These patterns are not automatic. The ey-brain coordination will scan top-down to conceptualize meaning. The connectors brings the meaning out of the sentence because the connectordiagram runs the attention to meaning in the read text. This because the analytical sentence are diveded into to parts; function and argument. The function are the connectives and the argument all the other parts. Effiancy reading deletes the argument and looks for the connectors like a computermodel (E.G. if x,...then....y). Reading is in this case a part of boolian mathematics.

The connective model


1. The attention and eyemovement are preselected towards the connectors or logical operators 2. The visual perception has a noise killing filter. 3. The semantic decoding are serial. It means that connectives are logical operators that are intentionality towards a construction of meaning. E.G. if, if....,then..., and, or,...and not controls the reading patterns.
We wanted to test those models and made a classical between-matched experiment to match the experimental group (dyslectics) towards a normal group. The background for the experiment was to compare dyslectics and normal readers eyemovements. Part 1 of the experiment, the first hypothesis are replication of Pavlidis (1981a) and the continuing of Just and Carpenter (1980). There have never been a replication with such sensetive equipment. Part 2 of the experiement is a continuing of Johnson-Lairds mental models. Hypothesis 3 and 4 tries to make a new perspective where we see the reading process as an informationdeductive process-model. It means that there are some logical reading combinations that are better than randomized searching for logical expressions. The logical words if, if ...then, and , or and the negation not. The research subject will read different deductions which are increasing in complexity. Then we measure how often the subject look at logical connectors. Do we read as computers?
The main problem reconsidered was: Do dyslectics use the same reading techniques independent of the complexity what they are reading. Out of this problem we sat up different hypothesis to test the two samples. Ha1. There are no fixation- or regression-differences between dyslectics and normal readers when they are following a non-semantic point with their eyes. Ha2.There are no differences regarding to scanning behavior between dyslectics and normal readers. Ha3. The dyslectics look less at logical operator when they are trying to solve deductive problems. Ha4. There are differences between dyslectics and normal readers when they are trying to solve deductive problems where the normal reader have a better reading behavior and the dyslectics reader dont shift reading technique when the complexity increases.

Methods

Design

< br> PegLeg experiment used a posttest only noneqiuvalent peer control group design with predefined groups (Neale & Liebert, 1986) and looked at differences between the experiment- and the normal group. The independent variable was dyslexia. The dependent variables were eyemovements, reading of deductive problems, solving deductive problems and looking at logical operators. All the variable were on intervall level and normally distributed. There were also added some controlvariables from WMS-R and Ravens test.

Classification of the dyslectic reader


The dyslectic reader were classified from Carlsten & Langelands discrepancy reading skill test for high school (4. ed, 1987). Carlsten & Langelands discrepancy reading skill test takes the people that scores 1.5 SD below average and classify them as dyslectics readers.

Subjects


40 teenagers with normal etiology were studied. People with asthma, diabetes, visionproblems and epilepsy were excluded. The experimentgroup (n=20) had a mean age of 18,2 year and the controlgroup (n=20) with mean age 18,19 year. Both samples were selected from a mechanical high school. The samples were only boys with a range from 17 to 21 years.

Apparatus and stimuli


The program Orbital infra red scanning version 1.31 were installed on a IBM PC. PC with 486DX processor with 33 Mhz frequenz. The visual stimuli were presented on a computerscreen VGA 640 X 400 70Hz (Model MAG Technology CO. No:Mx17S, 1992). Horizontal and vertical eyemovements were recorded by means of OberII, a system based on Infrared reflection from the eye. There were produced different stimuli in both eyes. The stimuli text were produced using the «Nyström» language. There were used fixation frames to prevent artifacts from headmovements. Systeminstallations were: Measuring frequenz: 100HZ Frame frequenz: 350ms Sensitivity: < 5 degrees Measure rangable: 30 degrees horisontally and 20 degrees vertically Infrared density: 0.76mW/cm2 Stimulusmaterials For measuringing voluntary saccades there were used a white moving diode. Ober2 standard interface were used when defing balance, gain calibration and linearization. Horisontal saccades: Follow a horisontal moving spot with the eyes (Pavlidis, 1981a). Vertical sacades: Follow a vertical moving spot with the eyes. Smooth pursuit: Follow a ballistic moving target. Scanning: Scan after letters in a number matrise. Pegleg: Read and solve the deductive problem. WMS-R (Figur memory, verbal association and visual span) and Ravens matrisetest (IQ control)

Procedure


The subjects were instructed to wear a pair of infrared goggles and gaze at the computerscreen 580 mm in front of them. The subjects gazed at the computerscreen and the first tasks were exposed of 4 different stimuli. In the first task the subject were supposed to follow a horisontaly moving dot with the eyes. In the second task the subject were supposed to follow a verticaly moving dot with the eyes. In the third task the subject should follow a dot that moved with constant speed in the x and y axes. In the fourth task the subject were supposed to follow a ballistic moving dot in the x axes. These tasks took approximatley 3 min. Task situation 2. The letters were replaced with x`s, which were presented on the screen as words. The subjects were supposed to replace the x`s with real letters. After that the subject should scan after 2 letters hidden in a number matrise as soon as possible. Task situation 3. There were presented 9 different logical expressions with increasing complexity. The subject were supposed to tell if the sentences were true or false. This part of the task took 8 to 14 min. The subjects were later tested on WMS-R and Ravens matrisetest.

Results


There were no significantly difference between experiment and the control group when they looked and fixated at a nonsemantic sign ( T2(38) = .518, p = .476, Mse = 68,53 ). There were no significantly difference between experiment and the control group regarding to regressions at a nonsemantic sign ( T2(38) = .876, p = .355, Mse = 8,50 ). Scanning behavior in a matrise There were no significantly difference between experiment and the control group when they scanned after letters in a X-matrise ( T(38) = 1.42, p = .247 ). Numbers looking at a logical operator Looking at logical operators there were significantly differences between the groups, but only when the deductive problems were increasing in complexity. In the first logical problems there were no differences between the groups if the saw more on the logical operators ( F(1, 37) = 1.48, p = .232, Mse = 12,98 ). The difference between the group grew bigger when the problems increased in complexity. The control group saw significantly more on the logical operators regarding to modus ponens problemes ( F(1, 37) = 9.95, p = .003, Mse = 3,39 ), regarding to modus tollens problems ( F(1, 37) = 10.36, p = .003, Mse = 10,27 ) and when the modus tollens problems were presented with a wrong grammer ( F(1, 37) = 24.16, p = .000, Mse = 7,60 ). There were no covariate interactionseffects between Gfaktor and looking at the logical operators ( T(38) = .237, p = .388 ). Readingbehavior when trying to solve deductive problems There were no difference betwenn experiment- and control group reagarding to read simple logical expressions ( F(1, 37) = 2.06, p = .160, Mse = 0,0001 ). The difference were significantly when presenting a modus ponens problem ( F(1, 37) = 35.39, p = .000, Mse = 0,00028 ), regarding to the modus tollens problems ( F(1, 37) = 45.09, p = .000, Mse = 0,00006 ) and when the semantic notation were changed together with a logical expression the significant differences were a fact ( F(1, 37) = 116,93, p = .000, Mse = 0,00004 ). Solving deductive problems The relation between solving deductive problems and Gfaktor (Raven) were P = .362 (One tailed). There were differences between experiment and the control group regarding to the total score for solving the logical deductive problems ( T(38) = -4.7, p = .000 ). There were no differences between experiment and the control group regarding to the solving of Ravens matrisetest ( T(38) = .37, p = .439 ).

Discussion


The conclusion of the PegLeg experiment are that the controlgroup had better solving capacity of logical deductive problems than the experimentalgroup. The experimentgroup had less readingbehavior when they were going to read the diffucult deductive problems. They saw less at the logical operators/connectives than the controlgroup on all tests. There were no difference between experiment and the control group measured with fixations and regression when the subjects followed a moving dot. There were either no difference in scanningbehavior to look after different letters. The results from the PegLeg-experiment contributes hypothesis 1 that the dyslexics dont make more fixations and regressions when they follow a moving target. The results is opposite to Pavlidis (1981a, 1985). He claims that the dyslexics has more regressions and fixations. We used more sensetive eyemovementrecording equipment than Pavlidis and we can not conlude that the dyslexics do make more fixations and regression, this supports findings from Olson, Wise, Connors & Rack (1989). The reason we dont find anything is maybe because that to follow a basic target you dont have to use much cognitive operations. The results contributes hypothesis 2, there are no differences in scanningpatterns. E.G. there may be different scanning techniques but there were equal fixations and regressions in both groups. The critics against this task may be that there were to small digitframe that the subjects should scan over. If there were a bigger frame the dyslexics would have made more fixations and regressions. Taking the view of hypothesis 3 we notice that the average normale reader gazes more at logical operators then the dyslexic-group. The reason may be that for the dyslexics reader all written information is equal because of the word-to-word lexical processing. The dyslexcis cant differ between a logical operator and related words. It means that they read in a staircase pattern, are more unsure and process the sentences argument as the function. There may be some formal elements that are missing. The results from hypothesis 4 contributes that normal readers have a better reading behavior when reading complex logical deductive problems. The results induce that the dyslexic reader makes more fixations, more regressions and more saccades. The reason is because that normal readers use the connective model of reading when solving logical problems and the dyslexics use the staircasepattern and they cannot filter out the noise. Therefor we have the beginning staircasepattern among the dyslexic readers and because of the cannot locate the logical operators they fail. My view on the results implicates that the dyslexics has a more passive perception as written in Held & Richards (1972). This because the dyslexics has more cognitive lag than normal readers. E.G. that the eye-mind delay are not zero. This is against Just & Carpenters immediacy-hypothesis (1980). The conclusion from PegLeg are that linguistic processing does not happen at the fixationpoint.There may be a physiological eye-mind delay. The experimentalgroup has not problems with their eyemovements as Pavlidis said (1990). The behavior of the eye depence of the lexical processing from word to word. It is the step between signal to symbol where the dyslexics fails. If the reader does not understand the problem the insigtinformation stays out because the reader cant rerepresent the problem to his own language. E.G. the reader get stucked in his own Hoeffding step. Artifacts from the PegLeg experiment You dont have scientific control over the independet variable. Since we dont have the developmental history of the subjects it means that we cannot say anything bout a casual structure (Neale & Liebert, 1986). There is impossible to say anything about causality and dyslexia from an abductive point of view because the system is too complex (Catch 22). We cannot induce dyslexia in some subjects and the n after measure the manupulation of the independent variable. There are also more problems in this design do we measure dyslexia or ability to solve logical deductive problems. We wanted to measure the dyslectics reading behavior when the decoded the deductive information blocks. The dyslexia definition is not outstanding. There is a lack of a general dyslexiadefinition in the field of dyslexia research. You could choose between discrepancycriterias, multivariate definitions, exlusionprinciples. Carlsten & Langeland is a discrepancy definitions which not is solid but it takes a stand. Therefor we got the problems with the intelligens. We try to control it with the Ravens test but maybe it isnt enough. A sceptical person will claim that measuring of logical deductions will be controlled by the intelligence (Johnson-Laird, 1991). When there were no difference between the groups in Ravens test, there may be a conclusion that deductions also is a matter of reading as boolian mathematics. PegLeg may be the new standard to measure dyslexia. You could make diagnosis when measuring the eyemovements under reading of logical expressions. You could then easily control the subjects fixations/regressions with comparisons with a normated mean fixations or regressions. We need to standardise the fixations and regressions. PegLeg is a no-budget study. If we could choose samples after CT-scanning or other physiological test it would be a benefit for the dyslexia-research. The consequences of the artifacts may have been different if there were full control over the variables. The conclusion of the PegLeg experiment were that logical operators in the language may be a step between the neuron-signal to the language-symbol were the dyslectics fail. The dyslecitic reader doesnt understand the logical problems and the lack of insighti nformation means that the reader cannot rerepresent the mental model to his own language. The mental model fail and the dyslecitc reader get stucked in his own Höffding step.

APPENDIX


XXX.testen This is a X-matrise. Lettertype Times New Roman size 14. Pretend that the x`s are words. xxx xx x xxxxxx xxx xxxx xx xxxxxxx xx. xxx xx xxxxxxxxxx, x xxx xxx x xxxxx xxx xxxxxx xxxxx. x xxx xxxx xxx xxxxxxxxxxx xx xxx xxxx. xxxxxx xxxxxxx xxxxxxxxx, x xxxxxxxxxxxx xx xx xxxx. xxxxx xxxxxxxx xxxx xxxxxx xxx xxx xxxx xxx xxxx xx xx. Scanning This is the scanning task. The subject search for 2 letters in the number-matrise. Lettertype Courier New size 14. 1 2 3 4 5 5 5 5 4 5 6 7 7 8 8 6 5 4 3 3 2 3 4 5 6 7 9 9 8 9 7 6 5 3 5 6 5 6 7 4 5 3 1 3 x 4 5 6 7 5 4 3 8 9 6 2 4 5 3 4 x 1 3 3 4 5 1 3 5 4 6 4 3 2 2 5 6 3 6 3 7 8 7 6 3 5 1 5 9 5 8 5 2 2 8 9 5 3 4 5 2 4 5 2 4 PegLegexperiments deductiontasks. Lettertype Times Roman size 14 on the computerscreen.Task 1. 1. Are proposition 1 and 2 contradictory? 1. Per is at school. 2. Kari is at school. Task 2.2. Are proposition 1 and 2 contradictory?1. Per or Kari is at school.2. Per is at school. Task 3.3. Are proposition 1 and 2 contradictory?1. Kari is at school and Per is not at school.2. Per is at school.Task 4.4. Are proposition 1 and 2 contradictory?1. Kari is at school or Per is not at school.2. Per is at school. Task 5.5. Are proposition 1 and 2 contradictory?1. If Per is at school, then Kari is at school.2. Per is at school.Task 6.6. Is proposition 3 true if 1 and 2 are true?1. Kari is home or at school.2. Kari is not home.3. Kari is at school.Task 7.7. Are proposition 1 and 2 contradictory?1. If not Per is home then Kari is home.2. If not Kari is home then Per is home.Task 8.8. Is the following proposition true? Not both Per and Kari are at school, if Kari is at school then Per is at school.Task 9.9. Is the following proposition true? Per or Kari are at school, if not Per is at school, then Kari is at school.


REFERENCES


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