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Dual logic and cerebral coordinates for reciprocal interaction in eye contact.

Lee RF - PLoS ONE (2015)

Bottom Line: Elucidated by dual logic deductions, the cerebral coordinate for reciprocal interaction suggests: the exogenous and endogenous systems consist of the empathy network and the mentalization network respectively; the default-mode network emerges from the resting state to activation in the endogenous system during reciprocal interaction; the cingulate plays an essential role in the emergence from the exogenous system to the endogenous system.Overall, the dual logic deductions are supported by the dfMRI experimental results and are consistent with current literature.Both the theoretical framework and experimental method set the stage to formally apply the scientific method in studying complex social interaction.

View Article: PubMed Central - PubMed

Affiliation: Princeton Neuroscience Institute, Princeton University, Princeton, New Jersey, United States of America.

ABSTRACT
In order to scientifically study the human brain's response to face-to-face social interaction, the scientific method itself needs to be reconsidered so that both quantitative observation and symbolic reasoning can be adapted to the situation where the observer is also observed. In light of the recent development of dyadic fMRI which can directly observe dyadic brain interacting in one MRI scanner, this paper aims to establish a new form of logic, dual logic, which provides a theoretical platform for deductive reasoning in a complementary dual system with emergence mechanism. Applying the dual logic in the dfMRI experimental design and data analysis, the exogenous and endogenous dual systems in the BOLD responses can be identified; the non-reciprocal responses in the dual system can be suppressed; a cerebral coordinate for reciprocal interaction can be generated. Elucidated by dual logic deductions, the cerebral coordinate for reciprocal interaction suggests: the exogenous and endogenous systems consist of the empathy network and the mentalization network respectively; the default-mode network emerges from the resting state to activation in the endogenous system during reciprocal interaction; the cingulate plays an essential role in the emergence from the exogenous system to the endogenous system. Overall, the dual logic deductions are supported by the dfMRI experimental results and are consistent with current literature. Both the theoretical framework and experimental method set the stage to formally apply the scientific method in studying complex social interaction.

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The transformation between the algebra and the logic.
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pone.0121791.g006: The transformation between the algebra and the logic.

Mentions: In the well-established abstract algebraic logic approach [38], a logic problem can be transformed to algebraic forms, and resolved with algebra, and transformed back to a logic solution. Given the dual system model in Fig 2, as well as the binary tasks (eyes open/closed) and responses (ON/OFF), the binary Boolean logic is mostly sufficient to formulate the dfMRI experiment in this study. Here the definition of the original Boolean logic is given as:B1 =  〈w f f; 0,  1;  ⊕, ∧, ¬〉.(A1)Here wff means well-formed formula. The truth-values are 1 for true and 0 for false. Although a two-value logic can have a total of 24 logic operations, all of them can be composed by a minimum set of operations ⊕, ∧, and ¬. The can be transformed to the Boolean algebraBr = Alg(B1) =  {F(x);x∈  [0, 1]b; +, *,  1+x}.(A2)Here, the Alg is the transformation from logic to algebra. The F(x) is the algebraic expression over variables x, and x has binary values 0 or 1. The logic operations ⊕, ∧, and ¬ coincide with the arithmetic operation +, *, and 1+x, meaning they have the same truth-table operation respectively. Note that addition (+) is performed modulo 2 here. As shown in Fig 6, the Br is a subset of a three-valued algebraCr=  {F(x);x∈ [1,  0,  −1]t;  +,  −, *,  1 + x}(A3)Here x has ternary values 1, 0, and -1. The arithmetic operation subtraction (-) is also performed modulo 2. Its corresponding logic operation (with the same truth-table operation, Table 4) is defined as collation with symbol ⊖. The logical meaning of 1 is true, 0 is false, and -1 is inconsistent. The practical explanation of the collation (β ⊖ α) can be described as α being the expectation value, β being the proprioception value. If the proprioception matches the expectations (either α = β = 0 or α = β = 1), then no action is needed (β ⊖ α = 0). However, if the proprioception comes as unexpected (α = 0, β = 1), then the proprioception will prompt action to address the unexpected (β ⊖ α = 1). More interestingly, if the expectation is there but the proprioception is not (α = 1, β = 0), then no proprioception can prompt action to address the unexpected, which results in inconsistency or “error” (β ⊖ α = −1).


Dual logic and cerebral coordinates for reciprocal interaction in eye contact.

Lee RF - PLoS ONE (2015)

The transformation between the algebra and the logic.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4401735&req=5

pone.0121791.g006: The transformation between the algebra and the logic.
Mentions: In the well-established abstract algebraic logic approach [38], a logic problem can be transformed to algebraic forms, and resolved with algebra, and transformed back to a logic solution. Given the dual system model in Fig 2, as well as the binary tasks (eyes open/closed) and responses (ON/OFF), the binary Boolean logic is mostly sufficient to formulate the dfMRI experiment in this study. Here the definition of the original Boolean logic is given as:B1 =  〈w f f; 0,  1;  ⊕, ∧, ¬〉.(A1)Here wff means well-formed formula. The truth-values are 1 for true and 0 for false. Although a two-value logic can have a total of 24 logic operations, all of them can be composed by a minimum set of operations ⊕, ∧, and ¬. The can be transformed to the Boolean algebraBr = Alg(B1) =  {F(x);x∈  [0, 1]b; +, *,  1+x}.(A2)Here, the Alg is the transformation from logic to algebra. The F(x) is the algebraic expression over variables x, and x has binary values 0 or 1. The logic operations ⊕, ∧, and ¬ coincide with the arithmetic operation +, *, and 1+x, meaning they have the same truth-table operation respectively. Note that addition (+) is performed modulo 2 here. As shown in Fig 6, the Br is a subset of a three-valued algebraCr=  {F(x);x∈ [1,  0,  −1]t;  +,  −, *,  1 + x}(A3)Here x has ternary values 1, 0, and -1. The arithmetic operation subtraction (-) is also performed modulo 2. Its corresponding logic operation (with the same truth-table operation, Table 4) is defined as collation with symbol ⊖. The logical meaning of 1 is true, 0 is false, and -1 is inconsistent. The practical explanation of the collation (β ⊖ α) can be described as α being the expectation value, β being the proprioception value. If the proprioception matches the expectations (either α = β = 0 or α = β = 1), then no action is needed (β ⊖ α = 0). However, if the proprioception comes as unexpected (α = 0, β = 1), then the proprioception will prompt action to address the unexpected (β ⊖ α = 1). More interestingly, if the expectation is there but the proprioception is not (α = 1, β = 0), then no proprioception can prompt action to address the unexpected, which results in inconsistency or “error” (β ⊖ α = −1).

Bottom Line: Elucidated by dual logic deductions, the cerebral coordinate for reciprocal interaction suggests: the exogenous and endogenous systems consist of the empathy network and the mentalization network respectively; the default-mode network emerges from the resting state to activation in the endogenous system during reciprocal interaction; the cingulate plays an essential role in the emergence from the exogenous system to the endogenous system.Overall, the dual logic deductions are supported by the dfMRI experimental results and are consistent with current literature.Both the theoretical framework and experimental method set the stage to formally apply the scientific method in studying complex social interaction.

View Article: PubMed Central - PubMed

Affiliation: Princeton Neuroscience Institute, Princeton University, Princeton, New Jersey, United States of America.

ABSTRACT
In order to scientifically study the human brain's response to face-to-face social interaction, the scientific method itself needs to be reconsidered so that both quantitative observation and symbolic reasoning can be adapted to the situation where the observer is also observed. In light of the recent development of dyadic fMRI which can directly observe dyadic brain interacting in one MRI scanner, this paper aims to establish a new form of logic, dual logic, which provides a theoretical platform for deductive reasoning in a complementary dual system with emergence mechanism. Applying the dual logic in the dfMRI experimental design and data analysis, the exogenous and endogenous dual systems in the BOLD responses can be identified; the non-reciprocal responses in the dual system can be suppressed; a cerebral coordinate for reciprocal interaction can be generated. Elucidated by dual logic deductions, the cerebral coordinate for reciprocal interaction suggests: the exogenous and endogenous systems consist of the empathy network and the mentalization network respectively; the default-mode network emerges from the resting state to activation in the endogenous system during reciprocal interaction; the cingulate plays an essential role in the emergence from the exogenous system to the endogenous system. Overall, the dual logic deductions are supported by the dfMRI experimental results and are consistent with current literature. Both the theoretical framework and experimental method set the stage to formally apply the scientific method in studying complex social interaction.

Show MeSH
Related in: MedlinePlus