the neuropsychological assessment of executive function is based on unsatisfactory experimental methods and clinical materials , even decades after the pioneering work by luria ( 1966 ) .
one of the major difficulties of executive assessment is the paradox that was smartly described by lezak ( 1995 ) : the clinician has to structure a more or less formal situation   in which patients can show whether and how well they make structure for themselves  ( p. 651 ) . many of the examination techniques ( strauss et al . , 2006 ) which are thought to be sensitive to executive , or frontal lobe , disorders ( wood and grafman , 2003 ; miller and cummings , 2007 ; banich , 2009 ; levine and craig , 2011 ; stuss , 2011 ) clearly allow the subject insufficient room toward self - induced problem structuring , decision making , and goal setting . yet , it is immediately evident that these processes are main components of executive behavior , as revealed by luria 's , lezak 's , and many others ' detailed descriptions of behavioral disturbances after frontal lobe damage .
the need for problem structuring is of particular importance in situations where executable behavioral and cognitive chunks are not readily available to the subject , or where their execution does not proximately lead to the aimed - for goal .
those situations enforce what freud had called probehandeln ( mental action sampling ) 100 years ago ( freud , 1911 ) .
following craig ( 1943 ) , if the organism carries a mental model of   external reality and its own possible actions within its head , it is able to try out various alternatives , conclude which is the best of them , react to future situations before they arise , utilize the knowledge of the past events in dealing with the present and the future , and in every day to react in a much fuller , safer , and more competent manner to the emergencies which face it  ( p. 61 ) .
some claims about the structure , the functionality , and the neuroanatomical distribution of mental models , including their potential relationships to frontal lobe damage , are presented below .
here , i develop the idea of hierarchically organized mental models which draws heavily on predictive coding theories of the perceptual system ( friston , 2002 ) . perception is considered as an active process of inference about underlying states of the world .
specifically , it is conjectured that perceptual analysis follows fundamentally an inversion purpose since it aims at retrieving the causes , i.e. , the parameters of the generative mechanism , from the effects , i.e. , the observed sensory data .
in other words , when observing a sensory phenomenon directed by any parameter  , perceptual analysis allows inducing from these observations inferences about  ( helmholtz , 1867 ) .
when the analysis generalizes over space and time , a prediction of future phenomena of similar nature becomes available , simply by exploiting the redundancy within the probability structure of  ( barlow , 2001 ) .
suppose a human observer is exposed to a rapidly changing environment where multiple states coexist ( either sequentially through time or simultaneously through space ) .
when confronted with this kind of fast - changing environments , the observer should ideally infer the state probabilities , implying that he or she represents the probability structure of the environment hierarchically . in order to do so
, he or she needs to learn a state hyper - parameter  , and to differentiate between state - specific parameters ( i.e. , 1 and 2 in the case of two coexisting states ; see figure 1 ) .
the capability to form such hierarchical generative models of fast - changing environments will greatly enhance the predictive performance of the observer .
the inferred probability structure of underlying states of the world is hierarchically represented , with  signifying a state hyper - parameter , 1 and 2 , denoting dissociable state - specific parameters ( just two levels of the hierarchy are drawn for illustration ) .
note that according to this analysis , inference , and prediction are operations on the same hierarchical data structure .
this view is compatible with predictive coding theories of cortical function ( friston , 2002 ) .
predictive coding theories posit that the perceptual system is structured as hierarchically organized generative models with increasingly more general nodes ( parameters ) at higher levels .
further , predictive coding theories propose that an internal representation of the world ( i.e. , the mental model ) generates predictions that are compared with stimulus - driven activity to calculate the residual error between the prediction and the sensory evidence . the residual error is then used to update the internal representation of the world so as to minimize the residual error imposed by future stimuli .
another implication of this analysis lies in the fact that the brain remembers the past to predict the future ( bar , 2011 ) .
the close relationship between experience and memory , as stored in mental models , on one hand and prediction and anticipation on the other is paralleled by the recently discovered fact that episodic memory and episodic future thinking share a common neural substrate in cerebral cortex ( schacter et al . , 2008 ) .
this led researchers to ask whether time in the brain is a one - directional variable , as psychologically experienced , or whether the brain is actually capable to travel back and forth through time ( suddendorf et al . , 2009 ) .
this analysis portrayed the perceptual system as being composed of hierarchically organized generative models . in
what follows i will conceptualize executive function , required to guide intentional behavior toward goals , as a hierarchically organized test - retest system , an idea which draws heavily on miller et al .
note that , while the analysis moves from the perceptual system to the executive system , it retains the idea of hierarchically organized mental models .
specifically , recursive activation of self - terminating operating units lies at the core of the suggested model of executive function .
frontal lobe damage often disrupts the patient 's capacity for intentional behavior , it leads in many cases to the appearance of stimulus - bound behavior and inflexible responding , and it sometimes limits the ability to initiate behavior at all ( duffy and campbell , 2001 ) .
the fundamental conjecture of this paper is that these behavioral syndromes which result from frontal lobe damage may be considered as observable effects of deficient mental models , as detailed below .
lashley ( 1951 ) had argued long ago that behavior is hierarchically structured , and miller et al .
, a tote unit would test a particular environmental state and , if a specified condition was not met , would execute a specific operation until the condition became true .
miller et al . ( 1960 ) suggested that all kinds of behavior are controlled by tote units and used the everyday example of hammering a nail .
( is the goal state achieved ? ) ] , an operation [ hammering ( and return to test ) ] , and an exit - operator [ to be executed if the goal state has been achieved ( see test - operator ) ] . crucially , the operation of a tote unit could be to select another tote unit , allowing for hierarchical structuring based on recursive processing ( corballis , 2011 ) , i.e. , by running a series of nested tote units .
details of the idea of recursive activation of self - terminating operating units are illustrated in figure 2 .
inspection of figure 2 reveals that mental models may be considered as hierarchical structures of self - terminating operating units , each capable of activating otherwise comparable units at sub - ordinate levels of the hierarchical structure ( botvinick , 2008 ; duncan , 2010a , b ) .
notice that the multiple - demand system framework ( duncan , 2010a , b ) provides partly similar accounts of the crucial features of internal models guiding sequential behavior in complex situations .
specifically , both views share the idea of hierarchically organized internal models ( see also miller et al . , 1960 ) .
the view which is presented here is oriented toward the manifold behavioral disturbances which usually follow frontal lobe lesions and which were shortly foreshadowed above , whereas duncan 's model ( duncan , 2010a , b ) is focused more on the neurocognitive mechanisms of complex problem solving and ( fluid ) intelligence .
illustration of a recursive mental tote model capable of controlling intentional behavior ( just two levels are drawn for illustration ) .
tote units are self - terminating operating units , each capable of activating otherwise comparable units at sub - ordinate levels of the hierarchical structure ( top - down arrows ) .
the exit - operator of the active tote unit passes control of operations to the super - ordinate tote unit ( bottom - up arrows ) , once the self - terminating condition is reached .
each tote unit is comprises three operators ( t , test ; o , operation ; e , exit ) .
activated test - operation - retest loops are running until the actual state matches the goal state .
the exit - operator is executed ( i.e. , e ( ) ) whenever the self - terminating condition is reached ( i.e. ,  = 0 ) , so that control of operations is passed to the super - ordinate unit .
only tote units at the lowest level of the hierarchical structure are capable of activating executable behavioral units , whereas units at the hyper - planes are solely capable of activating units at sub - ordinate levels of the hierarchical structure . in this example , a hyper - unit , labeled  , activates a unit at the lowest level of the hierarchical structure , labeled 1 , which in turn activates executable behavioral units ( solid arrows ) . in contrast , the connections between the un - activated unit 2 at the lowest level and executable behavioral units are not active ( dashed arrows ) . switching activation states
requires executing the exit - operator of unit 1 , once its self - terminating condition has been reached , i.e. , e(1 ) if 1 = 0 , and the activation of unit 2 by the hyper - unit . by way of this analysis , the current hypothesis of executive function offers a framework for understanding the effects of prefrontal lesions on behavioral performance in task switching paradigms ( robbins , 2007 ; shallice et al . , 2008 ; nyhus and barcel , 2009 ; kopp and wessel , 2011 ) .
the formation of such recursive mental tote models constitutes the cognitive basis for executive behavior , this being characterized by the constant occurrence of intentional , goal - directed , and well - organized units of behavior ( shallice , 1988 ) . the capability to model situations
hierarchically in one 's own mind and to achieve recursively derived goals of actions is a general purpose mechanism ( duncan , 2010a , b ) that can be applied to many seemingly different situations and with regard to a multitude of input and output modalities .
it gives the organism an adaptive advantage , specifically when confronted with the need to behave appropriately in complex and/or fast - changing environments ( e.g. , behrens et al .
duffy and campbell ( 2001 ) described three distinct prefrontal syndromes , the apathetic , disinhibited , and dysexecutive types , each associated with dysfunction in one of the three major prefrontal cortical regions ( i.e. , medial , orbital , and lateral , respectively ; see kouneiher et al .
, 2009 , as well as rushworth et al . , 2011 , for discussion of the behavioral functionality of these prefrontal regions ) . as a start , i present a scheme for representing these distinct behavioral syndromes of prefrontal dysfunction within the framework of recursive mental tote models .
the medial prefrontal syndrome is easiest to conceptualize . the common behavioral symptom of apathy , or in the most severe cases of akinetic mutism ,
could be viewed as resulting from a disconnection between otherwise intact recursive mental tote models and executable behavioral units ( see figure 3a ) .
consequently , patients with superior medial damage are usually slower on tasks that require speeded responses , a behavioral deficit which has been described as a failure of energization , that is , the process of initiating any response ( stuss , 2011 ) . since the structure of the recursive mental tote models is left intact , the failure of energization should present itself as a pure motivational deficit .
( a ) a potential lesion that might underlie the medial syndrome with predominantly apathetic symptoms .
note that the connections between both units at the lowest level of the hierarchical structure , 1 and 2 , and executable behavioral units are inactive ( dashed arrows ) .
( b ) a potential lesion that might underlie the orbital syndrome with predominantly disorganized symptoms . note that the connections between both units at the lowest level of the hierarchical structure , 1 and 2 , and executable behavioral units are active ( solid arrows ) .
( c ) potential lesions that might underlie the lateral syndrome with predominantly dysexecutive symptoms .
there are two putative lesion effects : first , they may impair the functionality of the exit - operators , as detailed in the text .
second , they may destroy units at any level of the hyper - planes ( this is solely adumbrated here by cancelling topmost arrows ) .
it should be noticed that the various types of lesion effects are not mutually exclusive .
they may occur together in one patient , in various degrees , depending on the nature , the locus , and the extension of his or her brain lesion ( duffy and campbell , 2001 ; stuss , 2011 ) .
disinhibited behavior is the cardinal feature of the orbital prefrontal syndrome which might express itself as increased distractibility on complex tasks and as environmental dependency in social situations ( lhermitte , 1986 ; lhermitte et al . , 1986 ; see fellows , 2011 , for a more recent conceptualization of the behavioral functionality of the orbitofrontal cortex ) .
in essence then , responding by these patients is stimulus - bound rather than guided by the recursive mental tote models ( see figure 3b ) .
thus , exogenously activated executable behavioral units may be carried out , without being activated by the endogenously structured system for controlling overt actions . by way of these direct routes from stimuli to actions , the recursive mental tote models loose their ability to exert control over behavior . the lateral prefrontal syndrome has always been the least tractable of all prefrontal syndromes , due to the complexities of the cognitive and behavioral disturbances that are characteristic for this syndrome . yet , within the framework which i presented above , the lateral syndrome starts to loose its chimeric character .
figure 3c illustrates the effects that lateral prefrontal lesions might have on the recursive mental tote models .
notice that primarily transitions from sub - ordinate to super - ordinate levels of the hierarchy became impossible in the lesioned model
. a brief look back to figure 2 reveals that these bottom - up transitions are produced by the exit - operators within the recursive mental tote models .
thus , the hypothesis states simply that lateral prefrontal lesions impair the exit - operators of the recursive mental tote models .
the impairment of bottom - up transitions might be brought into being by two dissociable processes .
first , lateral prefrontal lesions might impair the functionality of the exit - operators , rendering them unable to actually produce the required transitions .
second , lateral prefrontal lesions ( petrides , 2005 ) and also inferior medial prefrontal lesions ( ridderinkhof et al . , 2004 ) might impair state monitoring which is required for the decision whether or not a specified condition for self - termination has been met as a result of an elapsed operation of the unit , rendering it unable to actually self - terminate its activation . yet ,
in both cases , the lesioned model will produce inflexible responding and perseverative behavior , by leaving the organism unable to switch back and forth between units of the recursive mental tote models ( as detailed in the caption of figure 2 ) .
impaired exit - operators and impaired state monitoring render the behavior of patients with lateral prefrontal lesions perseverative , i.e. , they are expected to show a tendency to repeat previous actions over and over , albeit these are not appropriate any more .
there are three tote units , one at the higher level (  ) , representing the goal state of the problem at hand , and two at the lower ( 1 , 2 ) , representing subgoals .
if  passed control to 1 ( which , however , can not be exited any more , due to the effects of lateral prefrontal lesions ) , its assigned behavioral units will be repeatedly executed , whereas the solution to the problem at hand requires to pass control first to 1 and afterwards to 2 , via . in other words , these patients will appear stuck - in - set , unable ( a ) to flexibly adapt to actual requirements and ( b ) to solve problems smoothly .
whereas patients suffering from impaired exit - operators may be aware of the inappropriateness of their perseverative tendencies , patients suffering from impaired state monitoring may be characterized by a lack of awareness of their perseverative behavior , mainly because these patients should be generally unable to compare the results of actions with the intended goals .
however , there remains still another possibility how lateral prefrontal lesions might impair the functionality of recursive mental tote models .
instead of impairing exit - operators , these lesions may destroy units at super - ordinate levels of the hierarchically structured models ( as depicted in figure 3c ) .
an organism will have difficulty whenever it is confronted with problems that require contributions of the lesioned units for their solution . specifically ,
eminently novel , complex , and abstract problems may fall into this range of tasks ( goel , 2010 ) . apart from deficient problem solving skills , a general shift from abstract to more concrete attitudes for concept formation and reasoning may result from such structural lesions of recursive mental tote models , as for example evidenced by disturbed categorical performance on sorting tasks ( nyhus and barcel , 2009 ) .
finally , deficient decision making and planning for the long - term future ( damasio and anderson , 2003 ) may constitute another corollary of these structural lesions of recursive mental tote models .
further , fuster ( 2008 ) proposed in his influential book that the prefrontal cortex is organized hierarchically , such that control is supported in progressively rostral regions as decisions are made at more abstract levels ( see also koechlin et al . , 2003 ; badre , 2008 ; botvinick , 2008 ) .
consistent with the concept of hierarchically arrayed levels of control , recent neuroimaging studies have repeatedly demonstrated differences in functional activation along the rostro - caudal axis of lateral frontal cortex , ranging from lateral frontal polar cortex to premotor cortex , such that more anterior regions were associated with progressively more abstract action control ( badre et al . , 2009 , 2010 ) .
this body of neuroscientific knowledge may be reconciled with the current hypothesis by the assumption that the hyper - planes of the recursive mental tote models are hierarchically arrayed in the prefrontal cortex , such that progressively rostral regions support progressively higher levels .
first , a reduced output on fluency tasks , impaired organization and monitoring of material to be remembered , and of the subject 's own responses , are among the major cognitive deficits after frontal lobe damage ( milner and petrides , 1984 ) .
neuropsychological assessment of executive functioning should in the future more explicitly address the structuring of stimulus materials and behavioral responses in formal examinations , giving the subject sufficient room to think of the situations they are confronted with , thereby explicitly offering them the opportunity to establish mental models for themselves .
an appropriate conceptual as well as psychometric refinement of examination techniques would be most appreciated .
second , with the progress of those assessment instruments , new questions for empirical research could be posed .
there is a remarkable paucity of theoretical investigations into the elements of executive function in the neuropsychological literature ( but see hazy et al .
2009 ; bishara et al . , 2010 ; shallice and cooper , 2011 ) .
consequently , experimental methods and clinical materials suffer from the lack of theoretical understanding of executive function .
model - based approaches are needed in future studies of the cognitive neuropsychology of executive function . moving beyond traditional disciplinary boundaries
should be considered an initial step in the direction of getting formal with mental models , i.e. , the cognitive basis of executive function .
the author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest .
the author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest .
 executive function is traditionally conceptualized as a set of abilities required to guide behavior toward goals . here 
 , an integrated theoretical framework for executive function is developed which has its roots in the notion of hierarchical mental models . 
 further following duncan ( 2010a , b ) , executive function is construed as a hierarchical recursive system of test - operation - test - exit units ( miller et al . , 1960 ) . 
 importantly , it is shown that this framework can be used to model the main regional prefrontal syndromes , which are characterized by apathetic , disinhibited and dysexecutive cognition , and behavior , respectively . 
 implications of these considerations for the neuropsychological assessment of executive function are discussed . 
Prelude
The hierarchical structure of mental models
The behavioral functionality of mental models
Mental models and frontal lobe damage
Sequelae
Conflict of interest statement