and Rasmanathan (1982). With respect to R&D e x p e n d i ture, two interesting questions emerge. The first question is what the behaviour of the growth path of the economy would be in an integrated consumption, production, investment and R&D system, in particular when the system is facing capacity limits in terms of congestion, other d i s economies of scale, or depletion of exhaustible resources. Secondly, the introduction of spatial considerations generates a non-trivial dimension in that new technology in any region may be obtained by R&D internally, or by acquisition from external sources. In the latter case, the boost to productivity may be delayed and less effective since the adopted technology is not likely to be 'custom-made*. The question arises t h e r e fore what the optimal balance should be between adopting technology from external technology-leaders, and generating technology by means of own R&D expenditure.

In this paper we shall explore these questions by means of a multiregional dynamic (discrete-time) model. It will be shown that the system can generate a wide range of dynamic behaviour, including -for certain parameters -the dynamic evolutions occurring in models of population biology (notably the so-called May type of models, see e.g. Ma y (1976)).

. It is well-known that the periodic or chaotic behaviour of a May model is the result of specification of the 1.

Introduction

model in difference equation form (see e.g. [START_REF] Barentsen | Modelling Non-Linear Processes in Time and Space[END_REF], but it will be shown that the model developed here generates bounded non-linear dynamics even in differential equation form. Finally, the steering possibilities of the system (e.g. by means op optimized control) will be touched upon.

A Prototype Model for Economic Dynamics

In this section a simple prototype model for economic development will be formulated and presented stepwise. We commence with the assu m p tion that each of the regional economies under consideration is operating under the following production function regime (in difference equation f o r m ) :

where Y is actual production (or output) during the period (t, t + 1 ) , K ^ L the installed capital stock at the beginning of period t, and f a timedependent (i.e., varying in parameters) production function.

For the sake of simplicity, we will for the moment assume a simple production technology, i.e., where c is a technological coefficient representing average capital productivity during the period (t-l,t). However, this assumption is not as restrictive as it seems, since in a sense we may consider (2.2) an identity in which includes all factors which influence capital productivity. Thus, rather than making the a priori assumption that the elasticity of substitution between capital and other production factors is zero, we shall show below that the time trajectory of c can Incor porate both movements along the production frontier as well as shifts in this frontier.

With respect to capital accumulation, the following equation holds:

( 2 . 1)

(2 .2 )

(2.3)
where I stands for gross investment during period (t,t+l) and 6 is the rate of physical depreciation of the capital stock. We assume the f o l lowing simple investment function for capital expansion (or widening):

, (2.A)
where < 7^ is the fixed average savings rate. Clearly, this relationship takes for granted the existence of equilibrium between savings and c a p i tal increase. Assuming a given, savings behaviour, it is evident that a ^ acts as one of the driving forces or key parameters of our dynamic s y s tem.

It is now easily seen from (2.2) that if any growth rate is exx Y pressed as: g t -^t + l * ^t ^* t ' t*ie 8rowt^ rate of income (i.e., g fc) is (approximately) equal to the sum of the growth rate of capital (i.e., K € 6 t ) and the growth rate of capital productivity (i.e., g fc) :

Y K ^ f g t -g t + g t (2.5)
and that -by means of (2.3) and (2.4) -we find that 6 t ' (ai V 5) + 6 t ( 2 -6)

The latter relationship implies the obvious result that -in case of a negligible change in the production technology in period (t,t+l), i.e. f # Y g t-0 -the growth in income g t would be equal to the savings rate a times the capital coefficient (i.e. Harrod's conventional warranted growth rate) minus the rate of capital depreciation.

Since we have taken for granted period-by-period macroeconomic e q u i librium with respect to investment and savings, it follows that

st -gt -gc -<Vt -«

(2 . 9 )

Naturally, the case of a variable propensity to save violates (2.9); this will be considered later in Annex A, where the savings rate will be regarded as a control variable in an optimal control model.

Having presented now the basic elements of a simple growth model, we will introduce in the next section in a more detailed way the causes and consequences of changes in capital productivity. Consequently, the production function has to be adjusted, as R&D invest ments will imply a growth in efficiency due to a change in the capital coefficient (see [START_REF] Baumol | Feedback Models: R&D Information, and Productivity Growth, Communication and Information E c o n o m i c s[END_REF][START_REF] Mansfield | Industrial Research and Technological I n novation[END_REF][START_REF] Nelson | Research and Productivity Growth and Productivity D i f f e r ences[END_REF]. Naturally, the limits to growth themselves may be shifting, so that Yŵ ill increase with time and, as bottlenecks are overcome, further R&D expenditure may again have a positive effect on productivity. We may therefore assume the following specification for an adjusted (i.e., time-dependent) R&D impact parameter:

This relationship is depicted in Figure 1. It is clear that an analogous result might be reached by imposing a saturation level for c^.

In our case, it is easily seen that not only would R&D expenditure plausible to assume that becomes less when output increases, which

-max {i/* (1-Yt/Y®>. 0) (3.6)

V t V 0 Y t t
Figure 1. Decreasing marginal benefits of R&D expenditures.

fo become ineffective if output expands beyond , but it may also be e x pected that congestion and other external diseconomies set in which reduce capital productivity. In a broader framework, it may also be plausible to assume that the notion of a limited system capacity also refers to increasing labour scarcity along the growth path, which would tend to lead to substitution of capital for labour in response to higher real wages. Capital accumulation would therefore proceed, resulting in an increase in capital intensity (or a reduction in capital productivity).

The previous remarks suggest that we may replace (3.1) by the following simple relationship:

A € t " »'t R t -"t Y t (^ •1 * )
in which measures the congestion etc. effects on productivity when c output exceeds Y and, thus:

--- Kt+i

-(1-5) K t + aj_ «t K t (3.8) ft+1 " £t + i02>/* max (1 'Y t/ Y t ,0)' (3.9) -/ max (Yt/Y^ -1,0)] £(; K t Y t+ 1 " et+ l K t+ 1 (3-10) Y t4l " f <Y t> (3.11)
From (3.11) it can be seen that the time-trajectory of Y^ is considered exogenous to the system under consideration. However, instead of an autonomous trajectory of Y^ (e.g., based on a fixed technological progress leading to a permanent upward shift of the system's bottlenecks), it might also be possible to relate this upward shift of Q Y t to the average change in the production efficiency parameter in p r e vious periods. The linkages between the variables in the stock-flow system are depicted graphically in Figure 2. [START_REF] Brouwer | Qualitative Structure Analysis of Complex Systems, Measuring the Unmeasurable[END_REF][START_REF] Goh | Feasibility and Stability in Randomly Assembled Lotka-Volterra Models[END_REF][START_REF] Jeffries | Stability Nolistic Ecosystem Models, Theoretical Systems Ecology[END_REF][START_REF] Parker | Environmental Periodicity and Ecosystem Stability[END_REF]Pimm, 1982).

In par-^_ ticular, if n K > 2.57, such a May-type of model may exhibit wild fluctuations [START_REF] May | Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles and Chaos[END_REF]. For further discussions on the May model in the context of chaos theory, the reader is referred to Nijkamp and Reggiani (1988b). would remain non-negative), we would expect the system to converge to

«(t) 1 £ (0 ) = c > Y ★ - -71 Kt
the zero growth state, with (c, K) -(6/<i^t o ^ Y°/6) being a node type of singular point (e.g., Gandolfo, 1980, pp. 428-459). Further e x p o s i tions on the existence of such steady state points in an optimal control framework can be found in Figure Al Figure 3 shows that growth in the system is under these conditions initially accelerating, but the growth rate of capital productivity reaches a maximum at t-25 and subsequently declines until Y^ reaches the capacity level Y^ at t-37. At this point, the growth rate of capital accumulation reaches a maximum. Beyond t-37, Y will remain above Y ^ but will converge to the latter. Consequently, capital productivity becomes constant at a rate of (n+6)/o^-0.15 and capital and output grow at a steady state rate of 1 percent.

%

Figure 3. Growth converging to a steady state.

Legend: 1 : growth in capital productivity 2 : capital growth rate 3 : income growth rate

In figure 4 all parameters are the same as in Figure 1, but /i has been increased to five times its former value. Consequently, the c o n g e s tion and other diseconomies effects are now sufficiently strong to push at times below Y^ s o that growth cycles are generated with a variable periodicity but with decreasing amplitude. The system eventually c o n verges again to a steady-state growth of 1 percent. Thus far we have focussed exclusively on the dynamic properties of an economic growth system in isolation. In the next section we shall consider the consequences of allowing for spatial interaction in the form of diffusion and adoption of new technology generated by R&D in a multiregional system. It will be shown that such a system can generate growth patterns which have no tendency to converge to a steady state, even if the parameters are chosen such that the regions in isolation would do so.

It must be emphasized that the cyclical behaviour in

1 Tin» Figure 5. Simulation with a differential equation structure.

4• A Mu]tiregional Dynamic Model

In a system of regions, technology transfers from any one region would exert an impact on the R&D efficiency of other regions (see also [START_REF] Kamien | Market Structure and Innovations[END_REF][START_REF] Brouwer | Qualitative Structure Analysis of Complex Systems, Measuring the Unmeasurable[END_REF][START_REF] Scherer | Industrial Market Structure and Economic Performance[END_REF]. Such i n terregional spill-over phenomena may be taken into account by introducing a certain spatial R&D transfer function, which incorporates spill-over effects from R&D investments in other regions upon the regional production efficiency. However, as in the single region case, the effect of R&D on productivity would depend on how close the level of production is to the capacity level at which applications of the new technology have been exhausted and bottlenecks and other constraints prevent further increases in productivity. When capital accumulation generates output beyond this capacity level, productivity declines as a result of diminishing returns, congestion and other diseconomies e f fects.

Denoting regions by an index r (r-1,2,.. ,R), the process of spatial diffusion and adoption of technology described by

R . r r i ^ ir /i V r ™ cr n\ 1 V 1 £t+l " £t + " max (1'Y t/Yt >0) a 2 Y t 1=1 -/ max ( Y ^r -1,0) Y* (4.1) r-1,2 .... R i r in which v
represents the marginal efficiency of R&D expenditure in region i when the technology is adopted by region r. It is obvious that the dynamic behaviour of the system depends crucially on the R&D d i f f u sion and adoption matrix:

11 1R v . . . 1/ N - Rl RR v . . . v (4.2)
Naturally, the model discussed in the previous section is a special case in which N is a diagonal matrix and spatial linkages are absent. Using that for r -1,2,...,R, equation (4.1) can be w r i t ten in matrix form as

1 £t+l 1 ft 1 R £t+l R £t + max ( l -e ^/ Y ^. O ) 0- 0 -0 max (1-c^K^/Y^R ,0) 1 *2 1 £t n t • R a 2 R ' t < r a a x i c ^/ Y ^-l . O ) « ^(4.4) R / R VR ^c R - 1 1 M max( t ^ K t/ Y t -1 . 0 ) * Qualitatively,
the spatial interaction between regions in system (4.4) is characterised by a positive feedback l o o p : R&D expenditure in any one region leads to higher growth in other regions, which -in turn -boost R&D expenditure in those regions, giving a further impulse to growth in the original region. Thus, given a 'pooling' model for i n t e r regional technology transfer, a new evolutionary pattern of regional growth may emerge. However, the presence of capacity constraints implies that the system can again exhibit the great many types of dynamic b e haviour of the May m o d e l .

It can be easily verified that (eT , K r ) -(({r+nr )/a.r , a Y CC/6r ) cr is, as in the single region case, a singular point, when Y grows at a rate of nr (r-1,2,...,R).

However, stability of this steady state is extremely unlikely, in p a r ticular when the system consists of a mixture of large and small regions, with varying capacity growth rates n time trajectories would be common.

In that case, explosive

These results can again be illustrated by means of simulation. We shall consider here one case-study of three regions with one 9 l a r g e 9 region (K^-2000) and two 9 small' ones (K^--500). In all other o o o respects (initial technology, savings propensities etc.) the regions are identical. The technology adoption matrix N is given by: N = 0.001 0.0005 0 0.0001 0.001 0.0001 0.0001 0.0001 0.001

Hence region 3 does not adopt technology from region 1, while region c r 2 readily adopts this technology. It is also assumed that Y q -1000 for r -1,2,3 and grows at 1 percent per period. For simulation, (4.4) was replaced by its differential equation equivalent and the Runge-Kutta method was used for integration. Figure 6 shows that under these c o n d i tions regions 1 and 2 converge to a steady-state growth process, in which capital productivity is constant and output (and capital) grows at the 'natural' rate of 1 percent. In contrast, region 3 remains behind in production efficiency until t«25, but subsequently 'overtakes' both other regions. Moreover, while there is a tendency for productivity to come close to its steady-state value, at that stage persisting cycles eme rg e.

Differences in the growth paths between the three regions suggest that even if consumption per capita would be identical initially, this would not remain so due to differences in R&D expenditure and investment between regions. This can be seen from figure 7. It has b e e n assumed that populations are such that initially consumption per capita is equal across regions. Population growth in all regions is assumed to be 1 percent per period. Consumption per capita in regions 1 and 2 settles down at steady-state values (but at a much higher level for the latter).

However, consumption per capita reaches an even higher level in region 3, but this level cannot be sustained. In terms of the trade-off between consumption and investment d i s cussed in section 1, the question arises whether region 2 w o uld be able to reach the same (or even higher) levels of welfare with solely impo r t ing new technology rather than developing such technology itself (i.e. This can be seen from Figure 8.

Comparing Figures 7 and8, several conclusions emerge. First, the absence of any R&D expenditure in region 2 has -as expected -no impact on region 1, which is the 'technology' leader which reaches the capacity constraint the fastest. Secondly, without its own R&D expenditure, region 2 takes longer to maximize consumption per capita, but its steady-state level of consumption per capita is ultimately somewhat higher. formulation may then be desirable (see [START_REF] Kendrick | Control Theory with Applications to Economics, Handbook of Mathematical Economics[END_REF], and Nijkamp and Reggiani, 1988a, 1988b). Such a constrained dynamic optimization might then in principle prevent the variety of chaotic fluctuations inherent in the nonlinear dynamics of an interdependent multiregional growth system. The formal treatment of such an optimal control model is given in Annex A, in which the assumption is made that each region tries to maximize (the net present value of) an overall welfare function b y means of a proper choice of the savings rates for both capital investments and R&D investments.

Concluding Remarks

It follows immediately from (A12) that -U ce /?t(i.e.t the discounted marginal utility at time t). From (A12) and (A13) we see that A^ -Ag/y (i.e. the discounted marginal utility at time t per unit of the r e s p o n siveness of productivity to R&D expenditure).

Following Dorfman (1969), equation (All) shows that the loss to society that would be incurred if the acquisition of a unit of capital were postponed for a short time, is equal to the sum of the c o n t r i b u tions of that unit of capital to, firstly, the present value of welfare;

secondly, the change in productivity, and, thirdly, the change in the capital stock itself. Similarly, the loss to society of postponing productivity, growth for a short time is equal to the sum of the c o n tributions of such an increment in productivity to the present value of welfare, the change in productivity itself and the effect, on capital accumulation.

In the very simple case in which U(c) -C, we find U c - Equations ( A16) and (A17) are two non-linear equations in the two variables o ^ and o^. Since both equations can be divided b y the solution is independent of the choice of a discount rate p. However, the solution would depend on the value of Y°. Hence, the values of and a 2 would tend to vary over time (see also Nijkamp and Reggiani, 1988a). In the general case, the solution to the differential equation system (A10-A15) in the variables t, K, a and *2 w o uld not appear analytically tractable. Then simulation runs would have to be made to examine the possibility of stable trajectories.

  and (3.6) into (3.1) and recalling (2.2) and (2.3), the motion in the system can be described by the following set of n o n linear difference equations:

Figure 2 .

 2 Figure 2. A representation of the simple growth model.

  in Annex A. c Moreover, simulation experiments show that when is no longer constant, but increases at a constant rate n per period, this growth rate becomes the 'natural' growth rate of the system. In this case, average capital productivity settles at a value of (n+6)/a^ and output and capital will grow at rate n, with Y being identical to Y . Starting c with Yo <Yq , the time it takes to reach the capacity constraint decreases when either the investment ratio (a^), or the R&D propensity (cTj)» or the R&D effectiveness (^*) increases, but increases when the growth rate of Yis larger. Naturally, when output exceeds the capacity of the system, productivity will decrease the faster, the stronger the conges-* tion effect /i . These results are illustrated by means of Figures3-5. Figure3is based on the assumption that K^-1000 and the capital-output ratio equals 5, so that c^-0.2 and Y^-200. The saving ratio is 20 percent, 2 percent of the capital stock becomes obsolete each period and 2 percent of i n come is spent on R&D. Hence, a,-0-0.001. Since 5o 2v -/i , the productivity response is five times as c c elastic when ^t> Y t when Y t<Y^, and of opposite sign. Clearly, the Q evolution of Y^ might in principle differ for each region.

  Figure 4. Growth cycles generated by strong external diseconomies.

  Generally, we would expect the off-diagonal elements of N to be n o n negative with larger values for transmission between contiguous rather than non-contiguous regions. This may be reflected by a is a constant and d.^ measures the distance (or cost) of diffusion of technology from i to r.

  Figure 6. Capital productivity growth in a multiregional system with technology transfers Legend: 1: region 1 2: region 2 3: region 3

  answer is, for the parameter values chosen here, affirmative.

Figure 8 .FigureFigure 10 .

 810 Figure 8. Consumption per capita in a multi-regional system with one technology-follower

  1 and Aje p t , while -e pt/v. If, in addition, we restrict ourselves to the steady-state growth path with K and Y growing at rate n, we recall that € -(n+6)/cr^. Equations (A10) and (All) now become:

				YC
	s a l -o r ^) -	e	-Pt . -pt + e	Y C a1°2 r ' 6	-pt . 2e °1 a2 72 + 2 Y°U 6 '
	■pt	° \	2 Y^ 6	p e ' pt v			(A16)
	and
	/1	1 2	\ (n+S) -pt . -pt -e + e	" 2	(n+5)	■ e	-pt " °la 2 ,n+£x^ . 2 -s ~ +
	e',,t (n+S) • S e ' pl: -pe'pt			(A17)

In this Annex we will analyze the implications of introducing the savings rates o ^ and o^ as control parameter in an adjusted optimal control version of the model from sections 3 and 4.

Let capital accumulation be given by: where I is gross investment and a is the rate of depreciation. The in* vestment function is again equal to: with Y being output; R&D expenditure is also proportioned to output, i.e.:

where E measures the adoption of externally generated innovations. * However, v is not constant. The closer Y -<K gets to a capacity level capital productivity can even decrease as a result of congestion and other external diseconomies effects. Ve assume here the following simple relationship:

The effect of R on capital productivity e -Y/K is given by: *

Combining ( 1) -( 5), we get the equations of motion for e and K:

Hence, here the classical Ramsey-type optimal control problem arises in which 0^ and <72 are to be chosen such that the present value of w e l fare of the system is maximized.

Let p be the proper discount rate and U(.) an appropriate welfare function. This function is assumed quasi-concave, as usual, to ensure that the second-order conditions are fulfilled.

The optimal control problem can now be formulated as follows: The Hamiltonian related to (A8) is (see e.g. Miller (1979, p .


Roman Klinger
email: klinger@scai.fraunhofer.de

Philipp Senger
email: senger@scai.fraunhofer.de

Sumit Madan
email: madan@scai.fraunhofer.de

Michal Jacovi
email: jacovi@il.ibm.com

Online Communities Support Policy-Making: The Need for Data Analysis

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Decision-making processes for policies and their outcomes are often based on their perception and acceptance in the general public. An approach to gain a more representative opinion for a focused theme as well as to acquaint the public with the topic and present it from several perspectives, is to build a platform in which a policy maker (e. g. a member of government) solicits contributions from the public for a specific topic. The core functionalities expected from such a framework are: structured polls, moderated debates, and the ability to provide access from as many social media sites as possible. Structured polls should support questions with multiple choice or free text answers. Moderated debates should allow the public to provide more detailed feedback while also being exposed to others' thoughts, enabling decision makers to learn about aspects and perceptions not thought of before. In order to gain access to many participants, the framework needs to provide access to people in social media like Facebook, Blogger, Twitter, and others. 3As these social media are very well inhibited, polls or debate questions can lead to a huge number of contributions. A decision maker cannot be expected to consume all comments, and thus the framework also needs to provide support for efficient sifting through long debates. The need and a proposal for such framework, including several methods, are described in this paper. We focus on the analysis of textual data in debates.

Following is Sect. 1.1, in which we briefly cover related work. Sect. 1.2 then describes an implementation of a framework for policy-making support in online communities. The fundamentals as well as the combination of methods to support a decision maker by increasing the use of harvested data are presented in Sect. 2. Results are explained by means of a use case in Sect. 3, and a summary is given in Sect. 4.

Related Work

The analysis of weblogs (blogs) is a topic currently heavily investigated. As an example, the EU project SynC3 [18] is aiming at structuring the information of personal blogs to combine them with news information. The application BlogPulse [START_REF] Glance | Blogpulse: Automated trend discovery for weblogs[END_REF] was developed to discover trends in a set of 100,000 weblogs. The output are key person names, phrases, and paragraphs. Qiazhu Mei et al.

focused on the extraction of spatio-temporal data together with subtopics [START_REF] Mei | A probabilistic approach to spatiotemporal theme pattern mining on weblogs[END_REF]. Monitoring the development in blogs is described by [START_REF] Nanno | Automatically collecting, monitoring, and mining japanese weblogs[END_REF]. They cover technical issues like website extraction and cleaning as well. The important challenge of analyzing trends of opinions and sentiments is addressed by [START_REF] Pang | Opinion mining and sentiment analysis[END_REF]. Teufl et al. proposed a clustering and graph-based framework [START_REF] Teufl | Automated analysis of e-participation data by utilizing associative networks, spreading activation and unsupervised learning[END_REF] to limit the need for manual analysis. Maragoudakis et al. [START_REF] Maragoudakis | A review of opinion mining methods for analyzing citizens' contributions in public policy debate[END_REF] reviewed different opinion mining methods and developed a framework to use them. The impact of social media to elections (especially in the Netherlands) is proven by [START_REF] Effing | Social media and political participation: Are facebook, twitter and youtube democratizing our political systems?[END_REF]. The way how members of parliaments use Twitter for online discussions is investigated by [START_REF] Saebø | Understanding twitter use among parliament representatives: A genre analysis[END_REF].

Next to this work, some governments already have online platforms to get into contact with the population. An example is the platform ePetition4 in Germany allowing for signing a petition which forces the government to discuss the topic at a specific number of signatures. For each petition, a discussion forum is available as well. In Greece, the platform OpenGov5 allows for discussion of current laws in development. Research in these fields is often concerned with methods from the area of information extraction and natural language processing. A short overview of such approaches can be found in [START_REF] Mccallum | Information extraction: Distilling structured data from unstructured text[END_REF].

Policy-making Support in Online Communities

The EC project +Spaces 6 (dubbed positive spaces) aims at developing a workflow to allow policy and decision makers to interact with the inhabitants of virtual spaces [START_REF] Tserpes | +spaces: Intelligent virtual spaces for egovernment[END_REF]. As presented in Fig. 1, a government officer accesses the platform through a single front end. She can e. g. assemble a poll consisting of several questions, each with several answer possibilities and/or a free text field. Another possibility is to initiate a discussion and provide an initial statement for that. While polls have the focus on getting feedback for a 'closed' question, the second possibility allows for learning about novel ideas and insights a government officer may not have thought of.

After designing the poll or debate statement (what we call experiment), the experiment is deployed to the virtual spaces using the middleware and the connected management layer. +Spaces is focusing on Facebook, Blogger, Twitter, and Open Wonderland7 . The latter is an open source 3D world environment with similarities to Second Life8 but the advantage of being deployable on selfadministered servers and connectability due to source code availability.

Inhabitants of these worlds, namely people registered to Blogger, Twitter, or Facebook, can then participate in these experiments. Announcements are designed in a way such that viral dissemination is supported which is common in Facebook through 'sharing' and in Twitter through 're-tweeting'. This fact is supported by the numbers of participants of a pilot for poll experiments in 2011. Here, 77 participants made 473 contributions in different virtual spaces, 56 participants were recruited virally.

Through a notification mechanism, the data generated by the participants are propagated by the middleware to services to provide an analysis to the policy maker. Services as well as connectors to virtual spaces are modular and can be extended anytime. Figure 1 shows that one of the services developed in the +Spaces project is the proposed data analysis presented in this paper.

Our hypothesis is that such a way to prepare and present data, focusing on textual debates in this contribution, can support a policy maker by saving time and in getting an overview of the data. The fundamental idea is that by means of sentiments as well as main topics, debate contributions typically repeat themselves throughout a discussion-such characteristics need to be determined and shown to the user. In the following Sect. 2, the fundamentals of such methods and our adaptions are explained.

Methods

In the following, the methods for the analysis of semi-structured debates from online communities are described. They are designed to prepare the support of a policy maker.

Topic Modeling

The fundamental idea of modeling the topics of a debate is to present the main themes which are occurring. Additionally, the main words describing a topic are extracted. We follow two different strategies here, a k-means clustering [START_REF] Mackay | Information Theory, Inference and Learning Algorithms, chap. 20[END_REF] followed by an extraction of most important phrases; and alternatively a joint approach using latent Dirichlet allocation (LDA) [START_REF] Blei | Latent dirichlet allocation[END_REF]. The implementations from the Mallet toolkit [START_REF] Mccallum | MALLET: A Machine Learning for Language Toolkit[END_REF] are used.

Typically for topic modeling, n grams or single tokens are used as input. To support a good understanding of the textual context, we are using noun phrases instead or optionally in addition. To limit the dimensionality, each token is previously transformed to its stem 9 . Stop-words are removed as well as URLs, email addresses, and numbers.

k-means Clustering

The clustering method k-means [START_REF] Mackay | Information Theory, Inference and Learning Algorithms, chap. 20[END_REF] is an iterative approach to assign instances d i (0 ≤ i < n, with number of instances n) to a given number k (k ∈ N >0 ) of clusters. All instances in one cluster should have a high similarity with respect to some metric m(d q , d r ). Each instance is correponding with a debate contribution in our case.

In short, the Voronoi iterations to find k clusters work as follows: Randomly, the instances d i are assigned to k clusters. With respect to the metric m, the cluster centers are computed. Then, each instance is assigned to the closest cluster center, followed by re-computation of the cluster centers. This iterative algorithm stops when the clusters are stable or after a specified number of iterations.

The cosine similarity measure on the tf•idf-weighted term vector space is used as metric m here. Each instance is represented by a vector of weights w l for the occurring tokens in the lth instance. The weight w k,l for the kth token in the lth instance is w k,l = tf k,l • idf k , where tf k,l is the frequency of the kth token (term frequency) in the lth instance normalized by the frequency of the most frequent term in that instance, which is a local measure. The global measure inverse document frequency is the logarithm of the number of instances by the number of instances with the kth term [START_REF] Baeza-Yates | Modern Information Retrieval[END_REF].

The cosine similarity measure m(d q , d r ) := wq•wr |wq|•|wr| is the degree between two instances d q and d r with weight vectors w q and w r in that vector space [START_REF] Baeza-Yates | Modern Information Retrieval[END_REF]. To detect the most important terms representing all instances in each of the k clusters, we use the highest ranked terms with respect to tf•idf. Note that these tf•idf values are not the same as in the clustering: In contrast to measuring the similarity of contributions, similarities of clusters are taken into account here. Therefore, all terms in one cluster are handled equivalently and 0 ≤ l < k.

Latent Dirichlet Allocation

The basic idea of latent Dirichlet allocation is that instances are represented as random mixtures over latent topics, where each topic is characterized by a distribution over terms [START_REF] Blei | Latent dirichlet allocation[END_REF]. Again, we allow to use stemmed noun phrases. LDA combines the two steps of clustering and extraction of keywords presented in the previous section in a joint fashion. As all documents are assigned to several topics, we report the most probable topic only. The values of the parameters of the LDA implementation in the Mallet toolkit are adapted as described by [START_REF] Steyvers | Latent Semantic Analysis: A Road to Meaning, chap. Probabilistic topic models[END_REF].

Sentiment Analysis

Sentiment analysis is the assignment of an expressed sentiment to a text fragment. Typically, the classes positive and negative, and neutral are used [START_REF] Esuli | Determining term subjectivity and term orientation for opinion mining[END_REF][START_REF] Hu | Mining and summarizing customer reviews[END_REF][START_REF] Kim | Determining the sentiment of opinions[END_REF]. Most systems incorporate dictionary-based features; in the most straight-forward case, string matching with word lists with positive and negative connotation. An example for such system incorporating dictionaries next to other methods applied on online debate data has been presented by [START_REF] Somasundaran | Recognizing stances in ideological on-line debates[END_REF].

We apply a dictionary-based approach using the word lists of 6859 words (4818 negative, 2041 positive) provided by Hu and Liu 10 [7]. Let D + be the set of

d i ) is sent(d i ) = k s ik , where s ik = 1 if t ik ∈ D + and s ik = -1 if t ik ∈ D -.
As described in Sect. 2.1, the contributions are clustered into topics of similar content to provide the user with an overview what the debate is about. To enhance that with the associated sentiment, we assign the sentiment score of the documents of topic T i by sent(T i ) = 1 |Ti| di∈Ti sent(d i ), where 1 |Ti| is a normalization factor. The combination of sentiments for LDA could have been implemented by taking the probabilities of tokens representing a specific topic into account as well. A drawback would be the limited transparency of the approach to the user.

Concepts of User Interaction

In Sect. 2.1 and 2.2, the methods to support a user in analyzing a textual debate for a specific theme have been introduced and explained. The results of these analyzes need to be shown to a reader or decision maker in an intuitive way. We implemented a web service based on a relational database harvesting the necessary data. This database acts as a temporary storage of the clustering results and updates the content in real time when a new debate contribution is included. Figure 2 shows a schematic overview of the web-based interface, divided into two main sections: The header of the page (a) acts as a common part for automatic summarization of the debate and the possibility to parametrize topic modeling and the sentiment analysis. The lower part is divided into the graph view (b) and the textual view (c) onto the debate.

An introduction of the debate content is given by a tag cloud of the main phrases in the debate and a depiction of demographic data of the participants. The selection of methods and parameters presented in Sections 2.1 and 2.2 is user-specified. In the graph view section (Fig. 2(b)), a graph consisting of vertexes v i for each cluster T i and directed edges e j = (v k , v l ) is shown. Such edge is introduced if and only if ∃d m ∈ T k and ∃d n ∈ T l such that d m and d n are directly succeeding in the debate thread. A weight denoting the number of succeeding contribution pairs is additionally attached to that edge. In that way, the graphical depiction summarized the linear structure of the thread by means of topics. It makes loops in contributions of same topic or between different topics clearly observable. An example of a debate thread together with its graph view is shown in Fig. 3. Here, topic T 1 as well as T 2 consist of three contributions, while two are answering without changing the topic. The contribution with topic T 3 is leading back to T 1 , while there is only one transition between all different clusters of topics.

The textual view (Fig. 2(c)) consists of two different sections. Firstly, the found topics are presented together with additional information, i. e. the top words describing the topic of the cluster, the number of debate contributions |T i | in the ith topic and a normalized sentiment score sent(T i ). The second subsection of the textual view consists of the annotated text itself. The information added to the text is the annotation of words associated with a sentiment, the sentiment score of each contribution and a highlighting of the topic-distinguishing words of each cluster.

This view needs to be highly interactive by means of different filtering possibilities: The user can select a topic to limit the shown debate distribution to those in the topic. Additionally, it needs to be possible to show only contributions associated with a positive or negative sentiment or to filter the contributions by a specific word, be it freely specified or selected from the tag cloud.

Results and Discussion

Experimental Setup

As described in Sect. 1.2, one aspect of the +Spaces project is to create a platform for civil servants and policy makers which provides an easy to use and clearly arranged graphical user interface for practical usage within a political context. To reach this goal, an example debate has been annotated in cooperation with the policy makers for analyzing the usefulness of the presented approaches.

A debate about the current Greek financial crisis was selected [21] and annotated by two members of a focus group. This group has the function to evaluate and discuss the results coming from the +Spaces consortium and the members have a strong political background. The chosen political debate has a length of 39 contributions coming from 24 different participants. The total number of words in this debate is 3994, the average contribution length is 102, the standard deviation is 90.

The task of the annotators was to underline the most important terms, as well as to assign a sentiment. For simplicity, one of three sentiment classes (positive, negative, neutral ) were attached to each contribution. This task turned out to be complex for the special case of political debates; the inter-annotator agreement determined via Cohen's kappa [START_REF] Cohen | Weighted kappa: Nominal scale agreement provision for scaled disagreement or partial credit[END_REF] for the sentiment annotation is not substantial.

Header Section

The top part of the graphical user interface contains a tag cloud providing a first overview of the debate's content (cf. Fig. 4). The main tags (size is coupled logarithmically to frequency) show that the content of the debate is a political discussion concerning Greece and Greek people, the government and taxes. The tag "debt" provides an indication that the debate is about a financial topic.

Textual View Results

Figure 5 exemplifies the structured results of LDA applied to the debate introduced in Sect. 3.1. Each row in the table corresponds to a detected topic. The first column allows the user for filtering the debate contributions only showing the ones from the specified topic. The third and main column shows representative words and phrases together with the color used to highlight them in the debate text. The fourth column shows the number of debate contributions in this topic. This gives the user an impression of how dominant a specific topic is in comparison to the others. The fifth column shows the ratio of the number of found relevant words in this topic and in the whole debate. This value can be understood as specificity of the topic. 11 The last column shows the overall sentiment score of the contributions in the specific topic.

LDA automatically identified three different topics in this case, while a fourth cluster contains contributions that are unspecific (no important words found). 24 of 74 unique relevant words defined by annotators to be of interest (32.43 %) are detected. The k-means algorithm with tf•idf ranking determinates 15 of the relevant words (20.27 %). The three topics give a good insight in the main parts of the discussion: Topic 1 may be called Political Context in Europe, the 2nd Financial and Business Issues and the 3rd Greek Opinions.

With the knowledge of the main topics, the user may want to have a closer look at the detailed results of the topic modeling and the sentiment analysis according to the debate's text. Figure 6 exemplifies the contribution-based layout of this section. The important information provided to the user are the time when the contribution was written, the user information, the assigned topic id and the sentiment score of the particular contribution. The text itself is annotated with relevant words using the appropriate color. The topic assignment is stated by the topic id and the colored bar on the left border of the contribution.

In addition to the annotation of all relevant words of each topic, the textual view is enriched with the sentiment score. The annotations in the text are presented with a colored underscore and a [+] for a word with positive and [-] for a word with negative sentiment.

Graph View Results

Figure 7 shows the visualization of the resulting graphs based on LDA. As described in Sect. 2.3, the number of nodes is equivalent to the number of topics and the labeled edges encode the topics and their transition within the succeeding contributions. In k-means clustering, the number of topics is exactly as specified by the user, in contrast, LDA uses three clusters and leads to a well-arranged graph. The colorization of the nodes is associated with the colors in Fig. 5. The most relevant words of each topic are presented inside of each node. A link to the textual view of the contributions within this cluster is provided. The graph view enables the user to analyze the structure of the debate in a very condensed way.

Summary and Future Work

Analysis of textual debates from online communities and presenting them in a way that is clear and valueable for policy makers is a challenging task. In this paper we presented our approach to this challenge, incorporating topic modeling and sentiment analysis, and a web-based implementation of innovative visualizations for presenting the results in an easily perceivable way.

An overview of a debate is presented as a frequency weighted tag cloud. The determination of the main topics along with their most important words allows policy makers to get deeper understanding into a long debate, especially in the graphical view and the annotated text with different colors. Each topic is additionally assigned with the average sentiment score to not only show most important phrases but the associated emotions as well.

The manual annotation of data is a difficult task, as shown by the limited agreement of two annotators. Nevertheless, we could show on an example debate that despite of the comparatively low complience with manual annotation, the automated approach can lead to understandable and helpful results. How to evaluate such unsupervised methods is still question of research: While an annotator may find some clustering meaningful, another automatically detected one can as well be helpful while being less obvious.

Future work will focus on the execution of a pilot of the whole +Spaces platform, specifically for debates. We assume to retrieve a large amount of real world data and will optimize our approach on such contributions coming from Facebook, Blogger, and Twitter. Presumably, the language used in political debates performed on such platforms differs from texts on other platforms. The same holds for other topics, depending on the participating users and technical limitations, like the limited lengths of texts.

Fig. 1 .

 1 Fig. 1. Structure of the +Spaces platform

Fig. 2 .

 2 Fig. 2. Schematic structure of the graphical user interface for the interactive debate visualization

3 T 1 Fig. 3 .

 313 Fig. 3. Example debate thread with clustering and graph depiction.

Fig. 4 .

 4 Fig. 4. Frequency based tag cloud of the evaluation debate

Fig. 6 .

 6 Fig.6. Automatically annotated text of the evaluation debate [21] with the additional pseudonymized information about the user, the virtual space, the topic membership, the time stamp, and the sentiment score.

Fig. 7 .

 7 Fig. 7. Screenshot of the graph view of the evaluation debate with LDA.

http://www.facebook.com/, http://www.blogger.com/, http://www.twitter. com/

https://epetitionen.bundestag.de/

http://www.opengov.gr/

http://www.positivespaces.eu/

http://www.openwonderland.org/

http://secondlife.com/

Using the Snowball Stemmer http://snowball.tartarus.org

If the ratio is close to 1, nearly all relevant words are only mentioned in the topic specific contributions.

Acknowledgements

This publication is funded in the context of the Positive-Spaces project (http: //www.positivespaces.eu/) by the European Community's Seventh Framework Programme [FP7/2007-2011] under grant agreement no. 248726. We thank all other partners in the consortium of the project as well as the focus group in the Hellenic Parliament.


Adam Z Wyner

Katie Atkinson

Trevor Bench-Capon

Model Based Critique of Policy Proposals

Citizens may engage with policy issues both to critique official justifications, and to make their own proposals and receive reasons why these are not favoured. Either direction of use can be supported by argumentation schemes based on formal models, which can be used to verify and generate arguments, assimilate objections etc. Previously we have explored the citizen critiquing a justification using an argumentation scheme based on Action-based Alternating Transition Systems. We now present a system that uses the same model to critique proposals from citizens. A prototype has been implemented in Prolog and we illustrate the ideas with code fragments and a running example.

Introduction

Citizens contact their representatives about policies with a number of objectives. They may be seeking a justification of a current or proposed policy; they may wish to object to a current or proposed policy; or they may wish to make policy proposals of their own. Argumentation can support e-participation systems designed to meet any of these [START_REF] Macintosh | Providing argument support for eparticipation[END_REF]. In the first case a simple statement is all the response that is needed. For the second case it is necessary to identify, make precise, and attempt to meet, these objections. These situations are addressed in work such as [START_REF] Cartwright | Using computational argumentation to support e-participation[END_REF]. The third case is, however, different. Here what is needed is to obtain a precise, well formulated proposal from the citizen and then to identify its flaws and explain why the current policy is preferred. It is this situation that we will address in this paper. Our approach makse use of argumentation schemes, which hail from the informal logic literature and capture stereotypical patterns of reasoning that can be expressed as arguments. Every argumentation scheme is associated with a set of characteristic critical questions, that are used to identify possible challenges to instantiations of the argumentation scheme. Such challenges can be made against the different elements of the argumentation schemes and the relations between them. The particular argumentation scheme [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF] that is of relevance to our prototype is one that enables reasoning about, and justification of, actions. Some examples of the critical questions related to the argumentation scheme for practical reasoning are: Are the current circumstances as stated? Does the action have the consequences stated? Does the goal promote the value?

We will describe how the argumentation scheme and critical questions of [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF] can be used as the basis of a system to help a citizen to form a justification of a policy proposal and automatically provide a systematic and thorough critique of that position. The proposed system will be complementary to previous work using this argumentation scheme, notably [START_REF] Cartwright | Using computational argumentation to support e-participation[END_REF] and [START_REF] Wyner | Towards a structured online consultation tool[END_REF], in which the system proposed a justification and requested a critique from the user. In this paper the roles are reversed, so that we solicit a justification from the user and the system will provide the critique. We will illustrate our approach with a running example, relating to the use of speed cameras originally developed in [START_REF] Atkinson | Semantic models for policy deliberation[END_REF], and some fragments of a Prolog program that we have produced to make our definitions operational.

The argumentation scheme in [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF] proposes an action based on an understanding of the current situation, the consequences of actions and the desire to promote particular social values. These social values exist in a preference order that may vary from person to person according to their tastes and aspirations. The scheme is stated in [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF] as the practical reasoning argument scheme labelled AS1 :

Premise 1: In the current circumstances S (source) Conclusion: We should perform action A Premise 2: Which will result in new circumstances R (result) Premise 3: Which will realise goal G Premise 4: Which will promote some value V.

In this scheme, S is what is true before the action A, R is what is true after the action, G is the desirable consequence and V the reason why G is desirable.

In [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF] seventeen critical questions, which can be used as a basis to attack justifications using AS1, are given. A dialogue protocol based on this scheme will be very complicated, as demonstrated by the protocol for a similar scheme using sixteen of the critical questions given in [START_REF] Atkinson | A dialogue game protocol for multi-agent argument over proposals for action[END_REF]. As is noted in that paper, the protocol offers too much choice to be effective in practice. We must therefore look for a simpler way of proposing, defending and critiquing such justifications. Moreover, in addition to deploying the variety of available moves, difficulties can also arise when interpreting the critical questions. Although they can be understood informally, with the reader supplying an appropriate context, they are not always entirely precise. For example, one critical question against AS1 is whether the current circumstances hold. As we will see in section 3, this may be asked either because the questioner believes the action not to be currently possible, or because the questioner believes that the action will have different consequences given the circumstances that are actually currently true. To resolve these problems of vagueness and ambiguity, it is necessary to anchor the questions in a well defined semantical structure. This was done in [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF], which used Action-based Alternating Transition Systems (AATS) [START_REF] Wooldridge | On obligations and normative ability[END_REF] for this purpose.

Presenting justifications based on this scheme and receiving critiques was the subject of [START_REF] Wyner | Towards a structured online consultation tool[END_REF]. Here we will describe how an AATS and the argumentation scheme and critical questions of [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF] can be used to accept a justification and then automatically provide a critique. We believe allowing citizens to express their own ideas, and to receive feedback on possible problems with them, is an important part of engaging citizens in policy debates, and an important supplement to justifications of actual policy. Interacting with policy proposals in this way will help citizens to better understand why certain proposals were adopted and others rejected.

Section 2 will define an AATS, give a concrete instantiation of the AATS for our example, and give the Prolog predicates required to realise it. Section 3 will explain how the justification is elicited from the user, and the various steps of the critique. Section 4 will give an illustration using our example. Section 5 will give a brief discussion and some concluding remarks.

Model

An AATS is a formal structure that enables representation of states in an agent system and actions that cause transitions between states. Due to their precise formalisation, AATSs can be used in automated systems where agents need to have an explicit representation of states, actions and transitions. AATSs are useful for our tool because they enable us to map out in precise detail the space of a policy debate. As defined in [START_REF] Wooldridge | On obligations and normative ability[END_REF], the AATS made no reference to values. In order to adapt it for use with AS1, [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF] extended the structure to include labels on the transitions indicating which values are promoted and which demoted by following a transition. The extension of the original specification of an AATS to accommodate the notion of values is an Action-based Alternating Transition System with Values (AATS+V), defined as a (n + 9) tuple S = Q, q 0 , Ag, Ac 1 , ... , Ac n , ρ, τ, Φ, π, V, δ , where:

-Q is a finite, non-empty set of states; -q 0 ∈ Q is the initial state; -Ag = {1,...,n} is a finite, non-empty set of agents; -Ac i is a finite, non-empty set of actions, for each i ∈ Ag where Ac i ∩ Ac j = ∅ for all i = j ∈ Ag; -ρ : Ac Ag → 2 Q is an action pre-condition function, which for each action α ∈ Ac Ag defines the set of states ρ(α) from which α may be executed; -τ : Q × J Ag → Q is a partial system transition function, which defines the state τ (q, j ) that would result by the performance of j from state q -note that, as this function is partial, not all joint actions are possible in all states (cf. the pre-condition function above); -Φ is a finite, non-empty set of atomic propositions; and π : Q → 2 Φ is an interpretation function, which gives the set of primitive propositions satisfied in each state: if p ∈ π(q), then this means that the propositional variable p is satisfied (equivalently, true) in state q. -V is a finite, non-empty set of values.

-δ : Q × Q × V → {+, -, =}
is a valuation function which defines the status (promoted (+), demoted (-) or neutral (=)) of a value v u ∈ V ascribed to the transition between two states: δ(q x , q y , v u ) labels the transition between q x and q y with one of {+, -, =} with respect to the value v u ∈ V.

AATSs are particularly concerned with the joint actions of the set of agents. j Ag is the joint action of the set of k agents Ag, and can be represented as a tuple α 1 ,...,α k , where for each α j (where j ≤ k ) there is some i ∈ Ag such that α j ∈ Ac i . Moreover, there are no two different actions α j and α j ′ in j Ag that belong to the same Ac i . The set of all joint actions for the set of agents Ag is denoted by J Ag , so J Ag = i∈Ag Ac i . Given an element j of J Ag and an agent i ∈ Ag, i's action in j is denoted by j i .

Instantiating the AATS

In this paper we will use the same example as [START_REF] Atkinson | Semantic models for policy deliberation[END_REF], and use the AATS+V developed there. To fully describe a model using the AATS+V we need to specify the various components of the structure. We need the set of propositions Φ, combinations of which make up the possible member states of Q. Given Φ, we can constrain the size of Q by identifying logical relationships between members of Φ, such that for p 1 , p 2 ∈ Φ, ¬(p 1 ∧ p 2 ): states containing such combinations will then be impossible and so not be in Q. We need to give the set of agents, Ag and the actions they can perform. We need the set of values that may be promoted and demoted by the movement from one state to another. Finally, we need a transition matrix expressing ρ, τ , and δ. This matrix comprises a row for each state in Q and a column for each joint action in J. An entry in a cell indicates that the preconditions for the joint action are satisfied. Such entries comprise a triple consisting of the state reached if that joint action is executed, the set of values promoted, and the set of values demoted. These transitions are a reflection of a causal theory, which explains the effects of various actions, and an evaluative theory, which tells us when values are promoted and demoted.

Our example is an issue in UK Road Traffic policy, modelled in [START_REF] Atkinson | Semantic models for policy deliberation[END_REF] and used before that as an e-participation example in [START_REF] Cartwright | Using computational argumentation to support e-participation[END_REF] and [START_REF] Bench-Capon | A lightweight formal model of two-phase democratic deliberation[END_REF]. The number of fatal road accidents is an obvious cause for concern, and in the UK there are speed restrictions on various types of road, in the belief that excessive speed causes accidents. The policy issue that we will consider is how to reduce road deaths. One suggestion would be to deter motorists from speeding by introducing speed cameras, which would greatly increase detection and punishment of speeding offences. Points that might be contested are whether fines are sufficient to deter, and whether speeding is an important factor in road accidents. Additionally there are civil liberties issues associated with the loss of privacy resulting from the increased surveillance. One, more expensive, alternative to speed cameras would be to have a programme of education for motorists that could make them more aware of the dangers of speeding, better able to control their vehicles at speed, or both. This gives the set of propositions as: Φ = {R, S, P }, where R is that there are excessive road accidents, S is that there is excessive speeding and P that the intrusions on privacy are excessive.

These three propositions give rise to, potentially, eight states. We may, if we wish, exclude one or more of these as impossible. For example if we believe that it is impossible that there should be a reduction in road deaths without a reduction in speeding, no state with ¬R and S would be possible and so such states would not appear in Q. We also need to identify the current state, q 0 , which we take to be {R ∧ S ∧ ¬P }. The main agents involved are the Government, and Motorists, considered as a body. In some cases the consequences of an action are indeterminate (or at least cannot be determined using the elements we are modelling). To account for this we introduce a third agent, termed Nature. The action ascribed to Nature determines the outcomes of the actions of the other agents, where these outcomes are uncertain or probabilistic. The Government has three actions: introducing speed cameras, educating motorists, or doing nothing. Motorists may reduce their speed or do nothing. Nature has two actions according to which fatal accidents are or are not reduced as a result of the Government and motorist actions. For values we consider, the cost in terms of human life (L), compliance with the law (C), the financial cost to the Government (B for budget) and the impact of civil liberties (F for freedom). Figure 1 shows the transitions from the current state for the six possible joint actions: j 0 Government does nothing, motorists do nothing and nature does nothing. j 1 Government introduces cameras, motorists do nothing and nature does nothing. j 2 Government introduces cameras, motorists reduce speed and nature reduces accidents. j 3 Government introduces cameras, motorists reduce speed and nature does nothing. j 4 Government educates motorists, motorists reduce speed and nature reduces accidents. j 5 Government educates motorists, motorists do nothing and nature reduces accidents.

Accidents are always reduced when motorists are educated since either they do not speed, or can control their vehicles better.

Prolog Representation

To represent the AATS+V of Figure 1 in a Prolog program we state facts representing the propositions in Φ, the states in Q, the joint actions J and the transitions defined by τ . Propositions are in fact represented as pairs of literals to allow separate natural language forms for positive and negative occurrences. %literal(id,positive or negative, english text, other text) literal (

Critique

The process now is to solicit from the citizen a proposed action and a justification in the form of AS1, and to critique that proposal and its justification. The critique will proceed through a number of steps, each related to critical questions associated with AS1. In our e-participation setting, citizens will advocate a policy, either as part of a debate as to what should be done, or as an alternative to what the Government is currently doing. In response they will receive a reply suggesting why their proposal is not acceptable to the Government. Some of these responses will indicate errors: the citizen may simply be wrong about a current fact. Others will indicate possible problems, perhaps that a particular value is demoted: the citizen should be alerted to this problem, but may choose to accept it as a price worth paying. Thus some responses will indicate errors, whereas others will provide warnings. The subsections below describe the elements of a critique that can be automatically constructed to provide an instant response to such proposals. Then in section 4 we will step through a complete example to show how these elements fit together to build into a comprehensive whole.

Getting the Justification. To provide a target for the system's critique, the citizen must first instantiate AS1, by giving an action, the current state, the target state to be reached by the action (which will typically assume particular behaviours from the other agents involved), and the values this will promote. To get this information the citizen is first presented with a list of the propositions in Φ and indicates which are true and which false using a menu. The user is then prompted for the action the Government should perform. The choice is entered through the use of a menu containing the options in Ac Gov . The assumed consequences are obtained by presenting again the propositions in Φ with a menu. Finally the user is asked to give the most important value promoted by the action, using a menu with the elements of V .

Note that this form of justification can itself be generated from the Prolog progam using (with appropriate instantiations): argumentPro(A,S,R,V):transition(ID,S,R,J,X,_),member(V,X),jointAction(J,A,_,_), pp([government,should,A,in,S,to,reach,R,and,promote,V]).

where pp is simply a pretty print function. Note that if only S is instantiated in the query, argumentPro will generate every possible argument for actions from state S. Thus using transition(3,0,4,j1,[b],[f]) we can instantiate A to [introduce, speed, cameras], S to 0, R to 4 and V to b and so produce the argument government should introduce speed cameras in 0 to reach 4 and promote b. The presentation could further be improved by replacing the state numbers with the text versions of the literals they contain.

We now move through the particular points that make up a comprehensive critique of the justification. The critical question numbers refer to the critical questions presented in [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF]: here we use appropriate natural language forms.

Is the Action Possible? (CQ1, CQ13). The first thing to check is whether the believed facts are agreed. Thus if the user's answer suggests that literals X, Y , and Z are believed in the current situation, they should make up the initial state, q 0 and so state(0,X,Y,Z) should be in the program. If this is not so, we have state(0,X1,Y1,Z1), where one or more of X1 = X, Y 1 = Y and Z1 = Z. Thus the user believes we are in state q U where state(U,X,Y,Z) is in the program. Any disagreement as to the current state should be reported to the citizen. However, disagreement may or may not affect the justification. If argumentPro(A,0,R,V) succeeds, (where the user proposed to do A to reach q R and promote V ) the advocated action can still be performed in q 0 , and so the disagreement is not material, since the preconditions of the proposed action remain satisfied. The user can therefore be informed that either I believe the current facts to be X1, Y1 and Z1, but the action you propose is still possible or I believe the current facts to be X1, Y1 and Z1, and so the action you propose is not possible depending on whether or not argumentPro(A,0,R,V) succeeds. For example the action Do nothing is possible in any state whatsoever.

At this point, if the action is not possible, it is necessary either to terminate the discussion, or to accept what the user says and change which state is taken to be q 0 (and so considered currently true) in the program accordingly. Possibilities also exist for presenting the user with a justification of our beliefs about the current state, perhaps even initiating discussion using a persuasion dialogue in the style of [START_REF] Prakken | Formal systems for persuasion dialogue[END_REF] to resolve the differences. We will not go further into these possibilities here, however.

Can the Action have the Stated Effects? (CQ1, CQ2). Let the consequences claimed by the user be X2, Y 2, and Z2, and U 2 be the state where they hold. Now the actual consequences of action A will be given by a transition from state 0, so argumentPro(A,0,U2,Value) would need to succeed if the user's claimed consequences are correct. If this is so the disagreement on the current state does not affect the consequences of the action and so can be disregarded. For example Introduce Cameras will reach the same state whether or not privacy is currently respected. Otherwise the user must be informed that Performing A will not result in X2, Y2, Z2. Again we could stop here, offer reasons for our position, or engage in a dialogue in an attempt to convince the user of the true consequences of the action proposed.

Does the Action Promote the Value? (CQ4). Even if the action does have the consequences claimed, it may still not promote the desired value. For the citizens's justification to be acceptable, where the citizen claims V will be promoted, argumentPro(A,0,U2,V) must succeed. If this is not so, then the citizen must be informed that Although performing A will bring about X2, Y2 and Z2, the value V will not be promoted. For example, the citizen might claim that introducing cameras would reach q 5 and promote budget. Moving to q 5 does not, however, promote budget: that would require that S remained true.

Assuming, however, that argumentPro(A,0,U2,V) does succeed, the justification will have crossed the first hurdle, and represent an acceptable instantiation of AS1. The critique must now turn to whether the argument is acceptable when set against other objections.

Are There Negative Side Affects? (CQ8, CQ9). So far we have established that argumentPro(A,0,U2,V) succeeds. We need, however, to consider the other consequences of performing the action. Firstly it is possible that the action will demote some values as well as promoting V. Any such demotion would give us an argument against performing A. Such arguments can be discovered from the program using argumentCon(A,0,U2,W):transition(ID,S,R,J,_,X), member(W,X),jointAction(J,A,_,_), pp([government,should,not,A,in,S, to,avoid,R,which,would,demote,W]).

If this succeeds with one or more values binding W we will have one or more grounds for objecting to the original justification. For example the demotion of f is an argument against reaching q 5 by introducing cameras. Whether the argument is decisive will depend on the user's preferences. Most serious is if W = V , since the action represents a self-defeating way of advancing this value. So the user would be informed that You should not do A since this will demote the value you are trying to promote. If, on the other hand, W = V , the user only needs to be warned about the side effects to consider whether V is still worth promoting, so the message would be Performing A will demote values W1 ... Wn. Are you sure it is still worth promoting V? In this way, an advocate of speed cameras can continue to hold that view, but now does so with the awareness that freedom will be reduced.

Are there Other Ways to promote the Value? (CQ7). If there is an action B = A for which argumentPro(B,0,Any,V) succeeds, then it is possible to promote the desired value with a different action. This different action may be preferable to the chosen action, and so should be drawn to the citizen's attention. For example, if the citizen had suggested education as a way of promoting L, the critique could draw attention to the possibility of promoting the value by introducing cameras. Thus the system responds Performing B may also promote V. Are you sure you still wish to perform A?. This might cause the advocates of education to change their mind, particularly since they will have already been alerted to the fact that education will take them over budget.

Could Other Values be Promoted? (CQ11). If there is an action B = A for which argumentPro(B,0,Any,W) succeeds with W = V , then performing A precludes promoting this other value. Moreover there may be several such values. For our current purposes, we will not object if performing A promotes V and other values as well, but we should object if there are values which can be promoted from state 0, but are not promoted by A taking us to the state proposed by the user. In this case the user should be warned: If you perform A you will miss an opportunity to promote W1 ... Wn. Do you still want to perform A?, so that the user is aware of this, possibly preferable, opportunity. Of course, the user may prefer V and be content with the original choice. For example, an advocate of education to produce better drivers and reach q 3 will be told that C can be promoted by introducing cameras and reaching q 5 instead, but they may choose to disregard this, if they do not regard C to be of sufficient importance.

Will the Other Agents Do What they are Supposed To Do? (CQ17). Finally, suppose that argumentPro(A,0,U2,V) succeeds with jointAction(J, A, O1, O2) but there is also a transition such that jointAction(J, A, O3, O4) (where O1 = O3 or O2 = O4 or both) would move us from state 0 to some new state without promoting V. That is, our chosen action may fail to promote the desired value because one or more other agents do something other than what we had anticipated or hoped for. For example, if motorists do not modify their behaviour when cameras are introduced we will reach q 4 instead of the desired q 5 . Thus in such cases the system should pose the final objection Are you confident that O1 and O2 will be performed by the other agents?

Example

We now put this all together in a full example. Suppose our citizen wishes to propose education as the solution. First the citizen is asked for an opinion on the truth of P , R and S. Suppose that the user agrees that there is excessive speeding and too many deaths and intrusions on privacy are not at an acceptable level. The citizen is then offered a choice of the three Government actions: suppose educate motorists is chosen. When asked for consequences, the user replies {¬R, S, P }. The user does not believe that education will reduce speeding (which is seen as human nature), but does think that it will reduce fatalities. Finally the user is asked for the value promoted, and chooses b (budget). The system can now begin the critique.

The user believes the current state to be {R, S, P }, that is q 4 . The proposed action is also possible in q 4 , so the system reports: I do not believe that there are unacceptable intrusions on privacy, but the action you propose is still possible Suppose that the citizen responds by modifying his original proposal, and concedes that the intrusions of privacy are currently not excessive. The effect of the action is also agreed to take us from q 0 to q 3 . The value, however, produces a disagreement: the user believes that b will be promoted, whereas the program computes that b will be demoted. It therefore reports:

Although educate motorists will bring about there is excessive speeding, road deaths are at an acceptable level and privacy is respected, the value budget will not be promoted Moreover since b is actually demoted the system will add

You should not educate motorists since this will demote the value you are trying to promote

There are, however, ways in which b can be promoted: we can try to reach q4 by introducing speed cameras. Thus we can say:

Introducing speed cameras may promote budget. Are you sure you still wish to educate motorists?

Although the proposed action will promote l it fails to promote c. This value can be promoted by introducing speed cameras. The critique continues:

If you educate motorists you will miss an opportunity to promote compliance with the law by introducing speed cameras. Do you still want to educate motorists?

The final perspective, reliance on other agents, is not a problem in this instance since the proposed action fails to promote the value anyway.

Discussion

The above critique covers nine of the seventeen critical questions of [START_REF] Atkinson | Practical reasoning as presumptive argumentation using action based alternating transition systems[END_REF]. Some relate to the elements of the AATS+V: the propositions and actions included in the model cannot be questioned by the system. Rather we should expect the citizen to object that his position cannot be expressed. In such cases the system is not adequate for the citizen to provide his desired justification. But once the justification has been provided, consensus as to the propositions and actions can be presumed and so related critical questions will not arise. The other missing critical questions all concern goals, which are present in AS1, but have no obvious correspondence to the AATS+V. Such goals are probably best thought of as predicates defined in terms of the propositions in Φ. For example one might consider a society to be civilised if road deaths were not excessive and privacy respected, i.e ¬R ∧ ¬P . Thus the goal of a civilised society could be realised in state 0 by moving to state 2 or state 3. Thinking in terms of a set of basic propositions in Φ and a set of intensional definitions allowing for more complex aspirations to be expressed might be useful in a more complex domain.

Here, however, we will, like [START_REF] Atkinson | Semantic models for policy deliberation[END_REF], not include intensional definitions and goals in our current critique.

Policy proposals are based on a wide variety of different kinds of knowledge including: knowledge as to what is currently the case, knowledge of actions and their effects, awareness of the effect on values, knowledge of what other agents are likely to do and knowledge of preferences between competing values. This diversity is reflected in the range of perspectives from which an action justification can be critiqued. The use of an argumentation scheme such as AS1 enables the critique to systematically explore possible weaknesses with respect to all these aspects. What we have described above enables the systematic critique to be delivered, but while it raises questions, these are not argued for or resolved. We could easily provide simple textual justifications for the position we hold, but deeper exploration would require further argument and dialogue. This, however, would not be a simple extension. All the different kinds of knowledge that underlie the differences raised by the critique will require specific kinds of dialogues if these differences are to be resolved. Some of these dialogue types have been investigated: for example disagreements as to the current facts could be resolved using dialogues such as are presented in [START_REF] Prakken | Formal systems for persuasion dialogue[END_REF] and [START_REF] Black | An inquiry dialogue system[END_REF], but others have not. While there has been some very preliminary investigation of e.g. arguments between agents with different preferences [START_REF] Black | Choosing persuasive arguments for action[END_REF], much remains to be done for this topic and for dialogues disputing causal theories, agent behaviour and evaluative assessments. Techniques designed for straightforward arguments about the truth of a proposition are unlikely to be entirely suitable for these specialised topics.

The tool we have presented is based upon a precise formal model, but the front-end that the citizen interacts with uses only natural language. Many current tools for e-participation lack a formal and precise underpinning and as such offer little support for automated processes. Our contribution is that we have developed a program through which we can automatically elicit policy proposals and systematically generate a critique from our model. The formal model provides a level of support and consistency that takes our tool beyond the current state of the art. Nevertheless we see the system presented here as providing only the first step in a fully fledged critique system. What we have implemented so far provides organisation and breadth but lacks depth, since it uses, but does not justify, the model. In future work we shall explore support for the dialogue types required to open up these stubs.

Fig. 1 .

 1 Fig. 1. Transitions from q0

  1,1,[there,is,excessive,speeding],[]). literal(2,0,[speed,limits,are, generally,obeyed],[]). literal(3,1,[there,are,too,many, road,deaths],[]).

	%state(id, R, S, P). R S and P where the positive or negative
	% literals hold in the state. 0 is the current state
	state(0,1,3,6).	state(2,2,4,6).	state(3,1,4,6).
	state(4,1,3,5).	state(5,2,4,5).	state(6,2,3,5).
	%jointAction(id,government,motorist,nature).
	jointAction(j0,[do,nothing],[do,nothing],[there,is,no,effect]).
	jointAction(j1,[introduce,speed,cameras],[do,nothing],
		[there,is,no,effect]).
	jointAction(j2,[introduce,speed,cameras],[reduce,speed],
		[there,are,fewer,accidents]).
	jointAction(j3,[introduce,speed,cameras],[reduce,speed],
		[there,is,no,effect]).
	jointAction(j4,[educate,motorists],[reduce,speed],
		[there,are,fewer,accidents]).
	jointAction(j5,[educate,motorists],[do,nothing],
		[there,are,fewer,accidents]).
	%transition(id, source state, target state,
	%joint action, values promoted, values demoted).
	transition
	literal(4,0,[road,deaths,are,acceptable],[]).
	literal(5,1,[there,are,unacceptable,intrusions,on, privacy],[]).
	literal(6,0,[privacy,is,respected],[]).

Acknowledgments

This work was partially supported by the FP7-ICT-2009-4 Programme, IMPACT Project, Grant Agreement Number 247228. The views expressed are those of the authors and are not necessarily representative of the project.