Mazen Kebewar
email: mazen.kebewar@univ-orleans.frmazen.kebewar@gmail.com

The effect of debt on corporate profitability Evidence from French service sector

Keywords: Debt, GMM, Panel data, Profitability. JEL Classification: C33, G32, L25

Current study aims to provide new empirical evidence on the impact of debt on corporate profitability. This impact can be explained by three essential theories: signaling theory, tax theory and the agency cost theory. Using panel data sample of 2240 French non listed companies of service sector during 1999-2006. By utilizing generalized method of moments (GMM) econometric technique on three measures of profitability ratio (PROF1, PROF2 and ROA), we show that debt ratio has no effect on corporate profitability, regardless of the size of company (VSEs, SMEs or LEs).

Introduction

Explaining role of debt in firms' performance is one of the primary objectives of contemporary researches for more than fifty years [START_REF] Modigliani | The Cost of Capital, Corporate Finance, and the Theory of Investment[END_REF]. However, this role remains a questionable subject which attracts the attention of many researchers as [START_REF] Goddard | Determinants of profitability in European manufacturing and services: Evidence from a dynamic panel data[END_REF], [START_REF] Berger | Capital structure and firm performance: A new approach to testing agency theory and an application to the banking industry[END_REF], [START_REF] Rao | Capital structure and financial performance: evidence from Oman[END_REF], [START_REF] Baum | The Effects of Short-Term Liabilities on Profitability: The Case of Germany[END_REF], [START_REF] Weill | Leverage and Corporate Performance: Does Institutional Environment Matter?[END_REF], [START_REF] Nunes | Profitability in Portuguese service industries: a panel data approach[END_REF], [START_REF] Margaritis | Capital structure, equity ownership and firm performance[END_REF] and Kebewar (2012).

Indeed, researchers analyze the debt ratio and try to determine whether an optimal debt ratio exists or not. Optimal debt ratio is generally defined as the one which minimizes the cost of capital for the company, while maximizing the value of company. In other words, the optimal debt ratio is the one which maximizes the profitability of company.

Besides, the divergence between researchers can be observed in theoretical strand of literature. There are three essential theories which highlight the influence of debt on corporate profitability, namely: signaling theory, the agency costs theory and tax theory. First, according to signaling theory, the debt; in the presence of asymmetric information, should be correlated positively to profitability. According to the agency costs theory, there are two contradictory effects of debt on profitability, firstly it is positive in the case of agency costs of equity between shareholders and managers, secondly it's effect is negative, resulting from the agency costs of debt between shareholders and lenders. Finally, the influence of taxation is complex and difficult to predict because it depends on the principles of tax deductibility of interest, income tax and non-debt tax shield. Furthermore, the disagreement exists not only in the theoretical literature but also it is present in the empirical strand. A negative effect of debt on profitability was confirmed by [START_REF] Majumdar | Capital structure and performance: Evidence from a transition economy on an aspect of corporate governance[END_REF], [START_REF] Eriotis | Profit Margin and Capital Structure: An Empirical Relationship[END_REF], [START_REF] Ngobo | Structure du capital et performance de l'entreprise : le rôle modérateur des différences culturelles[END_REF], [START_REF] Goddard | Determinants of profitability in European manufacturing and services: Evidence from a dynamic panel data[END_REF], [START_REF] Rao | Capital structure and financial performance: evidence from Oman[END_REF], [START_REF] Zeitun | Capital structure and corporate performance evidence from Jordan[END_REF] and [START_REF] Nunes | Profitability in Portuguese service industries: a panel data approach[END_REF]. On the other hand, Baum et al. (2006[START_REF] Baum | The Effects of Short-Term Liabilities on Profitability: The Case of Germany[END_REF], [START_REF] Berger | Capital structure and firm performance: A new approach to testing agency theory and an application to the banking industry[END_REF], Margaritis and[START_REF] Margaritis | Capital Structure and Firm Efficiency[END_REF][START_REF] Margaritis | Capital structure, equity ownership and firm performance[END_REF], showed a positive influence. In addition, [START_REF] Simerly | Environmental dynamism, capital structure and performance: a theoretical integration and an empirical test[END_REF], [START_REF] Mesquita | Capital structure and profitability: the Brazilian case[END_REF] and [START_REF] Weill | Leverage and Corporate Performance: Does Institutional Environment Matter?[END_REF], find both effects in their studies. Besides that, [START_REF] Berger | Capital structure and firm performance: A new approach to testing agency theory and an application to the banking industry[END_REF], [START_REF] Margaritis | Capital Structure and Firm Efficiency[END_REF] and Kebewar (2012) finds the presence of a non linear effect (inverse U-shaped relationship). Finally, a non significant effect was confirmed by [START_REF] Baum | The Effects of Short-Term Liabilities on Profitability: The Case of Germany[END_REF] in American industrial companies.

Several factors may reveal reasons for the contradiction of results in empirical studies.

First, these empirical studies focus on different types of sample (countries, sectors, companies and periods). Furthermore, researchers have used different measures of profitability as a dependent variable 1 and various debt ratios as independent variable 2 . Finally, these studies applied different methodologies 3 . The empirical literature concerning the impact of debt on profitability leads us to make two inferences. The first one is that most of the empirical studies focused on listed companies. The second one is related to paucity of studies on the French companies as mentioned by; [START_REF] Goddard | Determinants of profitability in European manufacturing and services: Evidence from a dynamic panel data[END_REF], [START_REF] Weill | Leverage and Corporate Performance: Does Institutional Environment Matter?[END_REF], [START_REF] Margaritis | Capital structure, equity ownership and firm performance[END_REF] and recently in Kebewar (2012). These two avenues motivated our study. Moreover, current work is very important because debt is a risky choice whose consequences on the corporate profitability can be considerable (e.g. the risk of bankruptcy and its consequences for the stakeholders). So we will try to find, empirically, the effect of debt on profitability for French not listed companies. In addition, to improve the precision of estimation by reducing the heterogeneousness between sizes of companies, we study the behavior of these firms according to their size. Moreover, we will analyze not only the linear effect of debt on profitability, but also the non-linear effect by estimating a quadratic model which takes into account the squared of variable of debt in the equation of regression.

To do this, we will implement the generalized method of moments (GMM) estimation model on a sample of 2240 firms of service sector observed over the period (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006); these companies are divided into three 'size' classes VSBs (very small business), SMEs (small and medium enterprise) and LEs (large enterprise). According to the proponents of GMM model, it provides solution to the problems of simultaneity bias, reverse causality (especially between profitability and debts) bias and the conundrum of possible omitted variables.

The structure of this paper is as follows. First, we discuss the characteristics of the sample and variables. Then, we present the empirical results. Finally, we wrap up the work with main findings and conclusions.

1 ROA, ROE, ROI, PROF, Tobin's Q, Profit on sales, business performance, VRS: Technical Efficiency, CRS: Technical Efficiency, Profit Margin, Frontier efficiency and BTI: ratio earnings before interest and tax to total assets. 2 Ratio of total debt, ratio of short-term debt, and ratio of long-term debt. 3 OLS, GLS, DLS, Weighted least squares, fixed effect, random effect, variance decomposition model, covariance model, maximum likelihood, Method of simultaneous equations, quantile regression and GMM.

Data

Data description

The sample, which is obtained from the Diane database, consists of an unbalanced panel of 2240 French companies of service sector, over the period of 1999-2006. Our sample is composed of unlisted companies like Limited Companies and Limited Liability Companies. In addition, these companies belong to three classes of size (VSEs, SMEs and LEs) 1 .

Public enterprises are excluded from the study because of their special political leverage. Furthermore, we do not include companies with negative equity. In addition, outliers were removed according the procedure of [START_REF] Kremp | Nettoyage des données dans le cas de fichiers de données individuelles[END_REF] 2 . Thus, descriptive statistics and the distribution of firms by size are shown in Table (1) 3 .

Variables

Dependent variable

According to the literature, corporate profitability can be measured by several methods. In the context of our study and to compare our results, we use three measures of profitability:

1 According to the Classification of INSEE: very small enterprises (VSEs) which employs less than 20 employees, small and medium enterprises (SMEs) which employ between 20 and 249 employees, and finally (LEs) whose size is between 250 and 4999 employees. 2 We deleted the observations which are situated outside the interval defined by the first and third quartiles more or less five once the distance interquartile. 3 The composition of sample could be provided by requesting the author.

Explanatory Variables  Debt

In theory, debt ratio can be measured in different ways i.e. total debt ratio, debt ratio as short, medium and long term. In our study, we define the total debt ratio (DT) by dividing the sum of the short and long-term debt by the total assets.  Tangibility

Tangibility has two conflicting effects on profitability. On the one hand, we expect a positive effect by [START_REF] Himmelberg | Understanding the determinants of managerial ownership and the link between ownership and performance[END_REF]; they show that tangible assets are easily monitored and provide good collateral and thus they tend to mitigate agency conflicts between shareholders and creditors. On the other hand, we predict a negative correlation, because firms with high levels of tangible assets tend to be less profitable. Firms with high levels of intangible assets (in form of liquidity) have more investment opportunities in the long term, innovation and research and development [START_REF] Deloof | Does working capital management affect profitability of Belgian firms[END_REF][START_REF] Nucci | Is firm's productivity related to its financial structure? Evidence from microeconomic data[END_REF]. The negative relationship between tangibility and profitability has been confirmed in number of studies as [START_REF] Rao | Capital structure and financial performance: evidence from Oman[END_REF], [START_REF] Zeitun | Capital structure and corporate performance evidence from Jordan[END_REF], [START_REF] Weill | Leverage and Corporate Performance: Does Institutional Environment Matter?[END_REF] and [START_REF] Nunes | Profitability in Portuguese service industries: a panel data approach[END_REF]. In addition, [START_REF] Majumdar | Capital structure and performance: Evidence from a transition economy on an aspect of corporate governance[END_REF] and [START_REF] Margaritis | Capital Structure and Firm Efficiency[END_REF] find a positive relationship. To determine the effect of tangibility on profitability, we use the ratio (TANG); it is calculated by dividing the sum of net tangible assets to total assets.

 Tax

The tax impact on profitability of a company is difficult to predict, because it depends on the principle of tax deductibility of interest on debt. So, if a company does not take advantage of this principle, we expect a negative effect of tax on profitability. On the contrary, if a company takes advantage of this principle, this impact will be positive or not significant. [START_REF] Zeitun | Capital structure and corporate performance evidence from Jordan[END_REF] showed a positive effect of tax on profitability. The impact of tax on corporate profitability is highlighted by using the tax ratio in the regression equation. This ratio (TAX) is calculated by dividing the tax paid to earnings before interest and taxes.

 Growth opportunities

It is expected that firms having high growth opportunities have a high rate of return, because these companies are able to generate more profits from the investment. Therefore, growth opportunities should positively influence profitability. The positive impact of growth opportunities on profitability is confirmed by most empirical studies such as Psillaki and [START_REF] Margaritis | Capital Structure and Firm Efficiency[END_REF], [START_REF] Zeitun | Capital structure and corporate performance evidence from Jordan[END_REF] and [START_REF] Nunes | Profitability in Portuguese service industries: a panel data approach[END_REF]. On the other hand, Margaritis

and Psillaki (2010) find a negative effect only in the French chemical sector. Several measures to calculate growth opportunity for companies exists in literature. But in the context of our analysis, we use the ratio of growth opportunity (GROWTH) which is measured by the change in total assets from one year to another.

Methodology

The model in order to analyze the impact of debt on corporate profitability is as follows:

it i n n n t i t i t i t i t i dumt GROWTH TAX TANG DT PROF                   9 1 , 4 , 3 , 2 , 1 0 ,
Where, subscript 'i' denote the studied company and subscript't' represent the time period.

The dependent variable is the ratio of profitability (PROF1, PROF2 or ROA). Moreover, (DT), (TANG), (TAX) and (GROWTH) represent the ratios of debt, tangibility, tax and growth opportunities. Further, influence of time is taken into account by the introduction of annual dummies (dumt) that capture the specific year effect (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006). The individual fixed effect on companies is represented by the term ( i  ). Finally, the error term which is assumed to be independent and identically distributed (iid) which is represented by the term ( it  ).

Regarding the effect of non-linearity between debt and profitability, we estimate a quadratic model which takes into account the debt variable squared in the regression equation.

Thus, the model to estimate in this context is as follows:

it i n n n t i t i t i t i t i t i dumt GROWTH TAX TANG DT DT PROF                     9 1 , 5 , 4 , 3 , 2 , 1 0 , 2 ^
The null hypothesis of linearity effect is to test: (H0 :

0 2  
). If this hypothesis is rejected, we can conclude the existence of non-linearity between debt and profitability. According to the agency cost theory, the effect of debt on profitability must be positive when (

0 1   and 0 2 , 2 1   t i DT  
). However, if the debt ratio arrives at an adequately high level, this effect can become negative. So, our quadratic specification is consistent with the possibility that the relationship between debt and profitability may not be monotonic, it may switch from positive to negative at a high level of debt. Debt will have a negative impact on profitability when

( 2 1 , 2 /     t i DT
). A sufficient condition for the inverse U-shaped relationship between debt and profitability to hold is that (

0 2   ).
We suspect problems of endogeneity in the estimation equation related to causality of exogenous variables to the dependent variable (especially the debt variable). Therefore, traditional econometric methods such as Ordinary Least Square (OLS), fixed effect and Generalized Least Square (GLS) do not allow us to obtain efficient estimates of such model. So, to solve this problem, we introduce the generalized method of moments on panel (GMM)

proposed by [START_REF] Arellano | Some Tests ofc Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations[END_REF], [START_REF] Arellano | Another Look at the Instrumental-Variable Estimation of Error-Components Models[END_REF] and [START_REF] Blundell | Initial conditions and moment restrictions in dynamic panel data models[END_REF]. This method can provide solutions to simultaneity bias, reverse causality (especially between debt and profitability) and possible omitted variables. Moreover, it can control the individual and temporal specific effects. Indeed, GMM method is used to solve the problems of endogeneity not only at the debt variable, but also for other explanatory variables by using a series of instrumental variables generated by lagged variables.

The model is estimated by two-step System GMM. In order to choose the best model specification, we examined several specifications according to different assumptions about the endogeneity of variables.

Results

Descriptive analysis

Table (2) reports the changes in profitability ratios. We note a small decrease in profitability ratio (especially for PROF1 and PROF2). Regarding the evolution of profitability according to the size, we find that very small enterprises (VSEs) realize profitability higher than the small and medium enterprises (SMEs) and the large enterprises (LEs); that is to say, there is inverse relationship over the period between size and profitability. Moreover, we note that the decrease in profitability concerns only to the very small enterprises (VSEs) whereas other enterprises have profitability almost stable over the study period. -0,007 -0,002 0 -0,011 -0,001 0 -0,005 0 0,003 -0,002 0,001 0 Note: (VSEs) less than 20 employees, (SMEs) between 20 and 249 employees, (LEs) between 250 and 4999 employees.

Correlation between the variables

The correlation matrix for the variables is reported in Table (3). The results show that debt is negatively correlated with profitability, but this negative effect is negligible. Moreover, tangibility has also a negative relationship with all profitability ratios. On the other hand, growth opportunities and tax have a positive correlation with profitability. Looking at the relationship between the independent variables themselves, the results show that the multicollinearity is not a problem for the application of analytical techniques 1 .

1 According to test of VIF (Variance Inflation Factor).

Table (3) PEARSON CORRELATION MATRIX

Econometric analysis

We estimated the effect of debt on profitability for 2240 French service companies over the period between 1999 and 2006, by using various representatives of profitability ratio as (PROF1, PROF2 and ROA). Moreover, we used two different models (linear and nonlinear) to verify the presence of a nonlinearity of this impact. Furthermore, the estimation was detailed by studying specifically the behavior of companies according to their size (VSEs, SMEs and LEs). So, the results of the estimation of GMM method on panel data models with each of the profitability measures are displayed in Tables ( 4) to (8).

We can say that all our results are robust for the following reasons: First, the instruments used in our regressions are valid, because Hansen test does not reject the hypothesis of validity of lagged variables in levels and in difference as instruments. Secondly, we note that there is no second-order autocorrelation of errors for difference equation, because the test of second order autocorrelation (AR2) does not allow rejecting the hypothesis of absence of second-order autocorrelation.

We note that debt has no influence on profitability, either in a linear way, or in a non-linear way. In addition, when we present the analysis by using different size classes, we also find that there is no impact of debt on profitability regardless the size of the enterprise. This finding is consistent with [START_REF] Baum | The Effects of Short-Term Liabilities on Profitability: The Case of Germany[END_REF] on American industrial companies.

Regarding the control variables, we note, first, that the tangibility negatively affects profitability, this means that companies invest too much in the fixed assets which do not improve their performances, or they do not use their fixed assets efficiently. On the other hand, growth opportunities and tax affect positively the profitability; it means that companies have high profitability level when they have increased growth opportunities and taxes. 0,00 0,00 0,00 0,00 0,00 0,00 Arellano-Bond test for AR(2) -1,07 -1,34 -1,62 -1,82 -0,65 -0,66 P-value AR(2) 0,29 0,18 0,10 0,07 0,52 0,51 Notes: ***, ** and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. T-students are provided in parentheses. Sargan statistic is a Sargan-Hansen test of overidentifying restrictions. AR (k) is the test for k-th order autocorrelation. Estimation by one-step System GMM. Instruments: (DT) delayed t-3 and t 4, (DT * 2) delayed t-3 and t-4, the rest of explanatory variables are exogenous.

Table (6) THE EFFECT OF DEBT ON PROFITABILITY BY SIZE CLASS (DEPENDENTE VARIABLE: PROF1) (PROF1) TPE PME ETI

DT -0,142 0,013 -0,186 0,091 -0,126 0,044 0,008 -0,014 (-1,36) (0,10) (-1,49) (0,61) (-1,21) (0,20) (0,07) (-0,02) DT*2 -0,039 -0,117 -0,065 -0,074 (-0,34) (-0,82) (-0,34) (-0,13) TANG -0,020** -0,018** -0,020 -0,023** -0,017 -0,010 0,009 0,008

(-2,11) (-2,57) (-1,40) (-2,04) (-1,26) (-1,20) (0,43) (0,
0,010* 0,003 0,021** 0,008** -0,001 -0,004 0,005

0,005 0,000 0,014** 0,006** -0,003 -0,005** 0,000 - Estimation by two-step System GMM. Instruments: (DT) delayed t-3 and t 4, (DT * 2) delayed t-3 and t-4, the rest of explanatory variables are exogenous.

Conclusion

In this paper, we are interested in the effect of debt on profitability of French service companies. In other words, this article expands the empirical literature regarding the influence of debt on profitability.

There are three essential theories which highlight the influence of debt on corporate profitability, namely: signaling theory, tax theory and the agency costs theory. Furthermore, the disagreement between researchers observed not only theoretically but also empirically.

Lack of studies on French firms and the concentration of studies on listed companies and industrial companies have motivated our study. To do this, we examined empirically the impact of debt on profitability by using the generalized method of moments (GMM) on an unbalanced panel of 2240 French companies of service sector observed over the period 1999-2006. Our sample is composed of unlisted companies like Limited Companies and Limited Liability Companies. In addition, in order to improve the precision of the estimation by reducing heterogeneousness between different sizes of companies, we studied the behavior of these firms according to their size (VSEs, SMEs and LEs). Moreover, we analyzed not only the linear effect of debt on profitability, but also the non-linear effect by estimating a quadratic model which takes into account the squared of debt variable in the regression equation.

According to this study, we can underline that debt has no influence on profitability either in a linear way, or in a non-linear way. This finding is consistent with that of [START_REF] Baum | The Effects of Short-Term Liabilities on Profitability: The Case of Germany[END_REF] on American industrial companies. In addition, when we present the analysis using different size classes, we also find that there is no impact regardless the size of enterprise.

For potential research, it would be interesting to take into account some reflections. First, it will be interesting to extend this analysis across different components of corporate debt (longterm and short-term); because, according to most of the studies, contradictory effects have been found. Secondly, we ideally would add new specific variables for companies and sectors, for example, the ownership structure of the corporate capital and the environment in which companies operate. Finally, considering the fact that the relationship between debt and profitability can be non-linear, we can deepen our analysis by using econometric methods that can evaluate the effects of non-linearity as quantile regression and threshold models.

  *** 0.128*** 0.042*** -0.013 0.059*** 1,01 Note: ***, ** and * represent statistical significance at the 1%, 5%, and 10% levels, respectively.

Table (

 (

	PROF1, PROF2 and ROA. PROF1 is measured by dividing net income from operations by total
	assets. PROF2 is calculated by dividing earnings before interest and tax to total assets. Return on
	Assets (ROA) is measured by dividing net income from operations (to which income taxes are
	subtracted) by total capital.
	1) DESCRIPTIVE STATISTICS FOR VARIABLES
	CLASS SIZE	CLASS (1) 1 -19	CLASS (2) 20 -249	CLASS (3) 250 -4999	TOTAL
	Number of companies	1241	921	78	2240
	Number of observations	7001	5441	451	12893
	PROF1	0,091 (0,088)	0,078 (0,082)	0,073 (0,061)	0,085 (0,086)
	PROF2	0,098 (0,087)	0,086 (0,080)	0,078 (0,056)	0,092 (0,084)
	ROA	0,072 (0,073)	0,059 (0,065)	0,059 (0,053)	0,067 (0,070)
	DT	0,590 (0,202)	0,607 (0,192)	0,619 (0,164)	0,598 (0,197)
	TANG	0,190 (0,195)	0,227 (0,264)	0,199 (0,223)	0,207 (0,229)
	TAX	0,176 (0,132)	0,208 (0,146)	0,218 (0,156)	0,191 (0,140)
	GROWTH	0,056 (0,221)	0,070 (0,196)	0,079 (0,179)	0,063 (0,209)
	Note: Values without parentheses are the averages and those in parentheses are the standard deviation.

Table (

 (

	2) CHANGES IN THE RATIO OF PROFITABILITY
	YEAR	PROF1 PROF2 ROA	VSEs	(PROF1) SMEs	LEs	VSEs	(PROF2) SMEs	LEs	VSEs	(ROA) SMEs	Les
	1999	0,091	0,096	0,066	0,098	0,083	0,076	0,102	0,091	0,083	0,071	0,061	0,063
	2000	0,087	0,093	0,065	0,096	0,077	0,079	0,101	0,085	0,080	0,071	0,058	0,064
	2001	0,087	0,092	0,069	0,094	0,080	0,070	0,100	0,085	0,070	0,075	0,062	0,060
	2002	0,080	0,087	0,064	0,088	0,071	0,074	0,094	0,078	0,075	0,071	0,054	0,061
	2003	0,088	0,094	0,069	0,093	0,081	0,072	0,100	0,088	0,078	0,075	0,062	0,057
	2004	0,085	0,092	0,067	0,092	0,078	0,070	0,099	0,085	0,076	0,074	0,059	0,057
	2005	0,085	0,092	0,067	0,089	0,080	0,074	0,096	0,087	0,080	0,072	0,061	0,058
	2006	0,084	0,094	0,066	0,087	0,082	0,076	0,097	0,091	0,086	0,069	0,062	0,063
	Average	0,086	0,093	0,067	0,092	0,079	0,074	0,099	0,086	0,079	0,072	0,060	0,060
	Change

Table ( 4

 ( ) THE EFFECT OF DEBT ON PROFITABILITY (GMM :TWO STEPS)

		PROF1	PROF2	ROA
	DT	-0,142	0,013	-0,093	-0,052	-0,114	0,031
		(-1,36)	(0,10)	(-0,98)	(-0,43)	(-1,27)	(0,29)
	DT*2		-0,039		0,024		-0,043
			(-0,34)		(0,21)		(-0,42)
	TANG	-0,020**	-0,018**	-0,022**	-0,021***	-0,019**	-0,016***
		(-2,11)	(-2,57)	(-2,53)	(-3,13)	(-2,35)	(-2,87)
	TAX	0,149**	0,205***	0,154***	0,187***	0,078	0,127***
		(2,45)	(10,30)	(2,79)	(9,49)	(1,51)	(7,52)
	GROWTH	0,050***	0,049***	0,041***	0,042***	0,043***	0,042***
		(6,13)	(6,50)	(5,81)	(6,13)	(6,03)	(6,32)
	Iyear _2000	0,229	0,061	0,141	0,048	0,184	0,040
		(1,22)	(0,96)	(0,83)	(0,75)	(1,14)	(0,73)
	Iyear _2001	0,016*	0,006*	0,009	0,003	0,013	0,005*
		(1,66)	(1,93)	(1,05)	(1,00)	(1,56)	(1,65)
	Iyear _2002	0,008	0,000	0,004	-0,001	0,007	0,000
		(1,12)	(0,01)	(0,62)	(-0,51)	(1,07)	(-0,04)
	Iyear _2003	0,010*	0,003	0,005	-0,001	0,008*	0,003
		(1,67)	(1,04)	(0,84)	(-0,21)	(1,68)	(1,19)
	Iyear _2004	0,005	0,000	0,001	-0,002	0,004	0,001
		(1,26)	(0,24)	(0,32)	(-0,80)	(1,37)	(0,49)
	Iyear _2005	0,003	0,001	0,000	-0,001	0,003	0,002
		(1,08)	(0,45)	(0,09)	(-0,56)	(1,41)	(1,03)
	Constant	0,117**	0,047	0,106**	0,076**	0,100**	0,036
		(2,10)	(1,58)	(2,08)	(2,53)	(2,08)	(1,42)
	Observations	10653	10653	10653	10653	10653	10653
	Number of firm	2240	2240	2240	2240	2240	2240
	Sargan statistic	2,74	14,71	4,68	23,95	3,41	14,85
	p-value sargan statistic	0,91	0,79	0,70	0,25	0,85	0,79
	Arellano-Bond test for AR(1)	-9,09	-12,67	-9,38	-12,81	-9,64	-12,79
	P-value AR(1)	0,00	0,00	0,00	0,00	0,00	0,00
	Arellano-Bond test for AR(2)	-1,13	-1,36	-1,80	-1,90	-0,62	-0,69
	P-value AR(2)	0,26	0,17	0,07	0,06	0,53	0,49
	Notes: ***, ** and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. T-students are provided in
	parentheses. Sargan statistic is a Sargan-Hansen test of overidentifying restrictions. AR (k) is the test for k-th order
	autocorrelation. Estimation by two-step System GMM. Instruments: (DT) delayed t-3 and t 4, (DT * 2) delayed t-3 and t-4, the
	rest of explanatory variables are exogenous.

Table ( 5

 ( ) THE EFFECT OF DEBT ON PROFITABILITY (GMM : ONE STEP)

		PROF1	PROF2	ROA
	DT	-0,163	0,036	-0,129	-0,014	-0,132	0,048
		(-1,33)	(0,29)	(-1,11)	(-0,11)	(-1,24)	(0,44)
	DT*2		-0,060		-0,011		-0,063
			(-0,51)		(-0,09)		(-0,61)
	TANG	-0,022**	-0,016**	-0,025***	-0,021***	-0,021**	-0,016***
		(-2,14)	(-2,36)	(-2,58)	(-3,05)	(-2,35)	(-2,72)
	TAX	0,133*	0,206***	0,130*	0,186***	0,065	0,125***
		(1,85)	(9,98)	(1,90)	(9,19)	(1,04)	(7,05)
	GROWTH	0,050***	0,048***	0,041***	0,039***	0,043***	0,041***
		(5,96)	(6,42)	(5,71)	(6,05)	(5,90)	(6,33)
	Iyear _2000	0,279	0,057	0,220	0,047	0,227	0,044
		(1,24)	(0,85)	(1,03)	(0,71)	(1,16)	(0,76)
	Iyear _2001	0,019	0,007**	0,014	0,004	0,016	0,006*
		(1,63)	(2,02)	(1,23)	(1,16)	(1,53)	(1,89)
	Iyear _2002	0,010	0,001	0,007	-0,001	0,008	0,001
		(1,16)	(0,25)	(0,87)	(-0,34)	(1,11)	(0,27)
	Iyear _2003	0,011*	0,003	0,007	0,000	0,010*	0,003
		(1,67)	(1,32)	(1,05)	(-0,12)	(1,67)	(1,54)
	Iyear _2004	0,006	0,001	0,003	-0,001	0,006	0,002
		(1,39)	(0,62)	(0,72)	(-0,51)	(1,49)	(0,95)
	Iyear _2005	0,003	0,001	0,001	-0,001	0,003	0,002
		(1,15)	(0,53)	(0,36)	(-0,56)	(1,45)	(1,12)
	Constant	0,128**	0,042	0,124**	0,067**	0,110*	0,034
		(1,97)	(1,39)	(2,01)	(2,21)	(1,92)	(1,32)
	Observations	10653	10653	10653	10653	10653	10653
	Number of firm	2240	2240	2240	2240	2240	2240
	Sargan statistic	2,74	14,71	4,68	23,95	3,41	14,85
	p-value sargan statistic	0,91	0,79	0,70	0,25	0,85	0,79
	Arellano-Bond test for AR(1)	-8,37	-12,72	-8,34	-12,85	-8,90	-12,80
	P-value AR(1)

  ** and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. T-students are provided in parentheses. Sargan statistic is a Sargan-Hansen test of overidentifying restrictions. AR (k) is the test for k-th order autocorrelation.

									,75)
	Iyear _2005	0,003	0,001	0,006	0,003	0,000	-0,001	0,001	-0,004
		(1,08)	(0,45)	(1,62)	(1,27)	(-0,12)	(-0,67)	(0,12)	(-0,83)
	Constant	0,117**	0,047	0,146**	0,037	0,092**	0,023	0,037	0,071
		(2,10)	(1,58)	(2,19)	(1,02)	(1,70)	(0,39)	(0,55)	(0,30)
	Observations	10653	10653	5760	5760	4520	4520	373	373
	Number of firm	2240	2240	1241	1241	921	921	78	78
	Sargan statistic	2,74	14,71	2,02	22,95	4,72	11,68	4,83	20,93
	p-value sargan statistic	0,91	0,79	0,96	0,29	0,69	0,93	0,68	0,401
	Arellano-Bond test for AR(1)	-9,09	-12,67	-6,95	-9,88	-6,24	-8,40	-2,88	-1,61
	P-value AR(1)	0,00	0,00	0,00	0,00	0,00	0,00	0,00	0,11
	Arellano-Bond test for AR(2)	-1,13	-1,36	0,10	0,09	-3,17	-3,28	-1,36	-0,50
	P-value AR(2)	0,26	0,17	0,92	0,93	0,00	0,001	0,17	0,62
	Notes: ***, Estimation by two-step System GMM. Instruments: (DT) delayed t-3 and t 4, (DT * 2) delayed t-3 and t-4, the rest of explanatory
	variables are exogenous.

Table ( 7

 ( ) THE EFFECT OF DEBT ON PROFITABILITY BY SIZE CLASS (DEPENDENTE VARIABLE: PROF2)

		(PROF2)	TPE	PME	ETI
	DT	-0,093	-0,052	-0,123	0,023	-0,089	-0,113	-0,167	-0,414
		(-0,98)	(-0,43)	(-1,12)	(0,16)	(-0,93)	(-0,50)	(-1,22)	(-0,62)
	DT*2		0,024		-0,036		0,057		0,185
			(0,21)		(-0,26)		(0,29)		(0,35)
	TANG	-0,022**	-0,021***	-0,026**	-0,029***	-0,016	-0,013	0,012	0,012
		(-2,53)	(-3,13)	(-2,03)	(-2,62)	(-1,30)	(-1,57)	(0,56)	(0,60)
	TAX	0,154***	0,187***	0,100	0,165***	0,183***	0,199***	0,129***	0,110***
		(2,79)	(9,49)	(1,20)	(4,64)	(4,39)	(11,09)	(3,07)	(3,31)
	GROWTH	0,041***	0,042***	0,055***	0,056***	0,025***	0,026***	0,025	0,023
		(5,81)	(6,13)	(3,83)	(3,97)	(2,69)	(4,23)	(0,92)	(1,21)
	Iyear _2000	0,141	0,048	0,263	0,121	0,158	0,083	-0,197	0,020
		(0,83)	(0,75)	(1,41)	(1,48)	(0,72)	(0,86)	(-0,82)	(0,14)
	Iyear _2001	0,009	0,003	0,024	0,010*	-0,002	-0,004	0,003	0,004
		(1,05)	(1,00)	(1,55)	(1,71)	(-0,32)	(-1,08)	(0,28)	(0,38)
	Iyear _2002	0,004	-0,001	0,017	0,006	-0,009*	-0,011***	0,008	0,005
		(0,62)	(-0,51)	(1,58)	(1,21)	(-1,90)	(-3,42)	(0,92)	(0,65)
	Iyear _2003	0,005	-0,001	0,014	0,004	-0,004	-0,007**	0,003	0,001
		(0,84)	(-0,21)	(1,58)	(0,97)	(-1,07)	(-2,38)	(0,31)	(0,05)
	Iyear _2004	0,001	-0,002	0,009	0,003	-0,005	-0,006***	-0,009	-0,008
		(0,32)	(-0,80)	(1,54)	(0,90)	(-1,64)	(-2,70)	(-1,36)	(-1,23)
	Iyear _2005	0,000	-0,001	0,004	0,001	-0,002	-0,002	-0,008*	-0,012***
		(0,09)	(-0,56)	(0,95)	(0,37)	(-0,85)	(-1,19)	(-1,67)	(-2,33)
	Constant	0,106**	0,076**	0,125**	0,059*	0,092*	0,087	0,166*	0,230
		(2,08)	(2,53)	(2,13)	(1,66)	(1,86)	(1,45)	(1,95)	(1,14)
	Observations	10653	10653	5760	5760	4520	4520	373	373
	Number of firm	2240	2240	1241	1241	921	921	78	78
	Sargan statistic	4,68	23,95	4,26	28,64	5,73	13,40	4,25	14,42
	P-value sargan statistic	0,70	0,25	0,75	0,09	0,57	0,86	0,75	0,81
	Arellano-Bond
	test for AR(1)	-9,38	-12,81	-7,17	-9,89	-7,06	-8,48	-2,32	-2,48
	P-value AR(1)	0,00	0,00	0,00	0,00	0,00	0,00	0,02	0,01
	Arellano-Bond
	test for AR(2)	-1,80	-1,90	-0,75	-0,84	-3,22	-2,95	-1,11	0,12
	P-value AR(2)	0,07	0,06	0,46	0,40	0,00	0,00	0,27	0,90
	Notes: ***, ** and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. T-students are provided in
	parentheses. Sargan statistic is a Sargan-Hansen test of overidentifying restrictions. AR (k) is the test for k-th order autocorrelation.
	Estimation by two-step System GMM. Instruments: (DT) delayed t-3 and t 4, (DT * 2) delayed t-3 and t-4, the rest of explanatory
	variables are exogenous.

Table ( 8

 ( ) THE EFFECT OF DEBT ON PROFITABILITY BY SIZE CLASS (DEPENDENTE VARIABLE: ROA) *, ** and * represent statistical significance at the 1%, 5%, and 10% levels, respectively. T-students are provided in parentheses. Sargan statistic is a Sargan-Hansen test of overidentifying restrictions. AR (k) is the test for k-th order autocorrelation.

		(ROA)	TPE	PME	ETI
	DT	-0,114	0,031	-0,136	0,065	-0,107	0,136	0,004	0,086
		(-1,27)	(0,29)	(-1,23)	(0,49)	(-1,26)	(0,77)	(0,04)	(0,13)
	DT*2		-0,043		-0,075		-0,134		-0,149
			(-0,42)		(-0,58)		(-0,86)		(-0,28)
	TANG	-0,019**	-0,016***	-0,020*	-0,024**	-0,015	-0,010	0,007	0,011
		(-2,35)	(-2,87)	(-1,74)	(-2,46)	(-1,41)	(-1,53)	(0,37)	(0,52)
	TAX	0,078	0,127***	0,022	0,095*** 0,112*** 0,144*** 0,170*** 0,141***
		(1,51)	(7,52)	(0,27)	(2,98)	(3,17)	(9,84)	(4,33)	(4,99)
	GROWTH	0,043***	0,042***	0,055*** 0,053*** 0,028*** 0,029***	0,002	0,015
		(6,03)	(6,32)	(3,93)	(4,00)	(2,91)	(4,88)	(0,14)	(1,34)
	Iyear _2000	0,184	0,040	0,273	0,116	0,242	0,105	-0,287*	-0,084
		(1,14)	(0,73)	(1,47)	(1,57)	(1,32)	(1,49)	(-1,67)	(-0,62)
	Iyear _2001	0,013	0,005*	0,023	0,008*	0,006	0,002	0,021**	0,012
		(1,56)	(1,65)	(1,54)	(1,68)	(1,14)	(0,51)	(1,96)	(0,91)
	Iyear _2002	0,007	0,000	0,018*	0,006	-0,004	-0,007**	0,012	0,011
		(1,07)	(-0,04)	(1,67)	(1,52)	(-1,01)	(-2,52)	(1,52)	(1,21)
	Iyear _2003	0,008*	0,003	0,017**	0,007*	0,000	-0,002	0,004	0,001
		(1,68)	(1,19)	(2,02)	(1,88)	(0,12)	(-1,00)	(0,61)	(0,13)
	Iyear _2004	0,004	0,001	0,012**	0,006**	-0,002	-0,004	0,001	-0,004
		(1,37)	(0,49)	(2,17)	(2,06)	(-0,78)	(-1,90)	(0,26)	(-0,65)
	Iyear _2005	0,003	0,002	0,006*	0,004*	0,001	0,000	-0,002	-0,004
		(1,41)	(1,03)	(1,73)	(1,65)	(0,35)	(-0,11)	(-0,44)	(-1,03)
	Constant	0,100**	0,036	0,117**	0,034	0,081*	-0,006	0,038	0,036
		(2,08)	(1,42)	(1,99)	(1,10)	(1,82)	(-0,13)	(0,63)	(0,18)
	Observations	10653	10653	5760	5760	4520	4520	373	373
	Number of firm	2240	2240	1241	1241	921	921	78	78
	Sargan statistic	3,41	14,85	1,93	21,72	4,61	10,59	4,17	22,17
	P-value sargan statistic	0,85	0,79	0,96	0,36	0,71	0,96	0,76	0,33
	Arellano-Bond test for AR(1)	-9,64	-12,79	-7,43	-10,07	-6,65	-8,47	-2,86	-1,94
	P-value AR(1)	0,00	0,00	0,00	0,00	0,00	0,00	0,00	0,05
	Arellano-Bond test for AR(2)	-0,62	-0,69	0,31	0,40	-2,63	-2,67	-1,37	-0,48
	P-value AR(2)	0,53	0,49	0,75	0,69	0,01	0,01	0,17	0,63
	Notes: **


Elie Raad
email: elie.raad@mun.ca

Joerg Evermann
email: jevermann@mun.ca

Is Ontology Alignment like Analogy? -Knowledge Integration with LISA

Keywords: Algorithms Categories and Subject Descriptors H.1.2 [Models and Principles]: User/Machine Systems-human information processing, software psychology, I.2.0 [Artificial Intelligence]: General-cognitive simulation, I.2.4 [Artificial Intelligence]: Knowledge representation formalisms and methods Ontology, Alignment, Analogy, LISA, Cognition

Ontologies are formal descriptions of a domain. With the growth of the semantic web, an increasing number of related ontologies with overlapping domain coverage are available. Their integration requires ontology alignment, a determination of which concepts in a source ontology are like concepts in a target ontology. This paper presents a novel approach to this problem by applying analogical reasoning, an area of cognitive science that has seen much recent work, to the ontology alignment problem. We investigate the performance of the LISA cognitive analogy algorithm and present results that show its performance relative to other algorithms.

INTRODUCTION

Ontologies are explicit specifications of a conceptualization, describe knowledge about a domain [START_REF] Gruber | A translation approach to portable ontology specifications[END_REF], and are a key technology of the semantic web vision. They are typically described using the OWL Web Ontology Language and are intended to facilitate semantic interoperability between parties [START_REF] Hitzler | A reasonable semantic web[END_REF]. However, the distributed nature of the semantic web makes it possible and even likely that multiple parties independently develop ontologies with partially overlapping sets of concepts. While these ontologies may be comparable in their goals, they can vary greatly in the way they define and represent concepts. This variation is due to a variety of factors, ranging from the culture and linguistic particularities to the chosen level of abstraction, the expressiveness of the representation language, and the purpose of the ontology.

In the context of the semantic web, ontology alignment plays a crucial role to integrate different but overlapping ontologies. Ontology alignment attempts to establish correspondences between concepts of different ontologies that are similar in meaning but have different names or structure. We argue that a successful ontology alignment system should derive the same correspondences that a human user would derive 1 . While we explicitly state this argument here, its general acceptance is implicit in the fact that ontology alignment systems are evaluated against reference alignments that are created by humans [START_REF] Evermann | Theories of meaning in schema matching: A review[END_REF].

Existing research in the area of ontology alignment has focused on estimating lexical similarity between concepts (syntactic or semantic similarity), mapping structural correspondences between ontologies (tree-based or graph-based representations), and the role of human users (for assigning matchers' weights, fine-tuning parameters, confirming or rejecting alignment results, etc.) [START_REF] Cruz | Agreementmaker: efficient matching for large real-world schemas and ontologies[END_REF][START_REF] Hong-Hai | Matching large schemas: Approaches and evaluation[END_REF][START_REF] Wei | Matching large ontologies: A divide-and-conquer approach[END_REF][START_REF] Lambrix | SAMBO-A system for aligning and merging biomedical ontologies[END_REF]. While these approaches are based on well justified logical, linguistic, and statistical matchers, they do not explicitly take into account how humans derive correspondences between concepts.

Therefore, this work is an initial, exploratory study on how to develop ontology alignment systems that are explicitly based on human alignment processes. More specifically, we explore whether the cognitive process of analogy making or analogical reasoning can serve as the basis for ontology alignment systems.

The motivation of this work was drawn from the observation that two research domains, the semantic web and cognitive science, have many common elements: in particular the field of entity and/or concept mapping. Previously, this has been studied separately in the two research domains without efforts to bridge the two and transfer findings from cognitive science (analogical reasoning) to semantic web challenges (ontology alignment). Thus, the aim of this work is also to highlight this relationship and bring the work in the cognitive sciences to the attention of semantic web researchers.

Cognitive principles have also recently been applied to database schema matching, a problem similar to ontology alignment. Work in that area has empirically investigated how humans make schema matching decisions [START_REF] Evermann | An exploratory study of database integration processes[END_REF][START_REF] Evermann | Contextual factors in database integration -a delphi study[END_REF] and initial studies show that cognitive principles of similarity can in principle be applied [START_REF] Lukyanenko | A survey of cognitive theories to support data integration[END_REF][START_REF] Evermann | Applying cognitive principles of similarity to data integration-the case of siam[END_REF], but do not yet provide any evaluation of their effectiveness.

While there is a great amount of research on analogical reasoning and numerous computational models have been proposed, this initial exploratory study uses the LISA model [START_REF] Hummel | Distributed representations of structure: A theory of analogical access and mapping[END_REF], which has been shown to produce similar results to human subjects in many exper-imental studies.

The remainder of the paper is structured as follows. Section 2 introduces the cognitive research on analogical reasoning systems. Section 3 presents LISA, the analogical reasoning systems adopted in this research. Section 4 details the framework for implementing the ontology alignment approach using LISA. Section 5 describes our experimental method and results, including a comparison with existing ontology alignment approaches. Section 6 discusses the implications of our results, limitations of the study, and suggests several directions for future research.

ANALOGICAL REASONING

Analogical reasoning is a cognitive process that maps concepts from one domain (the base) to concepts of another domain (the target) and is based on three main principles [START_REF] Gentner | Structure-mapping: A theoretical framework for analogy[END_REF][START_REF] Gentner | Computational models of analogy[END_REF]: one-to-one mapping, parallel connectivity, and systematicity:

• First, humans are shown to construct and to strongly prefer ontologies that place each concept of the base domain in correspondence with at most one object of the target domain.

• Second, analogies become more useful when placing objects of the base domain in correspondence with objects in the target domain by virtue of the objects' structure rather than superficial similarities. This systematicity principle reflects people's perception on interconnected systems of relations. It drives analogies to prefer sets of relations that include common higher-order relations and to map knowledge such that a system of relations that holds among the base objects also holds among the target objects. For example, in the analogy "an electric battery is like a reservoir" there is no resemblance between the objects' surface attributes (e.g., shape, size, color). However, the analogy builds on the fact that both objects store potential energy, i.e. structural similarity.

• Finally, the principle of parallel connectivity states that if two relations are mapped to each other, their objects must also be placed in correspondence. For example, if the predicate stores (reservoir, energy) matches the predicate stores' (electric battery, energy') then reservoir must match electric battery and energy must match energy'.

Reasoning by analogy has received significant attention in cognitive systems research [START_REF] French | The computational modeling of analogy-making[END_REF][START_REF] Krawczyk | Structural constraints and object similarity in analogical mapping and inference[END_REF] and a number of computational models of analogy-making systems have been proposed, implemented, and experimentally evaluated [START_REF] Gentner | Computational models of analogy[END_REF]. We present three approaches that have undergone experimental evaluations and that show they are reasonable approximations for human analogical reasoning, albeit on simple, artificial problems. SME [START_REF] Falkenhainer | The structure-mapping engine: Algorithm and examples[END_REF] is a computational model of the structure-mapping theory of analogy [START_REF] Gentner | Structure-mapping: A theoretical framework for analogy[END_REF]. The domain knowledge in SME is represented using a graph structure where all entities of the domain, as well as their relations, are represented as nodes of the graph. The alignment process is driven by common relations and functions, while attributes are neglected. SME uses a local-to-global alignment process to reflect the cognitive processes during analogy making and begins by matching identical predicates and their associated elements. The resulting local matches are then integrated into structurally consistent clusters. Finally, a global mapping is established by maintaining consistent clusters and merging them into a small number of sets that are maximal in size. SME has been experimentally shown to generate analogies that are good matches to analogies made by human subjects [START_REF] Lovett | Solving geometric analogy problems through two-stage analogical mapping[END_REF]. LISA [START_REF] Hummel | Distributed representations of structure: A theory of analogical access and mapping[END_REF] is a hybrid connectionist and symbolic architecture. The LISA architecture separates the long-term memory (LTM) and the working memory (WM) component, closely reflecting actual cognitive constraints. LISA represents domain knowledge in a hierarchy of propositions, sub-propositions, predicates and objects, and semantic units; the latter are shared between the two analogs. Mirroring synchronous and asynchronous activation in human memory, the driver analog resides in the active memory and controls the sequence of activating ("firing") the propositions. The activation propagates to the semantic units and, because these are shared, to the recipient analog. The resulting patterns of activation determine the correspondence of elements between the two analogs.

SIAM [START_REF] Goldstone | Time course of comparison[END_REF] is a computational model of human similarity judgment. SIAM models the elements of two domains as a network of interconnected nodes that represents all possible feature-to-feature, object-to-object, and role-to-role correspondences. SIAM first computes similarities between the feature nodes. Then, SIAM identifies objects pairs that are consistent with the feature correspondences. Based on the object-object similarities, SIAM calculates the rolerole similarities while maintaining consistency. This process is repeated until the resulting similarity measures have converged.

In this work, we investigate the question whether existing computational models of cognition, specifically those of analogical reasoning, can be used as the basis for ontology alignment. We are particularly interested in exploring the utility of applying analogical reasoning models to the problem of ontology alignment and any of the above computational models could be adapted and used. While SME and LISA have had the greatest success in accounting for the range of phenomena in analogical thinking and learning [START_REF] Gentner | Psychology in cognitive science: 1978-2038[END_REF], in this first paper we focus on LISA.

LEARNING AND INFERENCE WITH SCHEMAS AND ANALOGIES (LISA)

In this paper, we only present a brief overview of the architecture and principles of LISA. More details are provided in the appendix and full documentation is found in [START_REF] Hummel | Distributed representations of structure: A theory of analogical access and mapping[END_REF].

LISA represents knowledge using propositions (P), sub-propositions (SP), predicates and objects, and semantic units. In Figure 1, propositions are shown as ovals (e.g., class(Article, Type)), sub-propositions as rectangles (e.g., article-class1), predicates as triangles (e.g., class1), objects as large circles (e.g., Article), and semantic units as small circles (e.g., magazine). While we realize that the publication domain in this example may be overused and not very interesting, we use it because the OAEI test cases (Section 5) are based on this domain.

The semantic units are shared by the base and target analogs while the remaining elements are local to each analog. Propositions are connected to their sub-propositions, which serve to bind roles (represented by predicates) to their fillers (represented by objects).

Objects and predicates are functionally equivalent within LISA's computational models, but are separated for conceptual clarity. The semantic units in turn are connected to objects and predicates. Not shown in this simple example is the fact that propositions can be used in place of objects to fill roles of sub-propositions, leading to a deeper hierarchical structure. One analog plays the role of driver, the other that of receiver. Figure 2 shows an example of the analogy-making process of LISA between a driver and a recipient analog. The two propositions are #owl:Class (#Article, rdf:#Type) in the driver and #owl:Class (#JournalPaper, rdf:#Type) in the recipient; note the shared semantic units. Propositions in the driver are activated ("firing") and this activation propagates through the two analogs connected by the shared semantic units. When a proposition is fired, it enters the active memory and activates its corresponding role-filler bindings (SPs) and its sub-units in turn. In the example, when the driver activates the proposition #owl:Class (#Article, rdf:#Type), its sub-propositions SP1 (Article and class1) and SP2 (Type and class2) are fired in sequence (i.e. asynchronously). When SP1 is fired, the semantic units connected to its object #Article (magazine, article, instance, not labelled in Figure 2) and predicate class1 (class1, OWL1, not labelled in Figure 2) become active at the same time, i.e. synchronously. Similarly, the semantic units connected to SP2 (Type and class2) are activated upon activation of SP2. Details of this activation propagation algorithm are shown in the appendix.

At the end of the process, a specific activation pattern of semantic units is associated with each fired SP. The analogy result is determined by identifying those recipient units whose connections to the shared semantic units best fits the activation pattern of the driver's units. In Figure 2, the activation pattern of semantic unit results in establishing a mapping between #owl:Class (#Article, rdf:#Type) and #owl:Class (#JournalPaper, rdf:#Type). In LISA, mappings are always between units of the same type (objects to objects, predicates to predicates). Hence, the mapping in the example is established between the objects #Article and #JournalPaper, #Type and #Type, and between the predicates #owl:Class and #owl:Class.

APPLYING LISA TO ONTOLOGY ALIGNMENT

Our framework for using LISA for ontology alignment consists of three components: 1) RDF parser, 2) LISA encoder, and 3) Ontology matcher. Our system accepts as input a source and a target ontology expressed in OWL. To apply LISA, the ontologies must be represented ("encoded") in the form of LISA proposition, subpropositions, objects, predicates, and semantic units as described in Section 3. This encoding admits many design decisions. In this section, we describe the choices we have made and refer the reader to our discussion of future work where we describe plans for exploring this design decision space.

RDF Parser

To represent an OWL ontology as a set of simple propositions, in a form similar to LISA propositions, we first represent the OWL ontology in RDF triples format 2 . Next, the extracted RDF data is represented in the form of N-triples3 , a particular surface grammar for representing RDF triples, to be more easily parsed and transformed to LISA input format. Table 1 shows an example of two OWL statements that are transformed to the N-Triple format.

LISA Encoder

The LISA encoder transforms the N-Triple representations into LISA input files. An RDF statement is a ternary relation between a subject, a predicate, and an object that is similar to a proposition in LISA (although LISA propositions can be of higher arity than three). This suggests an intuitive encoding of RDF subjects as LISA objects, RDF predicates as LISA predicates, and RDF objects as LISA objects. Sub-propositions, while important in the analogymaking process, are not explicitly represented in LISA input.

In our encoding, RDF subjects and RDF objects are represented as LISA objects if the RDF triple has a rdf#type predicate and an owl#class object. In other words, we represent OWL classes as LISA objects. We also encode RDF subjects and objects as LISA objects if the RDF triple has a rdf#type predicate and an object of type owl#ObjectProperty or owl#DatatypeProperty. In other words, we also represent OWL properties as LISA objects. Intuitively, when OWL classes and OWL properties are represented as LISA objects, we can then make statements in LISA about these objects, i.e. LISA propositions, which represent the statements in the OWL ontology about the classes and properties. Table 1 presents two examples, a class and an object property, that are transformed to LISA's input format. The "Defpreds" section of the LISA input defines the predicates and their semantic units, corresponding to the triangles and the small circles in Figure 1. The "Defobjs" section of the LISA input defines the objects and their semantic units, corresponding to the large and small circles shown in Figure 1. Finally, the "Defprops" section of the LISA input defines the propositions of an analog, corresponding to the ellipses in Figure 1. Further details about the LISA input format can be found in [START_REF] Hummel | Distributed representations of structure: A theory of analogical access and mapping[END_REF].

If the RDF triples are not of the above forms, i.e. the triples do not represent an OWL class or OWL property, their subjects and objects are encoded as LISA semantic units. More specifically, the semantic units are generated from RDF triple statements with the following predicates: rdf-schema#label, rdf-schema#comment, rdf-schema#subClassOf. In these cases, we parse the RDF subject and RDF object, i.e. the label or comment, and each parsed element is represented as a LISA semantic unit. Further, the anonymous classes in RDF triple statements may contain descriptions, constraints, and other semantic elements related to the owl#class objects (which are represented as LISA objects). Table 1 shows some cases of different predicates such as rdf-schema#label, rdfschema#comment rdf-schema#range, and rdf-schema#domain that their objects are parsed and encoded as semantic units.

Ontology Matcher

The encoded base and target analogs are then sent to the LISA algorithm presented in Section 3. We use the public version of LISA 4 . The generated alignments are influenced by the order and grouping with which the propositions are fired by the driver analog. To represent human cognitive constraints, only a small number of propositions can be activated together by the driver analog (approximately two to three propositions). In this first exploratory study, we fire propositions individually and in the order in which they are defined in the ontology (and thus appear in the LISA input specification). The exploration of different configurations of LISA is left to future work (Section 6).

In adhering to the main cognitive principles of analogical reasoning, LISA typically emits one-to-one mappings between objects and predicates of the two analogs, and each mapping has a confidence score. In the rare case when LISA emits a many-to-one mapping, we have used only mapping with the highest confidence score. No further post-processing of LISA results is performed.

EXPERIMENTAL EVALUATION

We conducted various experiments to test and evaluate LISA's performance on ontology alignment tasks. We begin by describing our experimental benchmark ontology alignment test set and the evaluation metrics. This is followed by our results and a comparison with existing approaches.

The OAEI 2010 Benchmark Dataset

To evaluate LISA's performance, we used the benchmark tests available from the Ontology Alignment Evaluation Initiative 5 (OAEI). OAEI is a consensus reference test set for evaluating ontology alignment systems. Since 2004, many ontology alignment systems participated in the annual evaluation contests and their performance has been published. We conducted our experiments using the OAEI benchmark series of tests in its 2010 version [START_REF] Euzenat | Results of the ontology alignment evaluation initiative[END_REF]. Detailed descriptions of all tests are found on the OAEI web page.

The reference (and source/base) ontology for the alignment tests has 33 named classes, 24 object properties, 40 data properties, 56 named individuals and 20 anonymous individuals in the academic publications domain. The 1xx set of tests is a simple test where a reference ontology is compared with itself or with its restriction to OWL-Lite. The 2xx set of tests are systematic tests where a reference ontology is compared with various modified versions of itself. The variations are obtained by 1) replacing entities by random strings, synonyms, names with different conventions or names in another language, 2) discarding or modifying comments, instances, properties, 3) suppressing, expanding, or flattening subsumption hierarchies, 4) expanding, replacing, or flattening classes. These two sets of tests are artificial in the sense that the reference alignments are not "created" by humans in the sense that human cognitive analogy processes were at work, but are the result of the specific transformations of the source ontology.

In contrast, the 3xx set of tests includes four real target ontologies, which have been manually aligned with the reference ontology. Thus, the reference alignments for these tests represent the result of human cognitive processes. The target ontologies in the 3xx set of tests comprise four real ontologies: 1) BibTeX/MIT (15 named classes, 40 data properties), 2) BibTeX/UMBC (16 named classes, 6 object properties, 25 data properties), 3) Karlsruhe (56 named classes, 72 object properties), and 4) INRIA (41 named classes, 40 object properties, 11 data properties). One reason for using the 2010 version of the tests is that published results are available for these non-synthetic tests with real ontologies, which have been omitted in later OAEI test suites.

To evaluate the performance of LISA, the alignments for OWL properties and classes are compared to the set of reference alignments using the precision and recall. For space reasons, we report only the composite F-score metric.

Results

Table 2 provides the F-scores and shows that LISA performs well on the 1xx and 2xx sets of tests. The F-scores show that LISA's performance was better than most systems that participated in the OAEI 2010 contest 6 .

The 3xx set of tests is the most relevant to measure the effectiveness of the alignment approaches, as it is the most realistic and, more importantly, the reference alignments are created by humans. The varying F-scores indicate that the slight decrease in recall is compensated by high precision. Over all the 3xx set of tests, LISA performed reasonably well and ranked 6th out of the 12 competing approaches, as illustrated in Figure 3.

A closer look at the tests shows that LISA's performance varies greatly between tests. First, elements such as labels, comments, instances in the ontologies are of considerable importance for LISA to perform well (e.g., test 101, 221, 228). This is not surprising as these elements are parsed to form the semantic units that connect the driver and recipient analog in LISA. Second, LISA did not perform well when the hierarchy of an ontology is flattened (e.g., 5 http://oaei.ontologymatching.org/ test 222, 237, 239, 246). In contrast, when the hierarchy is expanded (test 223), LISA scored well. This suggests that the structural information represented by a class hierarchy is important, as would be expected from the description of LISA earlier. Third, LISA achieved better results when the alignment did not include the alignment of properties, i.e. properties were suppressed (e.g., test 228, 233, 236). Finally, as we expected from our ontology encoding and importance of labels, the performance of LISA in Table 3 on "scrambled" tests (201-202 and 248-266), where concept names or labels are replaced by random strings, was relatively poor. Figure 4 shows the results of each of the test sets for LISA and for all the systems that participated in the 2010 OAEI contest [START_REF] Euzenat | Results of the ontology alignment evaluation initiative[END_REF]. When we compute the average F-scores across all tests for each of the systems, LISA is again ranked 6th out of the 12 systems, as illustrated in Figure 4.

DISCUSSION AND CONCLUSION

This paper has presented an application of LISA, a computational cognitive model of analogical reasoning, to the task of ontology alignment. To our knowledge, this is the first work to use human cognitive analogy-making in the ontology alignment context. This initial, exploratory application was intended to answer the question whether ontology alignments are like analogies. Our results are frequently better than the existing state-of-the-art. However, our approach does not yet dominate other approaches on all tests, especially those with real ontologies for which human reference alignments are available (the OAEI 3xx tests).

In light of this, one could answer our research question in different ways. Pessimistically, the performance of LISA might suggest that ontology alignment is not like making analogies. If it was, LISA should perform better, especially on the OAEI 3xx set of Table 2: Comparing LISA F-scores with systems that participated in the OAEI 2010 contest. tests. However, given that other cognitive models of analogy remain to be explored, we are not yet ready to come to this general conclusion. Perhaps LISA is not the correct model for analogical reasoning; after all, it has only been experimentally tested on small problems. It may be the case that the size of the ontologies in the alignment problems is such that humans use a different strategy than they would on small analogy problems. Hence, the reference alignments generated by humans may be generated by a different process than analogical reasoning. Thus, while LISA may accurately represent analogical reasoning, the task of ontology alignment is not based on analogies and thus the mismatch and relatively low performance on our evaluation. Finally, given the fact that LISA (and our ontology encoding) is highly configurable, perhaps our initial, naive application is inappropriate for the ontology alignment problem. This would suggest that significant further improvements can be achieved with this approach in the future.

T e s t # L I S

A A g r M a k e r A R O M A A S M O V C O D I E f 2 M a t c h F a l c o n G e R M e S M B M a p P S O R i M O M S O B O M T a x
L I S A A g r M a k e r A R O M A A S M O V C O D I E f 2 M a t c
In Section 1 we indicated that there is much variability in the way humans make alignment decisions [START_REF] Evermann | Contextual factors in database integration -a delphi study[END_REF][START_REF] Tordai | Let's agree to disagree: on the evaluation of vocabulary alignment[END_REF], and many times such decisions depend on the context of ontology integration [START_REF] Evermann | Contextual factors in database integration -a delphi study[END_REF]. This however, is an area of research that has not yet received much attention. As we are not aware of how the OAEI 3xx reference alignments are developed, there may be validity problems surrounding this issue in the sense that the reference alignments may be idiosyncratic to some group of people [START_REF] Evermann | Theories of meaning in schema matching: A review[END_REF]. This in turn may be the reason why not only LISA but most other approaches fail to recover the reference alignment: The concept of analogy or similarity held by researchers and encoded in their alignment algorithms does not coincide with the concept of analogy or similarity held by the creator(s) of the reference alignments. Later rounds of the OAEI contest introduced other tests for which human-based reference alignments are available. The performance of LISA on these recent tests remains to be explored.

Our future work will focus on three different avenues for improvement. First, LISA is configurable, for example in terms of the firing order of propositions, the grouping of propositions, etc. Moreover, LISA offers the ability to fire one or more propositions at the same time, as well as to reverse the driver and recipient analogs. Thus, systematic experimental comparisons are required to determine the optimal configuration of LISA for different alignment problems.

Second, the encoding of ontologies in LISA admits many design decisions. For example, we have chosen the intuitive route via an RDF representation of OWL ontologies and a more or less direct mapping to LISA representation elements. Other encodings are possible. For example, many of the OWL constructs that are now encoded as semantic units may be represented as LISA objects in their own right. This would strengthen the structure of the problem representation, yet at the same time reduce the number of semantic units by which activation progresses from driver to recipient. The effect that such a change in encoding might have remains to be explored in systematic experiments.

Third, while LISA has been demonstrably successful in explaining human analogies in the psychology lab, other computational models, such as SME, exist and remain to be explored, each with

T e s t # L I S

A A g r M a k e r A R O M A A S M O V C O D I E f 2 M a t c h F a l c o n G e R M e S M B

APPENDIX

The LISA algorithm is described in Table 4. Knowledge is represented using propositions ("P units"), sub-propositions ("SP units"), predicate and object units, and semantic units as described in Section 3. Each unit in a driver analog can have a mapping relationship and mapping weight with units of the same type in the receiver analog. These mapping relationships are dynamically created. Each unit has an activation value and can receive and transmit "input" to update its activation and that of connected units. The follow paragraphs describe central steps in the algorithm. For formal details, the reader is referred to Appendix A in [START_REF] Hummel | Distributed representations of structure: A theory of analogical access and mapping[END_REF].

Step 2a: Propositions (P units) operate in either parent, child or neutral mode. In parent mode, P units pass activation input to their sub-propositions (SP units). In child mode, P pass activation input to the SP they are part of. In neutral mode, P units pass activation input both upwards and downwards. Initially, P units in the driver analog are in neutral mode, except those actively selected into working memory (step 1), which are in parent mode. P units in the receiver analog update their modes on the basis of their inputs from SP units above and below and inputs from P units in the driver (either in parent or child mode) via mapping connections.

mi =      Parent ifSP ↑ -SP ↓ + P parent -P child > θ Child ifSP ↑ -SP ↓ + P parent -P child < -θ Neutral otherwise
Step 2b: Each SP unit consists of an excitor and an inhibitor unit. Each inhibitor causes the corresponding excitor's activation to oscillate over time. In combination with strong SP-to-SP inhibition, the inhibitors cause separate SPs to fire at different times.

In the driver analog, SP excitors receive excitatory input from P units above (p), inhibitory input from other driver analog SPs ( j ej) with a sensitivity s that decays from a maximum value immediate after an SP fires, and inhibitory input from their own inhibitors (I). The net input is

n = 1 + p - s j ej 1 + NSP -I
where NSP is the number of SPs in the driver with activation > 0.2.

An SP inhibitor receives input only from the corresponding excitor. P units in parent mode receive input from the excitors of the SP units below with net input n = j ej, where ej is the activation of the excitors of SP unit j. P units in child mode, predicate or object units receive input from the excitor and the inhibitor of the SP above with net input n = j (ej -Ij), where Ij is the activation of the inhibitor of SP unit j.

Step 2c: The global inhibitor becomes active whenever all SP excitors in the driver analog have an activation below a certain threshold. When active, it inhibits all units in the recipient analog to inactivity. Table 4: LISA Algorithm from [START_REF] Hummel | Distributed representations of structure: A theory of analogical access and mapping[END_REF] (P = Proposition, SP = Subproposition) Repeat until convergence of mapping weights:

1. Select a set of P units of the driver analog ("phase set PS") 2. Repeatedly update the state of the network in discrete time units t = 1 . . . 220 × |SP|. For each step do:

(a) Update modes of all P units in recipient and driver (b) Update inputs of all units in PS (P, SP, predicate and object units) (c) Update global inhibitor (d) Update inputs to all semantic units (e) Update input to units in recipient (f) Update activation of all units (g) Create mapping connections

Update mapping weights

Step 2d: Semantic units receive weighted input from predicate and object units in both the driver and receiver analog with the net input computed as j ajwij where aj serves to normalize activation to between 0 and 1. Input from the receiver analog occurs only after each SP in the driver has fired at least once.

Step 2e: Units in the recipient analog receive four inputs: withinproposition excitatory input P , within-class inhibitory input C (i.e. SP-to-SP, object-to-object, etc.), out-of-proposition inhibitory input O (i.e. P units inhibit SP units of other P units, and SP units inhibit predicate and object units of other SP units), and both excitatory and inhibitory input via the cross-analog mapping relationships M . The net input is computed as n = P + M -C -πO -πΓ Specific formulas for each of the these components for different kinds of units are given in [START_REF] Hummel | Distributed representations of structure: A theory of analogical access and mapping[END_REF].

Step 2f: At the end of each iteration and after computation of all excitatory and inhibitory input, all units update their activation according to ∆a = γn(1a)δa where γ is a growth rate and δ is a decay rate; n is the net input (excitatory minus inhibitory).

Step 2g: When the activation of a unit in the recipient analog first exceeds 0.5, mapping connections are created between it and units of the same type in the driver analog. These are important for step 7 in the subsequent iteration.

Step 3: Each mapping weight wij is updated, taking into account competing mapping hypotheses and ensuring a 1:1 mapping constraint.

Figure 1 :

 1 Figure 1: Example to illustrate the LISA architecture.

Figure 2 :

 2 Figure 2: Connections between a driver and a recipient analog via shared semantic units.

Figure 3 :

 3 Figure 3: F-scores for the OAEI 3xx tests, comparing LISA with systems that participated in the 2010 OAEI contest.

Figure 4 :

 4 Figure 4: Mean F-scores across all tests, comparing for LISA with systems that participated in the 2010 OAEI contest.

Table 1 :

 1 Example showing the transformation from OWL to N-Triples to LISA format.

		Ontology -Class Example	Ontology -ObjectProperty Example
		<owl:Class rdf:ID="Article">	<owl:ObjectProperty rdf:ID="event">
	OWL	<rdfs:label xml:lang="en">Article</rdfs:label> <rdfs:comment xml:lang="en">An article from a journal or magazine.</rdfs:comment>	<rdfs:domain rdf:resource="#Proceedings"/> <rdfs:range rdf:resource="#Conference" /> <rdfs:label xml:lang="en">event</rdfs:label>
			<rdfs:comment xml:lang="en">The event concerned with
			the proceedings.</rdfs:comment>
			<owl#ObjectProperty>
		<onto.rdf#Article> <rdf#type> <owl#Class> .	<onto.rdf#event> <rdf#type> <owl#ObjectProperty> .
	N-Triples	<onto.rdf#Article> <rdf-schema#label> "Article" . <onto.rdf#event> <rdf-schema#domain> <#Proceedings> . <onto.rdf#Article> <rdf-schema#comment> "An <onto.rdf#event> <rdf-schema#range> <#Conference> . article from a journal or magazine" . <onto.rdf#event> <rdf-schema#label> "event" . <onto.rdf#event> <rdf-schema#comment> "The event
			concerned with the proceedings." .
		AnalogExample -Class and ObjectProperty
		Defpreds // Definition of the predicates and their semantic units (in square brackets).
		class [ class1 OWL1 ] [ class2 OWL2 classes ] ;
		objProperty [ objProperty1 rdfproperty1 ] [ objProperty2 rdfproperty2 ] ;
	LISA	end ; Defobjs // Definition of the objects and their semantic units (following each object). Article magazine article instance ;
		Type instance subject ;
		Prop_#event event concerned proceedings #proceedings #conference ;
		end ;
		DefProps // Definition of the propositions, P1 and P2 in the following.
		P1 class(Article, Type) ;
		P2 objProperty ( Prop_#event Type ) ;
		end ;

Table 3 :

 3 Scrambled tests' F-scores, comparing LISA with systems that participated in the OAEI 2010 contest.

The issue of different humans arriving at different correspondences for the same problem[START_REF] Evermann | Contextual factors in database integration -a delphi study[END_REF]

, 21] is discussed in detail in Section 6.

http://www.w3.org/TR/owl2-mapping-to-rdf/

http://www.w3.org/2001/sw/RDFCore/ntriples/

http://internal.psychology.illinois.edu/ ~jehummel/models.php

Besides improving the performance of cognitive methods for ontology alignment using these approaches, work is also required to investigate the effect of reasoning support. As OWL ontologies admit inferences over the subsumption hierarchy, it is possible to also use inferred subsumption relationships in the ontology alignment algorithm, in addition to those explicitly axiomatized in the ontology. Furthermore, we intend to examine the scalability of LISA to larger ontologies than the OAEI benchmark test cases. A formal complexity analysis is complicated by the fact that LISA is a connectionist architecture with a convergence-based iterative algorithm, so that upper bounds to convergence must be developed, instead of time-complexity results.

In conclusion, our research has not only opened up possibilities for future work in the area, but has also contributed to a theoretical foundation of ontology alignment in the psychology of analogical reasoning. This can provide some guidance for the field of ontology alignment in that results from the ongoing work in cognition may be transferred to improve ontology alignment performance.