Paul Bedaride
email: paul.bedaride@loria.fr

Loria -Uhp Nancy

-Talaris

Using Description Logics for Recognising Textual Entailment

The aim of this paper is to show how we can handle the Recognising Textual Entailment (RTE) task by using Description Logics (DLs). To do this, we propose a representation of natural language semantics in DLs inspired by existing representations in first-order logic. But our most significant contribution is the definition of two novel inference tasks: A-Box saturation and subgraph detection which are crucial for our approach to RTE.

Introduction

Recognising textual entailment (RTE) is performing the following task: given two texts T 1 and T 2 in natural language, determine if we can infer T 2 from T 1 . As an example consider the three following sentences: A: "Adam has a son who has a son", B: "Adam has an offspring who has an offspring", C: "Adam is a grandfather"

We can infer B from A because a son is an offspring. We can also say that B and C are equivalent because a grandfather is a male who has an offspring who has an offspring and because Adam is a male name. But we cannot infer A from B or C because an offspring can be a son or a daughter.

As we can see, recognising textual entailments is far from trivial, involving many issues that are difficult to solve. The main issue is that natural language is highly expressive. Due to this expressivity, it is possible to express the same meaning in several ways, as in B and C. Furthermore modifying, adding or deleting a word in a sentence can completely change its meaning (e.g., Adam (dis)likes Eve). Another important issue, related to the first, is that there exists a huge number of synsets (i.e., sets of words with the same meaning). It is difficult to exactly map the relation among them (e.g., an offspring is a child) and to represent all background knowledge needed for detecting textual entailment. However, as the RTE task is widely considered to be relevant for such tasks as Question-Answering, information retrieval, multi-document summarization and information extraction, the task has received a great deal of attention in recent years.

Several different approaches to this task have been proposed and some of them have been compared in the RTE Pascal challenge [START_REF] Dagan | The PASCAL Recognising Textual Entailment Challenge[END_REF]. This challenge compares the different approaches using a corpus of annotated pairs of texts, usually referred to as T for Text and H for Hypothesis. For each pair, it is specified whether T entails H or not. One outcome of this comparison is that symbolic methods perform better than statistical methods. Symbolic methods -using techniques and intuitions rooted in semantics, syntax, logic, etc -typically have about 75% accuracy. Statistical methods -based on techniques like n-grams, lexicon, etc -have about 60% accuracy. The method that we describe in this paper is symbolic. It differs from other symbolic methods because it uses Description Logics. The first important reason to choose these logics for the RTE task is that they are decidable and there exists highly optimized reasoners (e.g., RACER [START_REF] Haarslev | Description of the RACER system and its applications[END_REF]) for different inference tasks. Moreover, we can (at least partially) represent background knowledge and the semantic representation of sentences in these logics. Other symbolic techniques which have already been investigated for the RTE task (e.g., lexical alignment to detect synonyms), could perhaps be integrated into our approach, improving the performance, but we are not going to discuss these possibilities here.

As Description Logics (DLs) are the core of our approach to textual entailment, we will start with a very brief introduction to these formalisms. Description Logics are formal languages for knowledge representation. They were inspired by Quillian's semantic network [START_REF] Quillian | Semantic memory[END_REF] and Minsky's frame semantics [START_REF] Minsky | A framework for representing knowledge[END_REF]. DLs classify knowledge in two parts: the T-Box and the A-Box. The T-Box contains terminological information which is general (good for representing background knowledge). The A-Box contains assertions which are specific (good for representing sentences). Another way to see the division between these two kinds of information is to regard the T-Box as rules which govern our world (e.g., laws from physics, chemistry, biology, etc), and the A-Box as depicting the world's individuals (e.g., a table, a chair, a man, etc).

Description Logics employ the notions of concept, role and individual. Concepts are classes of elements and are interpreted as a subset of a given universe. Roles are links between elements and are interpreted as binary relations of a given universe. Individuals are the elements of a given universe.

A knowledge base Σ is a pair T, A . T is the T(erminological)-Box, a finite set of expressions called General Concept Inclusions (CGI) with shape

C 1 ⊑ C 2 where C 1 ,C 2 are concepts. The intended meaning of C 1 ⊑ C 2 is that the set of individuals in C 1 is included in the set of individuals in 2 Paul Bedaride C 2 . C 1 . = C 2 is a notation for C 1 ⊑ C 2 and C 2 ⊑ C 1 .
Formulas of T are also called terminological axioms. A is the A(ssertion)-Box, a finite set of expressions with shape a:C or (a, b):R where C is a concept, R a role and a,b two individuals. The first expression means that the individual a belongs to the set of individuals satisfying C. The second expression means that the relation R holds between a and b. Formulas of A are called assertions.

In the description logic that we used, which is known as ALCI [START_REF]The Description Logic Handbook: Theory, Implementation, and Applications[END_REF], we can form complex concepts from atomics concepts. They can be made up by negation (¬), conjunction (⊓) and disjunction (⊔) of concepts. Roles can either be atomic, or the inverse (R -) of an atomic role. We can also use the universal quantifier (∀ Role.CONCEPT) to form a complex concept which is true for an individual i if all roles Role which have for first argument i, have for second argument an individual for whom CONCEPT is true. The existential counterpart is defined as in first order logic: (∃Role.CONCEPT) ≡ (¬∀Role.¬CONCEPT).

Several reasoning tasks can be handled in DLs once we have defined a knowledge base T, A . For example, instance checking tests if an individual is an instance of a specified concept. Relation checking tests if there exists a relation between two individuals. Knowledge base consistency tests if T, A is consistent. These tasks can be used for defining more complex tasks such as query individuals which find all instances of a concept.

We will define two novel reasoning tasks to use DLs for RTE. The most important of these is the subgraph detection task, which we will discuss in detail later; here we'll introduce the simpler A-Box saturation task. This consists of completing A-Box information according to a given T-Box. Given a knowledge base T, A , we say that A ′ is a saturation if for each individual a, atomic concept C and role R appearing in T, A there is an assertion a:C in A ′ if and only if T, A |= a:C, and an assertion (a, b):R in A ′ if and only if T, A |= (a, b):R.

For example we can have the following T-Box:

T = PARENT . = ∃Parent-of.SOMEONE GRANDFATHER . = ∃Father-of.PARENT
expressing respectively that parent is equivalent to someone who is the parent of someone and grandfather is equivalent to someone who is the father of someone who is a parent. We can also represent the sentence "Adam is the father of someone who is the parent of someone" by the following assertions:

A = a:ADAM, s1:SOMEONE, s2:SOMEONE (a, s1):Father-of, (s1, s2):Parent-of By applying the T-Box to the A-Box we can deduce that s1 is a PARENT thanks to the first rule and that a is a GRANDFATHER thanks to the second rule. If we add the two pieces of information to the A-Box, we obtain a saturated A-Box.

There exist automatic theorem provers for different DLs including ALCI the logic we are going to use. They handle efficiently several reasoning tasks, including instance and relation checking, concept and knowledge base consistency, and getting all instances of a concept. They can also perform A-Box saturation, but the more complex subgraph detection task will require a new algorithm.

Representation of sentences in DLs

To start with, we will explain how the meaning of a sentence can be partially represented as a DL formula. We say partially because the expressivity of DLs is limited and the meaning of a text is complex, so our representation is an approximation of the actual meaning of the text. For instance, many syntactic elements such as articles, quantifiers, and modalities will not be considered in our approach. The sentence "The cat eats an apple", for example, will be approximated by "cat eat apple".

During the definition of our representation we should remember that our final goal is recognising textual entailment, hence we should struggle to have the same representation for the same meaning whenever possible. The main idea of our approach is to represent each sentence by an A-Box, the background knowledge by a T-Box and then to check if the model of the entailed sentence is a subgraph of the graph of the entailing sentence.

We now describe our approach step by step. We first discuss how to represent sentences in DLs. We start by introducing predicate-arguments dependencies, then we discuss modifiers, and we finish by explaining adjectives and negation.

Predicates-arguments dependencies. Our representation of sentences is based on Davidson's semantics [START_REF] Davidson | Essays on Actions and Events[END_REF] which represents events as individuals. For example, the sentence "John loves Mary" is represented by the first order formula love(e) ∧ john(j) ∧ mary(m) ∧ agent(e, j) ∧ patient(e, m). Here e stands for the event of loving, j stands for the individual named John, and m stands for the individuals named Mary. j is the agent of the event e, and m is its patient.

By using Davidson's semantics we only need to use unary or binary predicates. This fits well with our DLs approach by making a correspondence between unary predicates and concepts, and binary predicates and roles. The sentence "John loves Mary" is represented in DL as e:LOVE, j:JOHN, m:MARY, (e, j):Agent, (e, m):Patient.

We have agreed then on a semantic form, but we don't know which set of basic concepts and roles we will use for representing the meaning of words and the relations between words. To define our signature (i.e., the set of basic concepts and roles), we use the linguistic database FrameNet [START_REF] Baker | The Berkeley FrameNet project[END_REF] based on frame semantics. FrameNet is composed of semantic frames which involve frame elements and which are evoked by certain lexical units. For instance, the Commercial transaction frame describes a common situation involving a buyer, a seller, some goods and some money and it is evoked by such words as buy, sell, pay, cost, spend, etc.

To specify the signature which allows us to represent verb semantics, we link the frame semantics to our representation, and we link frames to concepts which represent the sense of verbs, and frame elements to relations which connect verbs to their arguments.

For example, when we want to represent a verb like we start by looking up in FrameNet the corresponding frame. FrameNet tells us that the concept sell is represented by the frame COMMERCIAL TRANSACTION and by the thematic relations Buyer, Seller, Goods and Money. Then for the sentence "Adam buys chocolate in the supermarket for 2 euros", we have the following representation as a DL A-Box: The meaning of a verb can be affected by modifiers (e.g., place, time, manner, etc). For example in the sentence "The dog barks loudly", loudly affects the meaning of bark by adding to it the fact that the sound produced by the bark is noisy. We must be able to say that "The dog barks loudly" entails that "The dog barks" but not the converse. Verbs may have many modifiers of the same type, but this is not a problem with Davidson-style representations. For each modifier we simply conjoin a concept which represents the modifier sense to the A-Box individual corresponding to the verb. For example, the sentence "John bought a car on Monday 8 may at 5pm" has the following representation:

A =    ct:
A =    ct:COMMERCIAL TRANSACTION ⊓ MONDAY ⊓ 8 MAY ⊓ 5PM j:JOHN, c:CAR (ct, j):Buyer, (ct, c):Goods   
Adjectives. In Davidson's approach, adjectives are represented as unary predicates applied to the variable which represents the word to which the adjective is applied. This representation can easily be used in DLs for adjectives that modify nouns; such adjectives are essentially treated in the same way that verb modifiers are. But adjectives can also occur following the copula as in "The cat is big". How do we treat them? As our final goal is to recognize textual entailment, we have to be able to check that "The big cat" is equivalent to "The cat is big".

The simplest way to recognise textual entailment is to have the same representation for the same meaning. We will thus represent adjectives and the verb to be in the same way. That is, for adjectives we add a concept representing the adjective to the event individual which represents the word to which the adjective is applied. And we consider the verb to be as an isolated verb; we don't create any individual for it, but we add to the individual representing the subject of the verb the concept representing the verb's copula. That is, "the big cat" and "the cat is big" will be represented in the same way, by: c:CAT ⊓ BIG.

Negation. Even though, we have negation in our representation language, modeling natural language negation is difficult. The problem is scope. For example, for the sentence "The dog doesn't bark loudly" there are two possible interpretations. In the first interpretation, negation takes narrow scope and applies to loudly. In this reading we mean that the dog barks but that it doesn't bark loudly. In the second interpretation, negation takes wide scope and applies to bark loudly. It means that we don't know if the dog barks, but if it barks it doesn't do it loudly.

Scope is an ubiquitous phenomenon in natural language. Besides negation, it also plays a role for quantifiers and verb arguments (e.g., "John sees the girl with the telescope"). We can try to analyse all possibilities, but this soon leads to an exponential blowup (e.g., two negations in a sentence can give rise to four different interpretations, three negation to eight different meanings, and so on). Moreover, we must have a YES or NO answer for the RTE task, hence what should we do if the possibilities don't all agree?

Our choice of representation for negation is motivated by our mechanism for recognising textual entailment. This mechanism is a mix between logical implication and syntactic similarity. Let's analyse a concrete example. We take the following sentences: (A) "John didn't buy a fruit", (B) "John didn't buy a fruit at midnight", (C) "John didn't buy an apple", and (D) "John didn't buy a big fruit" because they represent the most common kinds of scope negation. With a standard reading of the sentences we are able to detect the following entailments (and only those): (A)⇒(B), (A)⇒(C) and (A)⇒(D).

To detect (A)⇒(B), we must have a logical implication between the negation of the verb (i.e., "buy") and the negation of the verb and its modifiers (i.e., "buy at midnight"). So we must have a scope for the negation on verb and its modifier, because otherwise we won't detect ¬BUY ⊑ ¬(BUY ∧ MIDNIGHT). To detect (A)⇒(C), we must have a logical implication between the concept FRUIT and the concept APPLE. Lexical knowledge will give us the implication APPLE ⊑ FRUIT, but we need the contraposed form ¬FRUIT ⊑ ¬APPLE. So we must have the negation of concepts associated with verb objects to detect this textual entailment. Finally, to detect (A)⇒(D), we must have a logical implication between the negation of the verb arguments (i.e., "fruit") and the negation of the verb arguments and their adjectives. This is similar to the first case, so we have a scope for the negation on the verb arguments and their adjectives ¬(FRUIT ∧ BIG).

Representing knowledge

Now that we have seen how to represent sentences in DLs by encoding them into the A-Box, we will see how we use background knowledge to detect textual entailments such as "a cat eats" ⇒ "an animal eats". The knowledge required to detect this entailment is lexical knowledge which explains that a cat is an animal, thus that the CAT concept is subsumed by the ANIMAL concept.

We use two repositories of lexical knowledge to detect textual entailment. The first is FrameNet, which we already used to represent text with the same meaning in the same way. The second is WordNet [START_REF] Fellbaum | WordNet: An Electronic Lexical Database (Language, Speech, and Communication)[END_REF], which records different lexical relations between synsets, like synonymy, antonymy or hyponymy.

To check that T entails H, we retrieve slt and slh, the synsets list of the words of T and H using WordNet. For each synset st and sh of slt and slh we check if there exists a lexical relation between them. If there exists a synonymy relation between st and sh we add the following CGI to the background knowledge: ST . = SH. If there exists an antonymy relation between st and sh we add the following CGI to the background knowledge: ST ⊑ ¬SH and SH ⊑ ¬ST. And finally for the hyponymy relation we have three different cases. If st is an hyponym of sh then we get the following CGI: SH ⊑ ST. If sh is an hyponym of st then we get ST ⊑ SH. And if sh and st share an hyponym we get ST ⊑ ¬SH and SH ⊑ ¬ST.

For example, to detect the textual entailment "a cat eats" ⇒ "an animal eats" we check lexical relations between senses of cat and animal using WordNet. We get that cat is an hyponym of animal and we obtain the CGI: CAT ⊑ ANIMAL. By applying this CGI to the representation of "a cat eats" we obtain the following saturated A-Box for the sentence "a cat eats":

A = {i:INGESTION, c:CAT ⊓ ANIMAL, (i, c):Ingestor}

Inference detection -Subgraph detection

We have now a way to represent sentences and use background knowledge to detect textual entailment, and this brings us to the second, and more complex, of our novel inference tasks: subgraph detection. It remains to specify how we check if a sentence entails another sentence. To understand what this involves, we must first note that a saturated A-Box can be represented as one or more oriented and labeled graphs (see, for example Figure 1.1). What we call subgraph detection is divided into three steps. First, we create A-Boxes for the pair (T,H). Then we saturate them with the T-Box created Figure 1.1: The graph H is a subgraph of the graph T by using WordNet. Finally we traverse the graphs corresponding to these saturated A-Boxes to check if the second is a subgraph of the first. By doing this we verify if all the information in H is also in T. The algorithm is shown on Figure 1.2.

We need to do this because existing theorem provers for DLs focus on tasks which involve one A-Box and one T-Box. There is no existing tool which handles relations between two DL knowledge bases, and this is what we required for RTE.

To illustrate our algorithm, we use the example in Figure 1.1 which aims to show the entailment between the sentence T:"John buys a cat at the pet shop for 50 euros" and the sentence H:"A shop sells an animal for 50 euros to John". These sentences are represented by the following A-Boxes: Now we need to check whether a graph gh is a subgraph of another graph gt. Our approach is divided in two parts: node checking and arc checking. The first step consists in checking that there exists a function f which links to each node nh of gh a node nt of gt such that the concept associated to nh is subsumed by the concept associated to nt. The next return F a l s e / * t e s t i f w i t h t h i s b i j e c t i o n t h e e n t a i l m e n t i s c o r r e c t * / de f t e s t B i j e c t i o n ( b i j : BIJ ) : BOOL i s fo re a c h ( s r c , t r g , name ) i n h . g e t R e l a t i o n s do : // t e s t a l l r e l a t i o n s i f n ot t . h a s R e l a t i o n ( b i j [ s r c ] , b i j [ t r g ] , name ) then return F a l s e return True . step is to check for each arc a of gh between nodes n1 and n2 if there is an arc between f (n1) and f (n2) in gt which have the same label as a. Now that we know how to check if a graph gh is a subgraph of a graph gt, we will check if the graph of the sentence H is a subgraph of the graph of the sentence T. The first step is to find if there exists a function f . In our example, finding this function is easy, and it is defined like this:

f (ct2) = ct1, f (j2) = j1, f (a2) = c1, f (s2) = ps1, f (
p2) = p1. Now for the second step we must check arcs, and we can see easily that the arcs of the graph of the sentence H exist in the graph of the sentence T via the function f . For instance, the arc Buyer between ct2 and j2 exists between f (ct2 and f (j2), that is to say ct1 and j1.

We have used a simple example, but subgraph checking works with more complex graphs. By more complex graphs we mean graphs containing identically labelled nodes, or more than one relation between two nodes. The limit of our algorithm is when we have existentially quantified information, because in the saturated A-Box we don't expand existentials. So if we compare the saturated A-Boxes of "Adam is the father of someone who is a parent of someone" and "Adam is a grandfather" we will have many nodes in the first sentence and only one in the second. Thus the first sentence implies the second but not the converse.

Tests and Conclusion

To test our algorithm we have made an implementation in Python which uses the DL prover RACER. The application takes a file as input which contains pairs T,H of texts which have been annotated by hand with respect to whether T entails H or not, and it generates the semantics1 by using the C&C Tools and Boxer [START_REF] Curran | Linguistically Motivated Large-Scale NLP with C&C and Boxer[END_REF], and adds the relevant lexical knowledge to detect entailment using WordNet. After computing all this information, it will use the algorithm we describe in the previous section to test if T entail H. We have tested our algorithm on PARC sentence pairs from the University of Illinois at Urbana-Champaign, which contains 76 pairs selected to show relevant issues important to the textual entailment. We can test our implementation on only 75 pairs, as the semantic generation step fails in one of them. We obtain the following results: These tests have shown that what we do works for what we want to do. That is to say, it works for detecting entailments between simple sentences (with verbs, noun, verb modifiers, noun modifiers and negation), with simple lexical knowledge. As we said at the start of the paper, the present system is not intended to handle entailments which need complex knowledge, or entailments which hold due to modality, time expressions, quantification or counting. The incorrect cases in the test set were usually of this kind.

Our approach is limited by the expressivity of our representation, which handles only a tiny fragment of the English language. Due to the expressivity of DLs, some fragments of English will be hard to represent. For instance, modality needs ideas form modal logic to be represented correctly (e.g., "John is an alleged murderer" is represented by the formula john(j) ∧ alleged(murderer(j)) in neo-Davison's semantic). Nevertheless, by using more expressives description logics, we can handle some other fragments, such as articulate connective examples (e.g., "if Mary comes, then John comes too").

Currently we are working on the implementation of a syntactic analyser which translates text into our DL representation by using FrameNet, and testing the use of more expressive logics. For instance, we can use the oneof operator O [START_REF]The Description Logic Handbook: Theory, Implementation, and Applications[END_REF] to have constraints on labelled nodes in terminological axioms. This could be useful for representing sentences with disjunction



  COMMERCIAL TRANSACTION a:ADAM, s:SUPERMARKET, c:CHOCOLATE, p:2 EUROS (ct, a):Buyer, (ct, s):Seller, (ct, c):Goods, (ct, p):Money   Verb modifiers.



  TRANSACTION j1:JOHN, ps1:PET SHOP, c1:CAT, p1:50 EUROS (ct1, j1):Buyer, (ct1, ps1):Seller, (ct1, c1):Goods, (ct1, p1):Money TRANSACTION j2:JOHN, s2:SHOP, a2:ANIMAL, p2:50 EUROS (ct2, j2):Buyer, (ct2, s2):Seller, (ct2, a2):Goods, (ct2, p2):Money We compute the background knowledge for detecting the entailment between these two sentences by using WordNet and we obtain the following T-Box:BK = CAT ⊑ ANIMAL PET SHOP ⊑ SHOP)By applying this background knowledge to the DLs representation of the sentences T and H we obtain the graphs of the Figure1.1.

  deftype BIJ = D i c t : {IND -> IND} deftype UNBIJ = D i c t : {IND -> ( L i s t : IND ) } / * t h e main f u n c t i o n * / de f main ( t :ABOX, h :ABOX) : BOOL i s b i j : BIJ // n o d e s t h a t h a v e j u s t on e c o r r e s p o n d a n c e u n b i j : UNBIJ // n o d e s t h a t h a v e more t h a n on e c o r r e s p o n d a n c e fo re a c h i n d i n h . g e t I n d i v i d u a l s do // g e t b i j and u n b i j i n d s = t . i n d s S a t i s f y i n g ( i n d . c o n c e p t s ) i f l e n ( i n d s )>1 then u n b i j [ i n d ] = i n d s e l i f l e n ( i n d s )==1 then b i j [ i n d ] = i n d s e l s e p r i n t ' ' no c o r r e s p o n d e n c e f o r i n d i v i d u a l ' ' + i n d . name s t o p return t e s t A l l B i j e c t i o n ( b i j , u n b i j ) / * f i n d a l l b i j e c t i o n s and t e s t them * / de f t e s t A l l B i j e c t i o n s ( b i j : BIJ , u n b i j : UNBIJ) : BOOL i s i f l e n ( u n b i j )<=0 then t e s t B i j e c t i o n ( b i j ) // we h a v e a b i j e c t i o n and we t e s t i t e l s e i n d , L i s t [ In d ] = u n b i j . pop fo re a c h i i n L i s t [ In d ] do i f t e s t A l l B i j e c t i o n s ( b i j +( i n d , [ i ] ) , u n b i j ) then return True u n b i j . append ( i n d , L i s d [ In d ] )

Figure 1 . 2 :

 12 Figure 1.2: Algorithm for subgraph detection

At present the system doesn't use FrameNet, and instead we take the verb as concept and basic roles as agent and patient. Becuase of this we will miss converse cases (i.e., to sell and to buy) in our test.

on individuals like "John loves Mary or Jane". We can also use hybrid logics [START_REF] Areces | Hybrid logics[END_REF] as H(@) for having more expressive constraints on labelled nodes, and to represent articulate connectives.


PhD Edith Ribot-Ciscar
email: edith.ribot-ciscar@univ-amu.fr

PhD Jean-Marc Aimonetti

PhD Jean-Philippe Azulay

Sensory training with vibration-induced kinesthetic illusions improves proprioceptive integration in patients with Parkinson's disease

Keywords: proprioception, vibration, illusory movement, training, voluntary movement

The present study investigates whether proprioceptive training, based on kinesthetic illusions, can help in re-educating the processing of muscle proprioceptive input, which is impaired in patients with Parkinson's disease (PD).

The processing of proprioceptive input before and after training was evaluated by determining the error in the amplitude of voluntary dorsiflexion ankle movement (20°), induced by applying a vibration on the tendon of the gastrocnemius-soleus muscle (a vibration-induced movement error).

The training consisted of the subjects focusing their attention upon a series of illusory movements of the ankle.

Eleven PD patients and eleven age-matched control subjects were tested. Before training, vibration reduced dorsiflexion amplitude in controls by 4.3° (P < 0.001); conversely, vibration was inefficient in PD's movement amplitude (reduction of 2.1°, P = 0.20). After training, vibration significantly reduced the estimated movement amplitude in PD patients by 5.3° (P = 0.01). This re-emergence of a vibration-induced error leads us to conclude that proprioceptive training, based on kinesthetic illusions, is a simple means for re-educating the processing of muscle proprioceptive input in PD patients. Such complementary training should be included in rehabilitation programs that presently focus on improving balance and motor performance.

Introduction

Muscle proprioceptive information is known to be of prime importance in the sense of posture and movement, and in the regulation of motor activities [START_REF] Roll | Kinaesthetic role of muscle afferents in man, studied by tendon vibration and microneurography[END_REF][START_REF] Windhorst | Muscle proprioceptive feedback and spinal networks[END_REF]. This peripheral muscle feedback seems to be spared in patients with Parkinson's disease (PD), as found through microneurographic recordings of muscle proprioceptive afferents [START_REF] Hagbarth | Muscle spindle activity in alternating tremor of Parkinsonism and in clonus[END_REF]. By contrast, the central treatment of this sensory feedback is impaired in PD patients as shown, for example, by the higher threshold for detecting passive movements [START_REF] Maschke | Dysfunction of the basal ganglia, but not the cerebellum, impairs kinaesthesia[END_REF][START_REF] Konczak | The perception of passive motion in Parkinson's disease[END_REF], localization errors in hand position matching tasks [START_REF] Lee | Reaching to proprioceptively defined targets in Parkinson's disease: effects of deep brain stimulation therapy[END_REF], and in altered proprioception-related evoked potentials during passive movements [START_REF] Seiss | Proprioceptive sensory function in Parkinson's disease and Huntington's disease: evidence from proprioception-related EEG potentials[END_REF]. Changes in the supraspinal processing of proprioceptive input in PD have been demonstrated by analyzing the effect of mechanical vibration applied to the tendon of a muscle stretched during voluntary movements [START_REF] Rickards | Proprioceptive control of wrist movements in Parkinson's disease. Reduced muscle vibration-induced errors[END_REF][START_REF] Khudados | Proprioceptive regulation of voluntary ankle movements, demonstrated using muscle vibration, is impaired by Parkinson's disease[END_REF].

Vibratory stimulation activates muscle spindle afferents, particularly primary endings [START_REF] Roll | Alteration of proprioceptive messages induced by tendon vibration in man: a microneurographic study[END_REF], where the muscle feedback is not only related to the movement performed, but also to the vibration-induced response. In healthy subjects, this increased feedback changes the sense of movement, where the subject has an impression that the movement was performed at a higher velocity, leading to a reduction in the amplitude of the desired movement and a vibration-induced movement error [START_REF] Capaday | The effects of muscle vibration on the attainment of intended final position during voluntary human arm movements[END_REF][START_REF] Cody | Proprioceptive guidance of human voluntary wrist movements studied using muscle vibration[END_REF].

In PD patients, this vibration-induced error is decreased, which indicates an altered processing of proprioceptive sensory information [START_REF] Rickards | Proprioceptive control of wrist movements in Parkinson's disease. Reduced muscle vibration-induced errors[END_REF][START_REF] Khudados | Proprioceptive regulation of voluntary ankle movements, demonstrated using muscle vibration, is impaired by Parkinson's disease[END_REF]. Changes in the cerebro-basal ganglia loop are thought to be responsible for this altered proprioceptive integration [START_REF] Maschke | Dysfunction of the basal ganglia, but not the cerebellum, impairs kinaesthesia[END_REF]. The defective utilization of such proprioceptive information contributes to the movement issues that characterize this disease, notably in terms of postural control [START_REF] Vaugoyeau | Impaired vertical postural control and proprioceptive integration deficits in Parkinson's disease[END_REF][START_REF] Vaugoyeau | Role of sensory information in the control of postural orientation in Parkinson's disease[END_REF]. Thus, any therapy that could alleviate kinesthetic deficits may be considered important in the treatment of these patients [START_REF] Maschke | The effect of subthalamic nucleus stimulation on kinaesthesia in Parkinson's disease[END_REF]. The present study aimed at improving the integration of muscle proprioceptive inputs by supraspinal structures. For that purpose, PD patients and age-matched healthy subjects completed a training task during which they were asked to focus their attention upon illusory movements that were induced by muscle tendon vibration, in order to identify the illusory direction and velocity. The effect of the training was evaluated by measuring the vibration-induced movement error, as previously described, and we hypothesized that this error would increase after training, only in PD patients, indicating a better use of muscle proprioceptive cues in the perception of ankle movements.

Materials and Methods

Subjects

Eleven patients with PD (range 50-73 years; mean ± SD, 63.2 ± 6.2 years; six females), all of whom had stimulating electrodes implanted bilaterally in the subthalamic nucleus, and 11 healthy subjects with no history of neurological or psychiatric disease (range 55-72 years; mean ± SD, 63.3 ± 4.9 years; four females) participated in this study. All patients were tested on their regular anti-Parkinsonian medications and with the deep brain subthalamic nucleus stimulation turned on, providing optimal conditions to reduce bradykinesia [START_REF] Lee | Reaching to proprioceptively defined targets in Parkinson's disease: effects of deep brain stimulation therapy[END_REF][START_REF] Maschke | The effect of subthalamic nucleus stimulation on kinaesthesia in Parkinson's disease[END_REF]. Details of the clinical characteristics and basic demographics of the PD patients are listed in Table 1. The study was approved by the local ethics committee and all subjects provided their written, informed consent for the participation in the study.

Experimental design and protocol

The subjects lay on their back on a comfortable massage table with their feet unsupported. A goniometer was placed on the left foot in healthy subjects, or the foot on the more severely affected side in PD patients, at the level of the malleolus and a mechanical vibrator was positioned on the distal tendon of the gastrocnemius/soleus (GS) muscles; both were kept in place by means of Velcro elastic bands (Fig. 1). At the beginning of the experiment, the subjects experienced a few trials of vibratory stimulation to familiarize them with the equipment used and the sensations of illusory movement.

The subjects were asked to perform active dorsiflexion movements. The movement was first given to the subjects by the experimenter passively moving the ankle joint. The movement consisted of a dorsiflexion of 20° for 2 s, with a beginning and stop signal given by two warning beeps before returning to the starting angle, which was the subject's own anatomically neutral ankle position. The experimenter imposed the same movement five times and the subjects had to focus on both the amplitude and velocity of the movement. The subjects were then asked to reproduce the same movement as accurately as possible three times, with verbal feedback on their performance. After this stage of motor learning, voluntary movements were performed under their own proprioceptive guidance exclusively and no feedback was given on the performance. Three experimental sessions were run: pre-training, training, and post-training. In all sessions, the subjects were required to keep their eyes closed.

The pre-and post-training sessions consisted in 30 dorsiflexions that were voluntarily performed by the subjects either in the absence (non-vibrated, NV, N=15) or in the presence (vibrated, V, N=15) of GS tendon vibration, and the vibrations were conducted in a random order. During these trials, the end ankle angle reached at the stop auditory cue was measured (see Fig. 1). Data were recorded using a portable PowerLab system (ADInstruments, New Zealand). After each movement, the subjects rested for 30 s.

In the training session, a second vibrator was placed on the tendon of the tibialis anterior (TA) muscle. The subjects were asked to remain totally relaxed and to focus their attention on the sensation of movement. A series of 40 trials were conducted where illusory movements of the ankle were elicited by activating either the GS (N=20) or TA (N=20) vibrating stimulator, in random order.

In 10 of these 20 trials, the GS vibratory stimulation was paired with a slow 1° manual stretching of the GS muscle, by the experimenter, in order to increase the velocity of the sensation of illusory dorsal flexion movement. Likewise, in 10 of the 20 trials with TA vibratory stimulation, a slow 1° manual stretching of the TA muscle was imposed to increase the velocity of the sensation of illusory plantar flexion movement. Immediately after each trial, the subjects were asked to verbally report both movement direction (dorsiflexion or a plantar flexion) and whether the perceived movement was of low (no stretching) or high (with stretching) velocity. All the participants (PD and control) felt clear sensations of illusory movement of the ankle joint and the parameters (direction and velocity) were as expected: a dorsiflexion or a plantar flexion when vibration was applied to the tendon of the GS or TA, respectively. Furthermore, for all the participants (PD and control) the velocity was perceived higher during the trials where a 1° stretching of the vibrated muscle was added.

Mechanical vibration

Vibrations (frequency: 80 Hz; peak-to-peak amplitude: 0.5 mm) were delivered via mechanical vibrators (DC motors with eccentric masses, 1.5 cm in diameter, 4 cm in length, Technoconcept, France).

In the pre-and post-training sessions, during the V trials, vibration lasted for 2s, i.e. the GS vibrator was turned on and off, on the go and stop auditory cues, respectively. In the training session, the GS or TA vibrator was activated during 8 s, i.e. a time sufficient to induce a clear sensation of ankle movement, but not for too long so as to prevent disagreeable sensations such as exaggerated plantar flexion displacements.

Statistics

The movement amplitudes measured without and with vibratory stimulation were compared before and after the training session, using a paired t-test, in each of the patient and healthy subject groups.

As in previous studies [START_REF] Rickards | Proprioceptive control of wrist movements in Parkinson's disease. Reduced muscle vibration-induced errors[END_REF][START_REF] Khudados | Proprioceptive regulation of voluntary ankle movements, demonstrated using muscle vibration, is impaired by Parkinson's disease[END_REF], the vibration induced errors in amplitude were expressed by the ratios of V/NV movement amplitude. The level of significance was set at an alpha of P ≤ 0.05 level (p values are given to three decimal places). Finally, the magnitude of the effect was estimated by calculating Cohen's d, where 0.2 is a small magnitude, 0.5 is a medium magnitude, and 0.8 is a large magnitude effect [START_REF] Cohen | A power primer[END_REF]. Statistical analyses were performed using commercially available statistical software (Statistica, USA).

Results

The results obtained with one PD patient are shown as an example representative of the population, in Figure 2. In the pre-training session, the patient underestimated the amplitude of voluntary ankle dorsiflexion performed, since the movement surpassed the target amplitude (28° ± 7, mean ± SD).

When vibrations were applied to the GS muscle tendon, the amplitude of the voluntary movement decreased slightly (22° ± 8) (Fig. 2A). In the post-training session, the mean movement amplitude decreased, but the movement was nevertheless overestimated (25° ± 2). The application of mechanical vibration on the GS muscle tendon also induced a reduction in the end point (16° ± 5), which was larger than in the pre-training session (Fig. 2B). The results are expressed by a V/NV ratio of 0.78 before training that decreased to 0.64 after training. The results obtained for the whole population of PD patients are reported in Fig. 3. The patients were able to make voluntary dorsiflexion movements on proprioceptive guidance only; however, these movements generally exceeded the required amplitude (28.7° ± 2.1, mean ± SEM). When mechanical vibration was applied to the GS muscle tendon (V trials) the mean amplitude decreased slightly, but it still overshot the target end point (26.6° ± 1.9). Moreover, the amplitude of the movements performed during these V trials did not significantly differ from that measured in the absence of vibration (NV trials, t=1.39, p = 0.196). After the training session, GS vibration caused a significant reduction in the dorsiflexion mean amplitude (21.1 ± 1.9) as compared to either the amplitude in V pre-training trials (t=3.08, p=0.012, d=1.00) or NV post-training trials (t=4.34, p=0.001, d=0.94). Importantly, the mean amplitude in the non-vibrated trials did not differ significantly between the pre-and post-training sessions. The same experiment was run on healthy subjects. On the whole, these age-matched subjects also underestimated the movement amplitude and performed dorsiflexion that reached 26.5° (± 2.1) in the trials without vibratory stimulation. When vibratory stimulation was applied to the tendon of the GS muscle, the mean movement amplitude significantly decreased to 22.2° ± 2.1 (t=6.86, p<0.001, d=0.59). After the training session, the mean movement amplitude with vibratory stimulation (19.0° ± 1.3) was also significantly lower (t=9.86, p<0.001, d=1.04) than that measured without vibration (23.7° ± 1.4). Akin to the PD group, the mean amplitude in the non-vibrated trials did not change significantly, as compared to the pre-training sessions.

As in previous studies, the results can be expressed by the V/NV ratio in both populations of subjects (Fig. 4). For PD patients, the ratio decreased significantly from 0.93±0.04 in the pre-training to 0.81±0.09 in the post-training session (t=4.91, p<0.001, d=1.01), while it remained unchanged in the two sessions (0.83± 0.04 vs 0.80± 0.03) for the control subjects. Moreover, the ratio reached after training in PD patients was not significantly different to the ones measured in the healthy subjects.

Discussion

Assessment of deficits in proprioceptive integration by means of v ibrationinduced movement errors in Parkinson's patients

Proprioceptive information arising from muscle spindles provides a major contribution to our movement sense [START_REF] Roll | Kinaesthetic role of muscle afferents in man, studied by tendon vibration and microneurography[END_REF] and mechanical vibration applied to muscle tendons is known to activate muscle spindle endings strongly, particularly the primary endings [START_REF] Roll | Alteration of proprioceptive messages induced by tendon vibration in man: a microneurographic study[END_REF]. Consequently, applying vibration on the stretched muscle during movement induces an increase in proprioceptive activity [START_REF] Roll | Alteration of proprioceptive messages induced by tendon vibration in man: a microneurographic study[END_REF]. In healthy subjects, this increase in muscle spindle activity is interpreted as if the movement was performed at a higher velocity and this leads to a deceleration and reduced amplitude of the voluntary movement, as compared to the desired movement, i.e. a vibration-induced movement error [START_REF] Capaday | The effects of muscle vibration on the attainment of intended final position during voluntary human arm movements[END_REF][START_REF] Cody | Proprioceptive guidance of human voluntary wrist movements studied using muscle vibration[END_REF]. We observed this phenomenon in the present population of healthy, older subjects, where dorsiflexion movements performed during vibration of the stretched GS muscle were significantly reduced in amplitude. This was because the movements felt like they were of larger amplitude, as compared to movements performed without vibration.

Conversely, in PD patients, movements performed in the presence of vibration of the stretched muscle did not differ significantly from those performed without vibration. This is consistent with previous studies investigating the effect at the level of the ankle joint (9) and the wrist joint [START_REF] Rickards | Proprioceptive control of wrist movements in Parkinson's disease. Reduced muscle vibration-induced errors[END_REF].

Considering that the peripheral sensory inflow coming from muscles appears to be spared in patients with PD (3), the well-documented proprioceptive abnormalities may be of central origin only [START_REF] Conte | Pathophysiology of somatosensory abnormalities in Parkinson disease[END_REF]. This central origin is corroborated by the finding that kinesthetic acuity improves by 20% in patients receiving deep brain stimulation, after a few months of treatment [START_REF] Maschke | The effect of subthalamic nucleus stimulation on kinaesthesia in Parkinson's disease[END_REF][START_REF] Shukla | Long-term subthalamic nucleus stimulation improves sensorimotor integration and proprioception[END_REF], which was also the case for the patients included in the present study. Regarding the probable central origin of the proprioceptive abnormalities in patients with PD, we sought to investigate whether a proprioceptive training based on kinesthetic illusions may improve the processing of proprioceptive inputs and for that purpose we evaluated the changes in the amplitude of the vibration-induced movement errors before and after such training.

Sensations of illusory movements as a means for reeducation in Parkinson's patients

Tendon vibration activates muscle spindle primary endings [START_REF] Roll | Alteration of proprioceptive messages induced by tendon vibration in man: a microneurographic study[END_REF] and the vibration-induced muscle proprioceptive message is interpreted, by subjects at rest with their eyes closed, as a movement that would have stretched the vibrated muscle [START_REF] Roll | Kinaesthetic role of muscle afferents in man, studied by tendon vibration and microneurography[END_REF][START_REF] Goodwin | Proprioceptive illusions induced by muscle vibration: contribution by muscle spindles to perception?[END_REF]. The induction of illusory movement has been demonstrated previously to promote rehabilitation, particularly in the recovery of voluntary movements after experimental limb immobilization. Muscle tendon vibration preserves functioning in central sensorimotor networks, which are normally altered by limb immobilization [START_REF] Roll | Illusory movements prevent cortical disruption caused by immobilization[END_REF]. In the same way, we recently showed that a rehabilitation program based on kinesthetic illusions reduces the deleterious effects of gradual motor impairment in patients suffering from muscular dystrophy [START_REF] Ribot-Ciscar | Functional impact of vibratory proprioceptive assistance in patients with facioscapulohumeral muscular dystrophy[END_REF].

The induction of illusory movement is advantageous as a means of training PD patients, since experiencing these sensations requires them to focus their attention on the muscle proprioceptive information, as the processing of these signals is degraded in PD. This is in contrast to training with passive movements, which involves not only muscle afferent feedback, but other movement-related sensory cues such as cutaneous, joint, and articular ones [START_REF] Aimonetti | Ankle joint movements are encoded by both cutaneous and muscle afferents in humans[END_REF][START_REF] Proske | The proprioceptive senses: their roles in signaling body shape, body position and movement, and muscle force[END_REF]. Furthermore, using microneurography in healthy subjects, we recently showed that muscle spindle activity was modified by descending processes when subjects focused their attention on imposed movements [START_REF] Hospod | Changes in human muscle spindle sensitivity during a proprioceptive attention task[END_REF][START_REF] Ribot-Ciscar | Fusimotor drive may adjust muscle spindle feedback to task requirements in humans[END_REF]. The focusing of attention in patients may thus be a means of optimizing the muscle afferent feedback.

Our proposed rehabilitation program seemed feasible, since it has been shown that vibration-induced illusory movements are normal in PD patients [START_REF] Moore | Vibration-induced illusions of movement are normal in Parkinson's disease: implications for the mechanism of the movement disorder[END_REF]. We confirmed here that all the patients experienced sensations of illusory movements of the ankle that were exactly as expected: the illusion of ankle dorsiflexion or plantar flexion with vibration applied on GS and TA muscles, respectively. Moreover, the velocity of the sensation was reported to increase when a slight stretching of the vibrated muscle was imposed. Therefore, the patients focused on their proprioceptive information, which was the goal of our training.

Increase in vibration-induced movement error following proprioceptive training

Presently, we showed that proprioceptive training increased the amplitude of the vibration-induced movement error significantly, as compared to pre-training in PD patients. Conversely, the ratio V/NV was unchanged in the population of control age-matched subjects, which allows us to conclude that this was not due to effects related to aging. Furthermore, the dorsiflexion movements performed in the absence of vibration (NV trials) did not differ between the pre-and post-training sessions. Therefore, the decrease in the V/NV ratio after training can be interpreted as a reduction in the amplitude of the movement performed during vibration. These results signify that proprioceptive training changed the processing of proprioceptive inputs in PD patients.

Previous studies have showed clinical and functional benefits in PD patients following a rehabilitation program, designed to have participants focus on proprioceptive feedback during physical exercises [START_REF] Sage | Symptom and gait changes after sensory attention focused exercise vs aerobic training in Parkinson's disease[END_REF][START_REF] Sage | A positive influence of vision on motor symptoms during sensory attention focused exercise for Parkinson's disease[END_REF][START_REF] Lefaivre | Can sensory attention focused exercise facilitate the utilization of proprioception for improved balance control in PD? Gait Posture[END_REF]. In these previous findings, the use of proprioceptive cues was reinforced by asking the participants to keep their eyes closed and to focus attention on specific portions of actual exercises. Therefore, the sensory feedback accentuated in these studies might have been from vestibular, cutaneous and/or muscular systems, and the physical exercise may have played a role in the described improvements. In the present study, we showed that specifically targeting the muscle sensory system, the sensitivity of which is known to increase with focusing attention [START_REF] Hospod | Changes in human muscle spindle sensitivity during a proprioceptive attention task[END_REF][START_REF] Ribot-Ciscar | Fusimotor drive may adjust muscle spindle feedback to task requirements in humans[END_REF], is suitable for the rehabilitation of the processing of muscle proprioceptive inputs. Cortical plasticity may allow such sensory input to bypass the dysfunctional basal ganglia, as has been previously suggested [START_REF] Sage | Symptom and gait changes after sensory attention focused exercise vs aerobic training in Parkinson's disease[END_REF]. Furthermore, we found a significant improvement with a single training session; further investigation. Impairments in muscle sensory integration is, at least partly, responsible for motor symptoms in PD, such as impaired balance [START_REF] Vaugoyeau | Impaired vertical postural control and proprioceptive integration deficits in Parkinson's disease[END_REF] and there is increasing evidence of the beneficial effects of exercise on motor performance in PD patients [START_REF] Ebersbach | Parkinson disease: Exercise matters in patients with PD-another piece of evidence[END_REF]. Therefore, among the rehabilitation programs available, proprioceptive training based on kinesthetic illusions may have a number of benefits: it is neither painful nor fatiguing, and its recreational nature may enhance the patient compliance with the treatment.

To conclude, proprioceptive training appears as a simple means to improve the processing of muscle proprioceptive inputs in PD patients. The duration of the improvement should be evaluated in further experiments, as well as its impact regarding posture and locomotion.

Fig. 1 :

 1 Fig. 1: Diagram of the experiment.

Fig. 2 :

 2 Fig. 2: Effect of the proprioceptive training on vibration-induced movement errors in a patient with Parkinson's disease. The figure illustrates the averaged trajectory of 15 dorsiflexion movements with (continuous lines) and without (dotted lines) vibratory stimulation applied to the tendon of the Gastrocnemius Soleus muscle, before (A) and after the training (B). The arrow labelled Go indicates the timing of the first auditory cue to begin movement. Note the increase in the difference in amplitude between the two curves after training.

Fig. 3 :

 3 Fig. 3: Mean amplitudes (± SEM) of dorsiflexion movements recorded for the population of patients with Parkinson' disease without (open bar) and with vibratory stimulation (grey bar) applied to the tendon of the Gastrocnemius Soleus muscle. Pretraining are uniform colors and post-training are hashed colors. * Significant difference at P < 0.001.

Fig. 4 :

 4 Fig. 4: Mean vibratory/non-vibratory (V/NV) movement amplitude ratios calculated in patients with Parkinson's disease (grey) and healthy subjects (black) in the pre-training (uniform colors) and post-training (hashed colors) sessions.

Table 1

 1

	Patient	Age (years)	Gender	More affected foot	Disease duration (years)	STN-DBS duration (months)	UPDRS III on on
	1	62	F	R	16	6	15
	2	70	M	R	10	6	10
	3	56	F	L	11	6	7
	4	64	M	L	7	12	9
	5	61	F	L	7	36	13
	6	66	F	L	5	3	7
	7	73	F	L	11	36	20
	8	63	M	L	10	12	13
	9	65	M	L	13	12	17
	10	50	M	L	9	3	9
	11	65	F	R	9	36	6

…  With dopa and during stimluation on STN-DBS: subthalamic nucleus deep brain stimulation UPDRS: unified Parkinson disease rating scale Patient characteristics

Acknowledgements

We are grateful to Elia Gomez and Jean-Paul Beaulieu for their help during the preliminary experiments and to Dr Rochelle Ackerley for improving the English. This work was supported by Centre National de La Recherche Scientifique and Aix-Marseille University grants.