IntroductionTraumatic lumbosacral spondylolisthesis is a very uncommon lesion. The literature testifies to this rareness, reporting only 22 cases over the last 50 years [1, 2, 4, 5, 7, 9-11, 13-15, 21, 22]. These include seven cases of pure bilateral dislocation [1,4,5,7,11,15,22]. The specific features of the lesion, as well as the different possible radiographic and clinical findings that characterize it, have encouraged many researchers to attempt to propose possible interpretations of the kinematics of the lesion. PathomechanicsThe mechanics of the lesion, on the basis of its rareness and its association with monolateral fractures of the lumbar transverse apophyses, which occur in a very high percentage of cases, has been the subject of numerous studies, the conclusions of which often appear to disagree.Hyperextension has been pointed to as an efficient traumatic vector [23]; other authors appear to disagree, believing that the main mechanism responsible for the lesion is constituted by the association between hyperflexion, compression and rotation [4,11,21,24], or by the action of the direct traumatic vectors [1,17].In the cases that came to our observation, an accurate history of each patient allowed us to generally reconstruct the dynamics of the trauma. The patient with a "pure" dislocation had undergone sudden hyperflexion of the lumbosacral spine, with his thighs flexed on the pelvis. This had been provoked by doing a somersault in the air and landing on his bottom. In the patient with fracture-dislocation, the main traumatic mechanism had been violent and direct posterior trauma in the lumbar spine (the patient had been thrown from a motorcycle ending up against a pole). This mechanism, in clear contrast to what has been affirmed by Roaf [20], appears to be similar to that described by Beguiristain et al. [1], and it may be likened to an actual lesion caused by the application of shear traumatic vectors. AbstractThe literature reports that traumatic spondylolisthesis of L5 is an uncommon lesion. The authors report their experience of three cases of this particular fracture-dislocation of the lumbosacral spine. They stress the importance of certain radiographic signs in the diagnosis: namely, the presence of unilateral multiple fracture of the transverse lumbar apophysis. As far as the treatment is concerned, they state the need for an open reduction and an internal segmental fixation by posterior approach. A preoperative MRI study appears mandatory in order to evaluate the integrity of the L5-S1 disc. In the event of a traumatic disruption of the disc, they state the importance of posterior interbody fusion by means of a strut graft carved from the ilium or, in case of iliac wing fracture (which is not uncommon in these patients), by means of interbody cages.Key words Lumbosacral spine · Fracture-dislocations · Traumatic L5-S1 spondylolisthesis · Surgical treatment ORIGINAL ARTICLE Eur Spine J (1999) 8 : 290-295

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In this paper we analyze the relationship between cyclic definitions and consistency in GelfondLifschitz's answer sets semantics (originally defined as 'stable model semantics'). This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is given a syntactic characterization. This condition may have a practical importance both for defining new algorithms for checking consistency and computing answer sets, and for improving the existing systems. The approach of this paper is to introduce a new canonical form (to which any logic program can be reduced to), to focus the attention on cyclic dependencies. The technical result is then given in terms of programs in canonical form (canonical programs), without loss of generality: the stable models of any general logic program coincide (up to the language) to those of the corresponding canonical program. The result is based on identifying the cycles contained in the program, showing that stable models of the overall program are composed of stable models of suitable sub-programs, corresponding to the cycles, and on defining the Cycle Graph. Each vertex of this graph corresponds to one cycle, and each edge corresponds to one handle, which is a literal containing an atom that, occurring in both cycles, actually determines a connection between them. In fact, the truth value of the handle in the cycle where it appears as the head of a rule, influences the truth value of the atoms of the cycle(s) where it occurs in the body. We can therefore introduce the concept of a handle path, connecting different cycles. Cycles can be even, if they consist of an even number of rules, or vice versa they can be odd. Problems for consistency, as it is well-known, originate in the odd cycles. If for every odd cycle we can find a handle path with certain properties, then the existence of stable model is guaranteed. We will show that based on this results new classes of consistent programs can be defined, and that cycles and cycle graphs can be generalized to components and component graphs. S. Costantini

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Intraoperative distraction appears to be truly effective in reducing severe lumbosacral olyshtesis in children. Posterior interbody fusion (and eventual sacral dome osteotomy) successfully combines the goals of solid fusion with the requirements of root decompression. No neurologic problems were seen as a consequence of distraction. The solidity of the posterior segmental pedicle instrumentation combined with the anterior strut graft eliminate the need for postoperative casting.

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Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the kernel of the program, is useful for studying existence and number of answer sets. A kernel program is composed of the atoms which are undefined in the Well-founded semantics, which are those that directly affect the existence of answer sets. The body of rules is composed of negative literals only. Thus, the kernel form tends to be significantly more compact than other formulations. Also, it is possible to check consistency of kernel programs in terms of colorings of the Extended Dependency Graph program representation which we previously developed. The second normal form is called 3-kernel. A 3-kernel program is composed of the atoms which are undefined in the Wellfounded semantics. Rules in 3-kernel programs have at most two conditions, and each rule either belongs to a cycle, or defines a connection between cycles. 3-kernel programs may have positive conditions. The 3-kernel normal form is very useful for the static analysis of program consistency, i.e., the syntactic characterization of existence of answer sets. This result can be obtained thanks to a novel graph-like representation of programs, called Cycle Graph which presented in the companion article (Costantini 2004b).