*2.4. 3/2-Institutions*

The concept of 3/2-institution has been introduced in [13]. Our presentation of 3/2 institutions follows that paper. A *3/2-institution* I = (*Sign*I , *Sen*I , *Mod*I , |=I ) consists of

Such that for each morphism *ϕ* ∈ *Sign*I , the *satisfaction condition*

$$M' \stackrel{\mathcal{T}}{=}\_{\varrho \Box} \operatorname{Sen}^{\mathcal{T}}(\varrho)\rho \quad \text{if and only if} \quad M \stackrel{\mathcal{T}}{=}\_{\Box \varrho} \rho \tag{5}$$

holds for each *M* ∈ |*Mod*I (*ϕ*✷)|, each *M* ∈ |*Mod*I (*ϕ*)*M* |, and each *ρ* ∈ dom(*Sen*I (*ϕ*)).

The difference between 3/2-institutions and ordinary institutions, from now on called *1-institutions*, is determined by the 3/2-categorical structure of the signature morphisms which propagates to the sentence and to the model functors. Consequently, the satisfaction condition (5) takes an appropriate format. Thus, for each signature morphism *ϕ*, its corresponding sentence translation *Sen*(*ϕ*) is a partial function *Sen*(✷*ϕ*) → *Sen*(*ϕ*✷) and, moreover, whenever *ϕ* ≤ *θ*, we have that *Sen*(*ϕ*) ⊆ *Sen*(*θ*). The sentence functor *Sen* can be either lax or oplax, and depending on how this is, we may call the respective 3/2-institution a *lax* or *oplax 3/2-institution*. In many concrete situations, it happens that *Sen* is strict, while some general results require it to be either lax, oplax or strict.

The model reduct *Mod*(*ϕ*) is a lax functor *Mod*(*ϕ*✷) → P*Mod*(✷*ϕ*), implying that for each Σ -model *M* we have a *class of reducts M* rather than a single reduct. In concrete examples, this is a direct consequence of the partiality of *ϕ*: in the reducts, the interpretation of the symbols on which *ϕ* is not defined is unconstrained, therefore there may be many possibilities for their interpretations. "Many" here includes also the case when there is no interpretation.

$$\operatorname{Mod}(\mathfrak{q})(\operatorname{Mod}(\mathfrak{q}')\operatorname{M}^{\prime\prime}) \subseteq \operatorname{Mod}(\mathfrak{q};\mathfrak{q}')\operatorname{M}^{\prime\prime}$$

and for each signature Σ and for each Σ-model *M* that

$$M \in \operatorname{Mod}(\mathbf{1}\_{\Sigma})M.$$

– The lax aspect of the reduct functors *Mod*(*ϕ*) means that for model homomorphisms *h*1, *h*2, such that *h*1✷ = ✷*h*2, we have that

$$\operatorname{Mod}(\mathfrak{q})(h\_1); \operatorname{Mod}(\mathfrak{q})(h\_2) \subseteq \operatorname{Mod}(\mathfrak{q})(h\_1; h\_2)$$

and for each *M* ∈ *Mod*(*ϕ*✷) and each *M* ∈ *Mod*(*ϕ*)*M* that

$$1\_M \in \operatorname{Mod}(\mathfrak{q}) 1\_{M'}.$$

The model homomorphisms do not yet play any role in conceptual blending or in other envisaged applications of 3/2-institutions. Hence, the lax aspect of model functors is for the moment a purely theoretical feature which is, however, supported naturally by all examples. Another technical note: according to the definition of 3/2-institutions. At the abstract level, there are several implicit ways to consider the "totality" of signature morphisms in terms of their syntactic and semantic effects. The following concepts have been introduced in [13]. A signature morphism *ϕ* in a 3/2-institution

$$\mathcal{Mod}(\varrho); \mathcal{Mod}(\theta) = \mathcal{Mod}(\theta; \varrho).$$

In general, in many concrete situations of interest, a signature morphism is *Mod*-strict whenever it is total. In [13], there is even a result of a general nature that supports this fact.

The seminal paper [13] presents in detail a series of examples of 3/2-institutions. Here, we recall from there three classes of examples in a very succinct form.


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**14**

*USA*

**Refractory Stress Urinary Incontinence**

Treatment of stress urinary incontinence (SUI) caused by urethral hypermobility or intrinsic sphincter deficiency with urethral sling procedures may yield up to a 80-90% success rate depending on the definition of success. (Nilsson et al. 2001; Liapis et al. 2002; Rodriguez & Raz 2003; Nilsson et al. 2004; Ward & Hilton 2004) In a minority of patients, however, there is persistence or worse incontinence after surgical therapy. In the general population, risk factors for midurethral sling (MUS) failure are BMI >25, mixed incontinence, intrinsic sphincter deficiency, diabetes mellitus, advanced patient age >75 years old and prior continence surgery. (Cammu et al. 2009; Stav et al. 2010) Potential surgery related reasons for failure include improper adjustment of the sling or misplacement of the suburethral tape. Female patients with urethral incompetence and severe incontinence due to multiple failed surgeries,

Patients with neurologic conditions have sacral arc lesions with paralysis of the skeletal musculature and an open urethra. All other patients who have failed multiple sling and anti-incontinence procedures may have severe symptoms of SUI and an open urethra with a low valsalva leak point pressure. These patients often have an incompetent, difficult to compress, urethra likely due to a combination of urethral denervation, and violation of the periurethral fascia, as well as their underlying risk factors for SUI. (Bump & Norton 1998) These patients have been shown to have low chances of cure after repeat anti-incontinence surgery and be more likely to suffer from complications including retention, osteomyelitis,

In the recurrent or refractory stress urinary incontinence female patient, a routine sling procedure providing only posterior support will not typically yield an appropriate response. Management options include repeat placement of a "tight" pubovaginal sling or replacement of a different type of sling, a spiral sling, periurethral bulking agents, adjustable continence therapy (ACT) device and the artificial urinary sphincter (AUS) prior to bladder neck closure with continent urinary diversion. This manuscript will review the evaluation and management options for recurrent stress urinary incontinence in this

There are a significant number of patients in the United States that undergo successful sling placement for SUI, however a minority will present with persistent or recurrent

neurologic injury, or congenital anomalies represent a unique surgical challenge.

**1. Introduction**

and pelvic abscess. (Petrou & Frank 2001)

challenging population.

**2. Evaluation**

Sara M. Lenherr and Arthur P. Mourtzinos *Lahey Clinic Medical Center, Department of Urology*