Representation theorems, similar to their counterparts, categoricity theorems, establish an isomorphism between certain algebraic systems. However, in contrast to categoricity theorems, they have received considerably less attention in the philosophy of mathematics. The paper attempts to rectify this shortcoming by excavating the philosophical potential of representation theorems through an analysis of one of their most popular interpretations in the mathematical literature, the completeness interpretation. The meaning of this notion of completeness and the mechanism through which representation theorems are supposed to achieve it are still unclear. The paper addresses both issues. First, it proposes a definition of completeness that best suits the informal notion used in the mathematical interpretation of the theorems. Second, it formally details the mechanism responsible for achieving it. In the process, I’ll issue some remarks on the significance and relevance of the formal reconstruction of the completeness interpretation for non-eliminative structuralism. For exegetical as well as evidential reasons, I’ll focus on Cayley’s representation theorem and use it as a case study.

This study examines how the values of authenticity and integrity can be integrated into territorial and landscape planning, moving beyond a restoration-based view of heritage. It focuses on the defensive architecture system of Castellón province (Spain), which features around 150 fortifications forming a continuous landscape between coastal and inland areas. In a context of urban pressure, rural depopulation, and heritage tourism, this research explores how the management of these assets can be aligned with coherent territorial strategies. The aim is to assess the material, visual, and symbolic coherence of the system and to understand the tensions between physical conservation, cultural authenticity, and landscape transformation. The methodology combines documentary review, spatial analysis using GIS, and fieldwork, applying qualitative indicators of material authenticity, territorial integrity, and scenic value adapted from ICOMOS guidance and established scientific literature. The results reveal a clear contrast: 62% of urban castles are restored or consolidated, while 71% of rural ones remain in ruins, and 82% preserve high visual integrity. This paradox shows that heritage sustainability is less dependent on formal reconstruction (only 14% are fully restored) than on maintaining relationships between architecture, environment, and community. This study proposes an integrated territorial management approach that links conservation, use, and landscape as interdependent components of a single cultural system.

The subject of the research is the expression of local cultural heritage elements in the visual system of the city brand and the methods of their visual translation. The object of the research is the elements of cultural heritage in the visual system of the city brand. Unlike the author's previous publication in the journal, this paper proposes for discussion a three-level way of expression: "cultural purification - form reconstruction - visual communication". Three translation methods are analyzed in detail: purification and recoding of symbols, pattern deconstruction and rhythm reorganization, as well as reconstruction and symbolization of the regional color spectrum. This study is devoted to the artistic expression of local cultural heritage in the design of visual elements of the city brand and substantiates how cultural symbols are translated into the image of the city. A method is used that combines theoretical research with case studies: collection and analysis of successful practices (Bishan, Luduan, Yunnan). Also semiotic analysis: interpretation of cultural symbols through the prism of the theory of signs (for example: Nuo masks as signs of ritual heritage). Visual Analysis of the Rhythm of Luduan Ornaments: A Field Study at the Stage of “Cultural Purification”. The study found that traditional cultural resources not only strengthen the recognition of urban culture through scientific visual reconstruction, but also expand the communication path of the brand system. This article provides a theoretical basis and methodological recommendations for the visual construction of urban brands, and considers a project path that can expand the possibilities of modern expression of cultural heritage. The scientific novelty of the study lies in overcoming the traditional linear model of “element extraction - simple application” by integrating three interrelated processes: decoding the cultural core, modern design reconstruction and optimization of communicative efficiency. The author develops a three-stage visual model (“cultural purification - formal reconstruction - visual communication”) that systematizes the logic of heritage transmission in urban branding, and also proposes three specific methods - symbolic purification, ornament restructuring and color adaptation - to improve the efficiency and applicability of the theory. Four principles of visual strategy are formulated: simplification, semantic consistency, modern aesthetics and systemic unity. Recommendations are given for integrating cultural heritage into visual systems of different types of city brands.

Although formal logics are supposed to express some aspects of human thinking, none of them achieve the desired success. These failures sometimes cause - at conferences - voices of resignation claiming that logic is not a science whose object is human thinking. And yet Aristotle considered logic to be an organon, or tool for practicing other sciences. Accepting this point of view, the present paper starts from the assumption that the main incompatibilities of formal logics with our thinking are due to the fact that the implications defined in these logics are very distant in nature from the conditional we use in everyday thinking. Our paper presents two proposals to formalize conditional in such a way that both they and the inferences defined by them do not have properties alien to our thinking. To achieve this goal, we make the assumption that the content of sentences must play a fundamental role in the formal reconstruction of both implication and inference. An essential idea of our approach is that the truth of a conditional is grounded in the inference relation between antecedent and consequent, and more precisely, it should depend on the possibility or impossibility of deriving a contradiction from acceptance and/or rejection of the antecedent and consequent content – an approach characteristic for inferentialism. Since the essence of the paper is a conditional, propositional logic is a sufficient field of consideration.

ABSTRACTThe floods in Western Europe in July 2021 demonstrated the diverse ways and varying paces at which neighborhoods recover from disasters. Based on two exemplary neighborhoods affected by the floods in the city of Hagen, Germany, this study examines the reconstruction process, highlighting the influence of social vulnerabilities and community resilience on private reconstruction processes. Despite differing contexts, both case studies demonstrated a significant reliance on external support during reconstruction. Individual needs varied based on social vulnerabilities within and between population groups, primarily manifesting as challenges in information dissemination and access to support services like funding and expertise. The findings reveal differences in the ability and capacity of neighborhoods to collectively address these vulnerabilities. While small neighborhood networks effectively facilitated information sharing in both cases, one case study relied more heavily on external assistance from nonprofit organizations for larger and longer‐term community‐driven initiatives. The study underscores the need for improvements in postdisaster reconstruction governance. Public authorities predominantly view neighborhoods as recipients rather than partners in the reconstruction process, without adequately addressing their social vulnerabilities within their governance approaches. Supporting local social infrastructures is crucial, as they connect formal reconstruction with the neighborhood, aiding resource access and resilience building.

Abstract This study addresses the often underestimated importance of physical dimensions and units in the formal reconstruction of physical theories, focusing on structuralist approaches that use the concept of “species of structure” as a meta-mathematical tool. Similar approaches also play a role in current philosophical debates on the metaphysical status of physical quantities. Our approach builds on an earlier proposal by Terence Tao. It involves the representation of fundamental physical quantities by one-dimensional real ordered vector spaces, while derived quantities are formulated using concepts from linear algebra, e.g. tensor products and dual spaces. As an introduction, the theory of Ohm’s law is considered. We then formulate a reconstruction of the calculus of physical dimensions, including Buckingham’s $$\Pi$$ Π -theorem. Furthermore, an application of this method to the Newtonian theory of gravitating systems consisting of point particles is demonstrated, emphasizing the role of the automorphism group and its physical interpretations.

The article discusses the broadly understood issue of food in the castle in Sieradz in the 16th century - 1st half of the 17th century, which was the capital seat of the county – starosty (Polish: starostwo) and also land, and later of the Sieradz voivodeship, an administrative and economic centre headed by startoste (Polish: starosta) – an official appointed for life by the king. Although the castle was destroyed about 200 years ago, its form and many aspects of everyday life are perfectly legible in the light of numerous archival written sources and, to a lesser extent, archaeological evidence, which allows for its analysis in the historical context of ‘food studies.’ They enable us to determine the location and formal reconstruction of places where food products were processed and stored (larder, kitchen, bakery, brewery, breeding and cultivation areas), make an attempt to recreate the inventory of the objects collected in these places, and capture the dynamics of the accompanying changes. An attempt was also made to hypothetically reconstruct the dishes and places where they were served, and the groups of people who consumed them. This enabled us to notice social stratification manifested in the standards of food and the conditions of its consumption.

We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is applied in an exemplary manner to a coherent and comprehensive formal reconstruction and analysis of historical proofs of a widely-studied problem due to Łukasiewicz. The underlying approach opens the door towards new systematic ways of generating lemmas in the course of proof search to the effects of reducing the search effort and finding shorter proofs. Among the numerous reported experiments along this line, a proof of Łukasiewicz ’s problem was automatically discovered that is much shorter than any proof found before by man or machine.

In this paper, I present a formal reconstruction of the classical argument for fatalism set forth by Aristotle in On Interpretation 9. From there, I expose two different formal solutions for avoiding the unwanted conclusion based on the traditional interpretation of Aristotle’s rejection of the Principle of Bivalence: On the one hand, Łukasiewicz's three-valued logic and, on the other hand, supervaluation semantics. I also address some criticisms made against these two proposals. To finish, I remark on some alternative interpretations of Aristotle’s intentions maintaining that the Stagirite philosopher rejected fatalism without abandoning the Principle of Bivalence.

IntroductionThe use of the dorsal hamate as a free osteochondral bone graft or vascularized bone flap has become the mainstay for large, comminuted middle phalanx volar lip fractures. To date, few studies have been conducted in the assessment of donor site morbidity for the hemi-hamate graft or flap, and none have discussed modes of repair or reconstruction of this donor site. MethodsA retrospective analysis of 14 hemi-hamate arthroplasty (HHA) procedures, including 6 vascularized and 8 non-vascularized grafts, from two surgeons was performed. Four hamate defect reconstruction techniques were utilized: no formal reconstruction, autologous bone grafting, gel foam, or synthetic bone substitute. The dorsal capsule was repaired with either extensor retinaculum grafting or by direct closure. Wrist range of motion, pain scores, and radiographic alignment were assessed. ResultsAt 6 months follow-up, all patients achieved full, pain-free wrist motion compared to the uninjured side, with visual analog scale pain scores of 0. Serial radiographs showed maintained carpal alignment without instability or subluxation. No differences based on the hamate defect reconstruction method or capsular repair technique was demonstrated. ConclusionSafe return to pain free, unrestricted wrist function is achievable after HHA, regardless of hamate donor site management. Adequate dorsal capsular repair appears critical to prevent instability. Further study is needed to compare techniques, but choice may be guided by surgeon preference in the absence of clear evidence.

Abstract One of Berkeley's best-known arguments for the view that there are no material objects is the so-called Master Argument. There are several good critical discussions of it. That invites the question: is there anything new to say? Well, it will be argued, there are a few things to say. First, although refutations by logical analogy have been advanced against the Master Argument, the strongest such refutation, one which demonstrates its incoherence, has not been. It is here. Second, there are few formal reconstructions of the Master Argument – the great majority of discussions treat it discursively – but a formal reconstruction, and one not found elsewhere, is offered here. Third, the formal reconstruction makes possible identification of the essential mistake of the argument. That mistake is equivocation. The common complaint that Berkeley illicitly introduces the act of conceiving into the content of the concept conceived is not quite correct; but to the extent that it is correct, it's explicable in terms of an underlying equivocation. Fourth, the article presupposes no acquaintance with Berkeley's work and is written in a conversational, easy-to-read style. Given that Berkeley himself wrote in a similar style, he could at least agree that the fourth point is a merit of the article.

The sacroiliac joint (SIJ) is the only mechanical connection between the axial skeleton and lower limbs. Following iliosacral resection, there is debate on whether reconstruction of the joint is necessary. There is a paucity of data comparing the outcomes of patients undergoing reconstruction and those who are not formally reconstructed. A total of 60 patients (25 females, 35 males; mean age 39 years (SD 18)) undergoing iliosacral resection were reviewed. Most resections were performed for primary malignant tumours (n = 54; 90%). The mean follow-up for surviving patients was nine years (2 to 19). Overall, 27 patients (45%) were reconstructed, while 33 (55%) had no formal reconstruction. There was no difference in the use of chemotherapy (p = 1.000) or radiotherapy (p = 0.292) between the groups. Patients with no reconstruction had a mean larger tumour (11 cm (SD 5) vs 8 cm (SD 4); p = 0.014), mean shorter operating times (664 mins (SD 195) vs 1,324 mins (SD 381); p = 0.012), and required fewer blood units (8 (SD 7) vs 14 (SD 11); p = 0.012). Patients undergoing a reconstruction were more likely to have a deep infection (48% vs 12%; p = 0.003). Nine reconstructed patients had a hardware failure, with five requiring revision. Postoperatively 55 (92%) patients were ambulatory, with no difference in the proportion of ambulatory patients (89% vs 94%; p = 0.649) or mean Musculoskeletal Tumor Society Score (59% vs 65%; p = 0.349) score between patients who did or did not have a reconstruction. The ten-year disease-specific survival was 69%, with no difference between patients who were reconstructed and those who were not (78% vs 45%; p = 0.316). There was no difference in the rate of metastasis between the two groups (hazard ratio (HR) 2.78; p = 0.102). Our results demonstrate that SIJ reconstruction is associated with longer operating times, greater need for blood transfusion, and more postoperative infections, without any improvement in functional outcomes when compared to patients who did not have formal SIJ reconstruction.

The problem of identity is central to epistemic transference. However, relative identity appears to be the only way to work out an epistemic useful notion of identity. Relative identity, on its part, is either parasitic on strict identity or not identity at all. If, on the contrary, we ought for a strict concept of identity capable of satisfying its requirements, we end up with a tautologic and epistemic worthless category. The paper provides an answer to this problem, which, while working with a strict notion, shows how it might still serve epistemic purposes. In doing so, it shows how a formal reconstruction of our objectual world and the identities we refer to poses a workable model upon which our messy epistemic one acquires stability. The paper focuses primarily on the Geach-Quine discussion on identity.

Abstract Fairness in machine learning is of considerable interest in recent years owing to the propensity of algorithms trained on historical data to amplify and perpetuate historical biases. In this paper, we argue for a formal reconstruction of fairness definitions, not so much to replace existing definitions but to ground their application in an epistemic setting and allow for rich environmental modeling. Consequently we look into three notions: fairness through unawareness, demographic parity and counterfactual fairness, and formalize these in the epistemic situation calculus.

AB097. SOH23ABS_156. An observational study looking at speech and swallow outcomes following formal free flap reconstruction versus no formal reconstruction in oral cavity cancer

IntroductionResection of the mandible and temporomandibular joint (TMJ) without formal reconstruction is a devastating condition that negatively affects all aspects of the patient’s life. We have approached the reconstruction of mandibular defects that include the condyle with simultaneous reconstruction with a vascularized free fibular flap (FFF) using Surgical Design and Simulation (SDS) and alloplastic TMJ prosthesis. The objective of this study is to report the functional and quality of life (QOL) outcomes in a cohort of patients that had undergone our reconstructive protocol.MethodsThis was a prospective case series of adult patients that underwent mandibular reconstruction with FFF and alloplastic TMJ prosthesis at the our center. Pre-operative and post-operative maximum inter-incisal opening (MIO) measurements were collected, and patients completed a QOL questionnaire (EORTC QLQ—H&N35) during those perioperative visits.ResultsSix patients were included in the study. The median patient age was 53 years. Heat map analysis of the QOL questionnaire revealed that patients reported a positive clinically significant change in the domains of pain, teeth, mouth opening, dry mouth, sticky saliva, and senses (relative change of 2.0, 3.3, 3.3, 2.0, 2.0, and 1.0 respectively). There were no negative clinically significant changes. There was a median perioperative MIO increase of 15.0 mm, and this was statistically significant (p = 0.027).ConclusionsThis study highlights the complexities involved in mandibular reconstruction with involvement of the TMJ. Based on our findings, patients can obtain an acceptable QOL and good function following simultaneous reconstruction with FFF employing SDS and an alloplastic TMJ prosthesis.Graphical

One of the most phylogenetically enigmatic taxa of Trombidiformes is the supercohort Eupodides (=Eupodina) consists of five superfamilies: Bdelloidea, Eriophyoidea, Eupodoidea, Halacaroidea, and Tydeoidea. However, this taxonomic system has not been supported by formal reconstruction of the phylogeny of these mite groups. In this paper, we present the results of the phylogenetic relationships of major lineages of Eupodides based on 18S rDNA, 28S rDNA, and COI sequences. By critically analysing the key morphological features of the mite taxa indicated by molecular analysis as the main eupodine lineages, we reconstructed a cladogram showing the cladistic hypothesis of the internal phylogenetic structure of Eupodides. Subsequently, the result was compared to the character evolution course suggested by tracing the morphological characters of eupodine mites on the reconstructed molecular tree. According to our data, Eupodides should still be classified as a monophyletic taxon grouping representatives of Bdelloidea, Eupodoidea, Tydeoidea, and Eriophyoidea; however, the taxonomic status of some superfamilies was not confirmed. Particularly, only the bdelloid clade with Cunaxidae nested within Bdellidae may correspond to the superfamily in the current taxonomic view. Additionally, the superfamilies Eupodoidea and Tydeoidea were demonstrated to be paraphyletic. Moreover, morphological, as well as molecular, data recovered Eriophyoidea nested within Tydeoidea.

The calcaneum is a rare site for primary bone sarcomas. Calcanectomy is not considered for high-grade malignancies due to anticipated issues with obtaining negative margins, providing adequate soft-tissue coverage, and preserving satisfactory function. A below-knee amputation overcomes these difficulties and is very functional and, thus, the preferred local control option. The aim of this study is to evaluate the role of total calcanectomy, without any formal reconstruction, in high-grade calcaneal sarcomas. Over 14 years, three patients with high-grade calcaneal sarcomas underwent limb salvage surgery as opposed to amputation for their primary malignancy. Total calcanectomy was undertaken using a Cincinnati incision. No formal “calcaneal” reconstruction was undertaken after resection, essentially leaving the patient with an excision arthroplasty through the subtalar joint. The Achilles tendon was reattached to the posterior talus. Negative resection margins were achieved in all cases with the primary wound closure. Two patients are alive with no evidence of disease at 15 and 10 years. The third patient, at over 1 year postoperatively, has no evidence of local disease recurrence but has had metastasectomy for documented pulmonary metastases at the presentation. The average musculoskeletal tumor society score was 85.5%, and the average Toronto extremity salvage score was 88.5%. In our experience, even high-grade malignancies at this unusual site are potentially amenable to limb salvage. Our results show that perhaps ablative surgery should not be considered inevitable. Good functional outcomes can be achieved without reconstruction, thus minimizing potential “construct”-related morbidities.

The lop ear deformity is defined by a deficient helix and scapha, underdeveloped anthelix, and downfolding of the helix. The terminology used is still confusing, and the treatment is not entirely structured. The aim of this study was to provide a new systematic surgical approach of this deformity based on our center's experience. All patients undergoing surgical correction of lop ears between 2007 and 2019 at Great Ormond Street Hospital were included. Patients' data, surgical techniques, and postoperative complications were recorded. Based on our records, we identified 3 surgical techniques for the correction of lop ears, based on the degree of deformity encountered. In a mild lop ear, correction was achieved with a modified otoplasty technique by improving the definition of the antihelix and superior crus. In a moderate deformity, additional remodeling of the lidded helix was performed (extended otoplasty), whereas for the severe lop ear, the amount of cupping and the deficient cartilage required formal reconstruction using a carved rib cartilage framework. There were a total of 109 patients and 146 lop ears: 58 mild, 27 moderate, and 61 severe lop ears. We feel that there is a point in the spectrum of congenital ear deformity when a severe lop ear becomes a conchal microtia and recommend this approach to simplify the management of these cases. This is intended to bring greater clarity to how to deal with lop ears, based on the severity of the deformity and the surgical techniques used.

Elbow joint serves important functions for the purpose of carrying out routine activities. Chronic dislocations of this joint block the smooth functioning of the elbow joint, thus hampering patient’s self-care and making day to day tasks difficult to perform. Chronic elbow dislocation is defined as a dislocation that has remained unreduced for 2 weeks. The extensive soft-tissue fibrosis and contractures along with skeletal changes that develop during this time usually prevent successful closed reduction. A total of 3 patients with chronically dislocated elbow joints were enrolled in the case series and were managed with the similar technique of open reduction of delivering out the distal humerus out and reduction without any formal reconstruction or augmentation of any of the ligaments by the same surgeon in the same hospital set up followed by the same post operative rehabilitation protocol. All the patients achieved considerably good, stable and painless elbow joint with significant improvement in range of motion as compared to pre operative one. The outcomes were measured using mayo elbow score (MEPS). Conclusion: This technique of treating elbow joint dislocation is very effective and gives patient a clinically stable, painless and mobile elbow joint. The results were evaluated with the Mayo elbow performance score (MEPS) which showed a considerable improvement in post-surgery score as compared to pre surgery one.