Over the last decades, an upsurge of studies concerning Roman domestic space has led to a critical reassessment of prior scholarship. Novel approaches have put major emphasis on the social dimension (Laurence and Wallace-Hadrill 1997; Wallace-Hadrill 1994; 1997; Zanker 1999). Concurrently, the emergence of new evidence from sites such as Cosa (Brown 1980; Bruno and Scott 1993) and Fregellae (Battaglini and Diosono 2010) has enriched a picture long dominated by the Vesuvian cities. Within this framework, the traditional nomenclature adopted by scholars to identify the spaces populating the Roman house has been critically reviewed (Leach 1997). Moreover, authors have confronted canonical views of the use of space as an intersection between literary text (Vitruvius’ treatise in the first place) and material evidence such as the content of excavated houses (Allison 2004). Ultimately, Andrew Wallace-Hadrill (2008; 2016) has criticised and dismissed the very idea of a progressive Hellenisation of the traditional atrium house (a house with a central courtyard), its consequent atrophy, and the following dispersal of its purely Roman characteristics.

Notably, some of these studies have advocated a reappraisal of the traditional evolutionary account of the atrium introducing the possibility for this space to be open at different stages of its life (Nappo 1997; Wallace-Hadrill 1997). Consequently, scholars have ceased to see the presence of the impluvium (central basin) as a decisive indication of a compluviate (inward sloping) roof. New questions concerning the roof systems of the atria, previously solved through the sole equivalence impluvium/compluvium, have emerged. In this context, Kemal Reha Kavas (2012) has called for a reassessment of the traditional atrium house with an emphasis on a reviewed epistemological approach with case-by-case scrutiny of the material evidence.

Concurrently, various scholars (Hanen and Kelley 1989; Fogelin 2007) have identified the inference to the best explanation (IBE) as an effective procedure for the interpretation of archaeological data. In my recent contribution to the European Journal of Archaeology (Campanaro 2021), I have stressed the IBE’s contribution to the improvement of transparency in the 3D reconstruction processes.

This paper proposes that IBE-based methodologies can be used effectively to re-evaluate the classic feature of the Roman house, the atrium. It addresses the question of whether individual atria were completely roofed over or not. In this regard, it illustrates the application of a novel IBE-based model for archaeological reasoning to the case study of the atrium of the House of the Greek Epigrams (V 1, 18) in Pompeii. It puts special emphasis on the three-dimensional (3D) aspects connected with the interpretation of archaeological data. Accordingly, it presents a 3D reconstruction as a product of the IBE-based process.

Over the last few decades, there has been a resurgence of studies concerning Roman domestic space (Wallace-Hadrill 2007; Bergmann 2012; Clarke 2013; Hales 2013; de Haan 2016). In this context, the atrium house has received much attention from scholars focusing on its origins and its development over time (McKay 1975; Carandini 1990; De Albentiis 1990; Dwyer 1991; Carandini and Carafa 1995; Ellis 2000; Sewell 2010; Anderson and Robinson 2018; D’Auria 2020; Esposito 2021). Concurrently, a growing body of literature has started critical scrutiny of its canonical form based on the Vitruvian description and the surviving material, especially from Pompeii (Tamm 1973; Evans 1978; Wallace-Hadrill 1997; Leach 1997; Allison 2004; Wallace-Hadrill 2007). Amongst those contributions, Birgitta Tamm (1973) has called for a more accurate study and comparison of archaeological material to provide a fresh look into the text by Vitruvius. Other scholars have emphasised examples that go beyond the canonical form presented by traditional accounts such as double atrium houses (Lauter 1975) and atrium houses without side rooms (Evans 1978). Furthermore, the critical work on the vocabulary of the Roman house by Eleanor Winsor Leach (1997) and Penelope Allison (2004) regarding the content and fixtures in excavated houses have suggested a more nuanced picture and multifunctionality of spaces.

In this context, Wallace-Hadrill (1997) has noted how a combination of Vitruvius’ descriptions and the material evidence from the Late Republican and Early Empire, notably Pompeii, has forged the account of the development of the Roman house. Scholars reading Varro (LL 5,161) and Vitruvius (6.3.1–2), have long embraced a connection between compluvium/impluvium and the atrium form to the point that, often, uncovered central courts have not been read as atria at all (Auer 2014: 34). The House of the Skeleton in Cosa is a particularly significant case in point. The complex, despite being equipped with an impluvium, was manifestly unroofed. The presence of driplines that define the contour of overhanging eaves are evidence of this feature (Bruno and Scott 1993: 117; Wallace-Hadrill 1997: 228; on similarities between Cosan complexes and Greek prostas houses, see Sewell 2010: 114). A study by Salvatore Ciro Nappo (1997) concerning the so-called row houses in Regio I and II in Pompeii similarly yielded significant results. In many respects, they resemble, yet with some exceptions, the typical atrium house, with fauces opening on a central space, a sequence of front rooms/central court/back rooms/garden, and the contrasting type of large/small or open/closed rooms (Wallace-Hadrill 1997: 222; see also Anderson and Robinson 2018: 54; on the row houses as a Roman adaptation of the Greek prostas layout, see Sewell 2010: 131). Nappo identified four types of dwellings featuring open courtyards, subsequently either converted into a covered space or retaining this configuration during the later stages of their life (Nappo 1997: 100, contra Esposito 2021: 205 who, by analogy with D’Auria 2020: 100–102, hypothesises testudinate atria featuring small terracotta compluvia). This is evident in the House of the Garden of Hercules (II 8,6), the Domus of Euxinus (I 11,12), Houses I 9,8; I 13,8; and I 14,3. Two interesting cases are provided by House I 15,1 for which stratigraphic tests confirmed the absence of a cistern under the impluvium, and House I 20,4 which, albeit equipped with an impluvium, at no stage was covered by a compluvium. According to Wallace-Hadrill (1997: 231–234), various houses in Reg. VI, ins. 5, the Casa Dei Fiori (VI 5, 19), Casa delle Forme di Creta (VII 4, 62), Casa di Ganimede (VII 13, 4), and the Casa del Gallo (VIII 5, 2) are all examples which could suggest that we may ‘be looking for the sort of traces of drainage-systems that would be compatible with atria with inward sloping roofs that extended no further than a walkway sheltered by overhanging eaves’ (233). Other examples would further contribute to defining the issue at stake. In House II 8, 4–5, close to Porta Nocera in Pompeii, a partially roofed central court equipped with a cistern lacked the traditional system of compluvium/impluvium. Thus, the water collected in the atrium would have been drained via the sloping pavement into a cistern close to the tablinum. Since more water would have been collected in the rear of the house, the main purpose of the atrium would have been that of a light well (Dentamaro 1997). In House I 11,14, the rectangular impluvium, with its longer side parallel to the street, had been covered with a shed roof and was illuminated through a circular opening (opaion; Tilloca 1997). Similarly, the atrium of House I 11, 9 would have been covered with a shed roof only during the last phase, whereas previously its function would have been that of a light well (Cerato 2000). Another interesting example can be found in Joanne Berry’s study of the House of the Beautiful Impluvium (I 9,1). During the last phase of the house, the atrium, roofed over at a previous stage, would have been left completely uncovered (Berry 1998, 53). Likewise, in the House of Amarantus (I 9,12), the atrium would have never been roofed (Wallace-Hadrill 1997: 223). In Fregellae Domus 4, which is lacking an impluvium, Giovanna Battaglini and Francesca Diosono (2010) identified the presence of an open roof of some kind, different from an atrium testudinatum.

The presence of open atria has, therefore, entered the scene as an alternative configuration, resisting the idea of the impluvium as the hallmark of a specific roof system. This would imply a new effort by scholars not to adopt reconstructions that assume that the atrium was necessarily covered. The question of the roofing of the atrium emerges as crucial in architectural terms but more importantly in connection with the epistemological choices underpinning the archaeological interpretation of the physical remains. According to Kavas (2012), the historiography of the Roman house has, until recently, applied idealist deductive methods to shape the implications of the material evidence to find confirmation for the Vitruvian descriptions.

Contemporary approaches should instead privilege a close study of the evidence and the stratigraphic information (for recent approaches to Vitruvius, see Milnor 2013; Nichols 2017: 90; Oksanish 2019). Thus, the reconstruction of the Casa della Caccia Antica (VII 4, 48) by Penelope Allison and Frank Sear (2002: 60) and that of the Samnite house by Anne Laidlaw et al. (2014: 265–268), who nevertheless place great reliance on the correspondence of the different parts of the house to Vitruvius’ rules, have to be considered interesting examples.

Kavas calls for the abandonment of the deductive method in favour of more empirical inductive approaches. Importantly, he notes that ‘material evidence yields the acquisition of three-dimensional architectural forms in the context of environmental problems and practical solutions while [the] Vitruvian text is based upon two-dimensional typological preconceptions’ (Kavas 2012: 144). He, therefore, suggests a critical review of the established historiography concerning the roof structure of the atrium house, with a major emphasis on the three-dimensional aspect connected to the advocated empirical inductive approach.

Real progress in the field would, therefore, require a ‘convergence’ of impulses often cultivated in isolation combining the application of novel theoretical frameworks with close scrutiny of the evidence (Wallace-Hadrill 1997: 219).

In the following, I will demonstrate how it is possible to respond to these calls, with the aid of a particular type of inference, the inference to the best explanation (IBE; Campanaro 2021), and a three-dimensional approach to the interpretation of the archaeological data. In this regard, the labels ‘open’/‘partially roofed’/‘unroofed’ used in this paper all refer to a form of central courtyard with ‘inward sloping roofs that extended no further than a walkway sheltered by overhanging eaves’ (Wallace-Hadrill 1997: 233).

Inference to the best explanation, or abductive reasoning, has often been identified as one of the three major types of inference, together with deduction and induction. In deductive argumentation, the last proposition, inferred from the premises, is necessarily true if the premises are true. An application of such a ‘rigid standard’ is exemplified by Edith Evans’ analysis of the study by Noak and Lehmann-Hartleben about Houses VIII 2,39 and VIII 2,36 in Pompeii (1978: 175). These complexes, characterised by the absence of alae at the time of the eruption, would allegedly have included them at an earlier stage. According to Evans, the attempt of fitting the Vitruvian mould (the presence of the alae) resulted in a ‘bizarre interpretation’ whereby side rooms with a limited width of 1 m entail little or no use of those very spaces. In the case of an inductive argumentation, the truth of the conclusion can likely be inferred from the premises. In a very simple case, an archaeologist specialising in domestic architecture, having examined many cases of domestic structures, can use induction to suggest that most of them have a hearth (Fogelin 2007: 608). In abductive reasoning, the premises do not entail the conclusion like in a deductive pattern. The following example by Samir Okasha (2002: 29; Campanaro 2021: 413) may help to illustrate the concept: The cheese in the larder has disappeared, apart from a few crumbs/Scratching noises were heard coming from the larder last night/Therefore, the cheese was eaten by a mouse. Here, the conclusion can be inferred as the one that best explains the given set of data.

In recent years, a renewed interest in the structure of logical reasoning has stressed the importance of IBE as an effective pattern for the enhancement of archaeological argumentation (Hanen and Kelley 1989; Fogelin 2007; Smith 2015). In addition, I have highlighted (Campanaro 2021) how IBE-based methodologies can help build better arguments in archaeology and address issues of transparency of the processes underlying 3D virtual reconstructions in the field of cultural heritage. As noted by Lars Fogelin (2007), IBE and archaeology have long been silent companions. Despite this, one would be inclined to assume that archaeologists frequently make use of induction for their explanations. This is also evident, from Kavas’ arguments. Notably, Fogelin has pointed out that ‘traditional forms of induction often rely implicitly on inference to the best explanation’ (2007: 606). His case about analogical reasoning as discussed by Alison Wylie (2002: 136–153) is particularly relevant, considering the use of analogies often made in the process of 3D reconstructions for cultural heritage purposes. At the core of this form of reasoning is the notion that ‘some principles of connection exists between the traits being compared’ (Fogelin 2007: 607). This means that if A includes certain traits and B shares those traits plus some others, the latter can be attributed to A as well. Nevertheless, to establish this connection, analogical reasoning must employ IBE. Fogelin also addresses the case of statistical induction. A classic example suggests that by observing many black ravens one may conclude that all the ravens are black. The more prior observations, the stronger the induction. Nevertheless, this would be hardly tenable in the case of particularities of the past. Fogelin (2007), therefore, claims that adopting multiple lines of evidence may improve an argument, but not in terms of statistical induction. Though not solving the Humesian problem (a non-uniform world is conceivable, e.g. the sun may not rise in six million years), as no other system of reasoning does, IBE may address particularities of the past.

Despite its seminal contribution to the affirmation of IBE for archaeological reasoning, past literature has not offered specific examples for its application. Recently, Campanaro (2021) has defined an IBE-based model to record the complete chain of archaeological reasoning adopted for this paper. This model consists of four main phases (Figure 1): the selection of records (SR) from an existing archive (R), the formulation of hypotheses (H), the definition of competing accounts (A), and the selection of the best explanation amongst several plausible candidates making use of seven virtues: generality (a good explanation should be employed for a wide array of phenomena); modesty (the explanation should not overreach); refutability (explanations should be refutable); conservatism (the explanation should not principally aim at overthrowing well-established principles); simplicity (explanations should not be more complicated than necessary, e.g. Occam’s razor,); empirical breadth (a good explanation should address several empirical phenomena and not be contradicted by others) and multiplicity of foils (the more ‘layers’, the better the explanation; Quine and Ullian 1978; Fogelin 2007; Campanaro 2021).

The House of the Greek Epigrams (V 1,18.11–12) is located in the northern part of the Insula V 1 in Pompeii (Figure 2). First excavated in 1875 and greatly damaged during the Second World War as well as the 1980 earthquake, this complex has given rise to many questions of great importance for modern archaeological research, still far from being thoroughly answered (Staub Gierow 2007). New excavations and accurate studies aimed at understanding the building history of the house, the function of the rooms, and the daily life of their owners have been carried out as part of the Swedish Pompeii Project (http://www.pompejiprojektet.se/project.php; Robinson 2007; Robinson 2008: 126–28; Staub Gierow 2005; 2007; 2008; 2009: 216–17; Leander Touati et al. 2018). Interestingly, the House of the Greek Epigrams is the only house of this insula that was not evacuated before/during the eruption of Mount Vesuvius and where, thus, an abundance of artefacts has been brought to light.

In the following, I will analyse specifically the roofing of the atrium (b) of the House of the Greek Epigrams (Figures 3, 4) by employing an IBE-based methodology.

In a first step, all records concerning the main topic of the investigation are collected (Figure 5: SR), in particular, those concerning the question of whether the front hall (atrium) of the house was roofed over or not during its last phase. Accordingly, elements from the existing documentation (R) that concern the state of the house are selected and added; these comprise recent and past excavation reports (except for any related interpretations, which form part of the hypotheses group) and photographic documentation including reproductions from the 19^th century, etc. When multiple sources are present, they are distinguished using the format Ri/Rj/…/Rz; for example, in the case of the wall paintings described in the reports of the Swedish Pompeii Project and appearing in previous photographic documentation, reproductions, and reports from the 19^th century: R.1.1/R.2.5/R.5.1 (Figure 6).

In a second step, hypotheses (Figure 6 H) are formulated. For the case study in question, these are:

The third stage of the IBE-based model consists of the development of accounts, combining one or more of the hypotheses defined in the previous stage and their possible refinement. This involves a process of coherence-making through subtraction, addition, or reinterpretation, such as subtracting elements from an incoherent set or adding elements to increase coherence. In the following, I will illustrate this process through the workflow of the reconstruction.

Figure 11, A1 and A2, represents two different accounts explaining the records in SR, including a subset of hypotheses. At present date, two alternative 3D models of the accounts have been created (Figure 12 a–b). The first account presents the possibility that the front hall of the House of the Greek Epigrams was covered with a roof structure of the type of the atrium tuscanicum. The second account, building on the work by Nappo (1997) and Wallace-Hadrill (1997), would instead suggest the possibility that the central space was only partially roofed over.

The three-dimensional nature of these structures, which has very often been taken for granted, especially in the case of the atrium tuscanicum, has required further investigation. In this regard, Jean-Pierre Adam (1994) has devoted much effort to trying to illustrate technical aspects concerning the roofing of spaces in the Roman house. Simpler solutions such as shed roofs (and partially roofed atria would enter into this definition) can be more straightforwardly reconstructed (Adam 1994: 207). Conversely, identifying the elements composing the structure of a compluviate space has been more challenging. Over time, scholars have dealt with this topic in connection with monument protection and conservation practices (Salassa 1999; Pierattini 2009; Bergamasco et al. 2018). Chiara Salassa (1999) analyses the works of scholars who have visited Pompeii since its excavation began in 1748. Amongst those studies, the French scholar François Mazois (1812), offered an innovative rendering of the structure of the atrium tuscanicum, with each element corresponding to a specific Vitruvian label. This model had been generally accepted and Johannes Overbeck (1968 [1866]) was alone in his critical investigation of Mazois’ work. Whilst the latter described the secondary beams (interpensiva) framing the opening of the compluvium (arca) as resting on the main beams (trabes), Overbeck imagined the interpensiva notched to the main beams. As noted by Roger Ulrich (2007: 167–172), several details do not argue in favour of the solution illustrated by Overbeck, such as missing details regarding the joinery, Vitruvius’ preoccupation with the loads imposed (6.3.1), and the use of supra in the description of the arca (6.3.4), as resting on the main beams, and making ‘better structural sense’ (Ulrich 2007: 171). For this specific study, the solution adopted in the 3D reconstruction of the roof uses the studies of Mazois and Ulrich (Figure 13). Notably, Alessandro Pierattini (2009) addresses the technical issue of the roofing of atria with irregular forms. Suggesting a corrective to the solution of the tegulae colliciae (special angular tiles, see Salassa 1999), he stresses how the evidence of not-square atria must admit tigni colliquiarum (corner beams creating the valleys) not necessarily meeting the walls in the corner.

The pitch of the roof creates another relevant challenge. Various scholars have suggested an inclination of the roof ranging from 15 to 20 degrees, to prevent the roof tiles from sliding down, water from backing up, and wind suction (Rook 1979: 295–96, Gerding 2013: 142). Nevertheless, the position of the main beams, bearing the weight of the compluviate roof, in the wall would still remain a major issue. The dimensions of the atrium of the Casa del Bicentenario (V 15) in Herculaneum, dating back to the Early Augustan period, are an interesting comparative to the House of the Greek Epigrams. This allowed the use of information concerning the position of beam holes and the section of the main beams as comparanda for the reconstruction of the structure supporting the atrium tuscanicum, otherwise requiring a major interpretative leap.

The last stage of the process concerns the selection of the best explanation at the present stage of knowledge from the pool of available candidates. For this purpose, this study has assessed the accounts against the seven virtues.

Generality: both accounts seem to comply with the requirement to explain a wide array of phenomena not contradicted by others. A1, as shown in Figure 10, can explain a broader range of observations. This would also impact the empirical breadth.

Modesty: A1 will also be the account displaying more modesty by ‘keeping the assumptions down’ (Quine and Ullian 1978: 40). It is obvious that at the present stage of knowledge A2 would require more assumptions to justify the presence of a partially roofed space. In this respect, uncertainties concerning the collection of water (sloping of the floor towards the impluvium and the absence of dripping lines) or the use of the space as a mere transitional area or strongly dependent on the season would argue against this account. Similarly, the argument that two different large-scale building programs would have both discarded the possibilities offered by a roofed-over space to convey a message about the owner’s prestige would require a certain number of assumptions.

Refutability: A1 and A2 equally possess refutability, being both falsifiable (for example imagining future evidence contradicting one theory or the other). According to Quine and Ullian (1978), the degree of refutability is measured by ‘how dearly we cherish the previous beliefs that would have to be sacrificed to save the hypothesis. The greater the sacrifice, the more refutable the hypothesis’ (1978: 48). Therefore, refutability would depend on the current state of research, or ‘the network of currently accepted propositions’ (Gawronski and Bodenhausen 2015: 14–15) concerning the roofing of a Roman house. This would place a higher degree of falsifiability on the account that a prestigious house had a roof of the type of an atrium tuscanicum (A1), rather than being completely unroofed (A2).

Conservatism: A2 appears to be the less conservative of the accounts, since ‘in order to explain the happenings that we are inventing it to explain, the hypothesis may have to conflict with some of our previous beliefs; but the fewer the better’ (Quine and Ullian 1978: 40).

Simplicity (or Occam’s razor): this would also identify A1 as the simpler of the two accounts, in that ‘the longer the leap […] the more and wilder ways of going wrong’ (Quine and Ullian 1978: 41).

Multiplicity of foils: according to Fogelin (2007: 620) ‘an explanation that can account for both where and when a particular event occurred is usually better than an explanation that only accounts for when a particular event occurred’. This virtue will again see account A1 as preferable, insofar as it can address more layers (e.g. why the individual solution was chosen – prestige – and when – the time when the house received its late second-style decoration).

Considering what has been examined, the solution best explaining the information at our disposal would be the one suggesting that the front hall, previously unroofed, would have been covered with a roof of the type of the atrium tuscanicum when the house also received its second-style decoration. The present study with its illustrated chain of reasons would identify the best explanation at the present state of knowledge, leaving space for new arguments if/when further typologies of information enter the picture.

Therefore, a 3D reconstruction has been selected as the final product of the detailed analytical process using the described IBE-based workflow (Figure 12a). This model should not be considered a mere illustration of the final interpretation chosen as the one best explaining the different records. The process of the 3D reconstruction has a fluid relationship with the chain of reasoning during the entire process, as a means of refinement of the different hypotheses concerning the inquiry (see Figure 5). In this context, Cameron Shelley (1996) has highlighted the importance of spatial reasoning—or visual abduction—in archaeology and anthropology. An example of how the 3D reconstruction process itself can influence the refinement of hypotheses is the question of how to cover irregular areas. The examples in the literature usually deal with very regular plots and are mostly represented in two dimensions. The very act of reconstructing in three dimensions the structure of the roof allowed investigations into the feasibility of the proposed solution (position, dimension, and pitch of the different roofs). In addition, by visually inspecting the 3D model it has been possible to appreciate the differences in spatial terms of the proposed solutions helping the process of validation (e.g., appreciation of the decorative program based on the distance, Figure 8).

Once built, the 3D model can contribute to fostering the generation of new data. These may derive from the visual inspection of the model itself, or specific typologies of 3D investigations (for example the analysis of the contribution of natural and artificial light, Campanaro in press.; or the measurement of human visual attention within the virtually reconstructed space of the house, Campanaro and Landeschi 2022).

This paper has investigated the question of the roofing of the atrium of one specific Pompeian house, in the context of a critical revision of prior scholarship. Thus, the present study has answered the important call made by Wallace-Hadrill (1997) and Kavas (2012) for a renewed epistemological approach to the study of the atrium house, combined with a close case-by-case investigation of the material evidence. This research has proposed IBE as an approach for the interpretation of archaeological data, analysing it in relation to induction. In this regard, it has illustrated Fogelin’s theory concerning the reliance of induction on IBE and the resulting advantage in adopting an IBE-based pattern of reasoning. Accordingly, a novel IBE-based model for archaeological reasoning has been applied to the case study of the roofing of the atrium of the House of the Greek Epigrams in Pompeii.

The relevant findings in this paper have shown how the methodology described can effectively be applied to address issues concerning the roofing of the atrium. In this sense, the inclusion of different typologies of sources, merged into different hypotheses and eventually organised in alternative accounts, actualises the ‘convergence’ of impulses evoked by Wallace-Hadrill. Furthermore, the fluid essence of the model itself leaves the best solution —at the present state of knowledge for the specific case study in question — open to future contributions. Additionally, the adoption of a three-dimensional critical approach, based on the scrutiny of the material evidence but also the use of 3D reconstructions, has shown to be particularly effective in the process of refinement of the proposed hypotheses.

Importantly, the methodology described, given the great degree of adaptability, would have the potential to be extended to other issues of relevance for the study of the Roman house.