Jad Oueis
email: jad.oueis@insa-lyon.fr

Razvan Stanica
email: razvan.stanica@insa-lyon.fr

Fabrice Valois
email: fabrice.valois@insa-lyon.fr

Catherine Rosenberg

Network-aware User Association in Public Safety Oriented Mobile Networks

In many disaster scenarios, communication infrastructure fails to provide network services for both civilians and first responders. One solution is to have rapidly deployable mobile networks formed by interconnected base stations, that are easy to move, deploy, and configure. Such public safety-oriented networks are different from classical mobile networks in terms of scale, deployment, and architecture. In this context, we revisit the user association problem, for two main reasons. First, the backhaul, formed by the links interconnecting the base stations, must be accounted for when deciding on the association, since it may present a bottleneck with its limited bandwidth. Second, the mission-critical nature of the traffic imposes strict guaranteed bit rate constraints, that must be respected when associating users. Therefore, we propose a network-aware optimal association that minimizes the bandwidth consumption on the backhaul, while still respecting the stringent performance requirements.

I. INTRODUCTION

A major challenge in the aftermath of natural and man-made disasters is communication. Ensuring reliable communication, notably between first responders, such as paramedics, firefighters, and police officers, is crucial for saving people's lives [START_REF] Manoj | Communication Challenges in Emergency Response[END_REF]. However, communication failures are common in emergency situations, as recently seen with the tropical storm Harvey, which caused service outage in up to 90% of the cell sites in some of the affected regions [START_REF]Communications Status Report for Areas Impacted by Tropical Storm Harvey[END_REF].

As a result, we recently witnessed an increased investment in public safety (PS) oriented networks, tailored to meet the stringent requirements of first responders, in terms of reliability, resiliency, and security [START_REF] Oueis | Overview on LTE Isolated E-UTRAN Operation for Public Safety[END_REF]. LTE has already been adopted as the building technology for these networks, due to its large existing ecosystem, high bandwidth, low latency, and real-time communication capabilities [START_REF] Oueis | Overview on LTE Isolated E-UTRAN Operation for Public Safety[END_REF]. One of the foreseen solutions is to have easily and rapidly deployable networks, replacing the communication infrastructure when the latter is damaged or destroyed, or in isolated areas where no infrastructure preexists [START_REF]Study on architecture enhancements to support isolated Evolved Universal Terrestrial Radio Access Network operation for public safety (Release 13)[END_REF]. The key elements of rapidly deployable networks are small-sized base stations (BSs), that are easy to move, configure and deploy, potentially in an autonomous manner. Deployment platforms include aerial platforms (e.g., balloon fleets [START_REF]Google Loon project[END_REF], drones [START_REF] Bor-Yaliniz | The New Frontier in RAN Heterogeneity: Multi-Tier Drone-Cells[END_REF]), and terrestrial networks (e.g., BSs mounted on vehicles or wearable as backpacks [7]).

Several differences exist between classical and PS mobile networks. In classical mobile networks, each BS of the radio access network (RAN) usually has a dedicated backhaul link towards the core network. This architecture requires a standalone core network hardware and backhaul provisioning. In PS networks, the architecture must be simplified, since a dedicated core network may not be available, and the BSs are supposed to be as autonomous as possible. Hence, the core network functionalities are to be co-located with the BSs [START_REF]Study on architecture enhancements to support isolated Evolved Universal Terrestrial Radio Access Network operation for public safety (Release 13)[END_REF], through function virtualization, for example [START_REF] Gomez | Enabling Disaster-Resilient 4G Mobile Communication Networks[END_REF]. In this case, all traffic, usually forwarded to the standalone core network, is now routed locally on the links interconnecting the BSs and forming the backhaul. Moreover, PS networks are relatively small-sized. They interconnect only a few BSs, generally less than 10, depending on the needed coverage area, and serve a limited number of users (e.g., first responders), depending on the scale of the emergency situation in question. Furthermore, the traffic in PS networks is mostly intra-cellular, i.e., between users belonging to the same network. Indeed, even when communication with external networks is possible, it is usually rare.

In this paper, we first revisit the user association problem, i.e., assigning each user to a BS, in the context of a rapidly deployable PS mobile network. User association is usually based on RAN metrics, with the assumption of an overprovisioned backhaul. However, the backhaul in our scenario may represent a bottleneck, especially since the links between BSs, forming this backhaul, have a limited bandwidth. With multiple BSs potentially sharing the same backhaul link to forward their traffic, ignoring the backhaul will eventually lead to poor network performance. On top of that, traditional association schemes do not take user requests into consideration when deciding on the association. Nevertheless, with the stringent performance requirements imposed in PS networks, users must be granted services with a guaranteed bit rate. Indeed, video streaming lag during a critical rescue operation cannot be tolerated. Moreover, we revisit the user attachment problem, i.e., assigning the flows of each user to a specific gateway. Usually, each user is attached to one default gateway responsible of locally routing all of its flows. We argue that an optimized attachment would further reduce the traffic on the backhaul by reducing the signaling load caused by gateway selection and management.

The contributions of this paper are twofold. First, we formulate a network-aware user association optimization problem. The problem balances different constraints: the limited resource availability on the RAN, the guaranteed throughput requested by each flow between two users, and the data and signaling traffic routed on the backhaul. The problem is solved with the objective of minimizing the backhaul bandwidth consumption.

Second, we separate the user association from the user attachment. We propose different attachment schemes, and formulate the corresponding optimization problems. Each problem returns both the optimal user association and the optimal attachment to a gateway, with the same objective described above.

Results show that our network-aware association significantly reduces traffic on the backhaul in comparison with a traditional RAN-based association scheme, leading to a backhaul bandwidth consumption reduction of 40%. Moreover, when the attachment is optimized alongside the association, the backhaul consumption reduction is even more important, with the backhaul signaling traffic further reduced.

The remainder of the paper is organized as follows. An overview on related work is presented in Sec. II. In Sec. III, the network model is described. We present the user association and attachment optimization problems in Sec. IV, and discuss numerical results in Sec. V. Sec. VI concludes the paper.

II. RELATED WORK

The conventional association policy in mobile networks is based on the downlink (DL) signal strength, where a user associates to the BS from which he gets the maximum signal to interference plus noise ratio (SINR) on the DL [START_REF] Liu | User Association in 5G Networks: A Survey and an Outlook[END_REF]. Several studies deemed this best SINR approach as ineffective for several reasons, including its poor load balancing [START_REF] Kim | Distributed α-optimal User Association and Cell Load Balancing in Wireless Networks[END_REF], and its complete disregard for the uplink (UL) [START_REF] Boostanimehr | Joint Downlink and Uplink Aware Cell Association in HetNets with QoS Provisioning[END_REF] and the backhaul [START_REF] Sapountzis | Optimal Downlink and Uplink User Association in Backhaul-limited HetNets[END_REF].

A multitude of association policies outperforming the best SINR approach have been proposed, for different network architectures, and with different objectives [START_REF] Liu | User Association in 5G Networks: A Survey and an Outlook[END_REF], such as optimizing rates or delay in homogeneous networks [START_REF] Kim | Distributed α-optimal User Association and Cell Load Balancing in Wireless Networks[END_REF], balancing BS loads in heterogeneous networks (HetNets) [START_REF] Ye | User Association for Load Balancing in Heterogeneous Cellular Networks[END_REF], and optimizing coverage in self-organizing networks [START_REF] Fehske | Concurrent Load-Aware Adjustment of User Association and Antenna Tilts in Self-organizing Radio Networks[END_REF]. The majority of the existing works tackle the problem from a RAN point of view, completely ignoring the backhaul. Nevertheless, some backhaul-aware association policies were proposed, notably for backhaul-limited HetNets [START_REF] Sapountzis | Optimal Downlink and Uplink User Association in Backhaul-limited HetNets[END_REF].

To the best of our knowledge, the user association problem has not been studied yet in the context of rapidly deployable networks. Besides the different network architecture, the major difference with prior works is that we consider a guaranteed throughput approach, where a user is granted the exact throughput it asks for. Moreover, we jointly account for both the RAN and the backhaul when deciding on user association.

III. NETWORK MODEL

We consider a PS mobile network, where J is the set of rapidly deployable BSs, L is the set of bidirectional links interconnecting the BSs, and U is the set of user equipments (UEs).

Backhaul-The core network entities are co-located with the BSs. We focus on two main entities: the mobility management entity (MME), handling network management such as paging, authentication, and gateway selection, and the serving gateway (S-GW), handling local data routing. We consider that network management is ensured by a single MME entity, co-located with one of the BSs, and that each BS of the network is colocated with a S-GW. All signaling traffic passes through the MME, and all data traffic passes through the S-GW. Hence, all traffic is routed locally via the links interconnecting the BSs, referred to as inter-BS backhaul links since they form the backhaul network. Without loss of generality, we consider that, regardless of the inter-BS links technology, there is no contention between the links for resource utilization. We assume that potentially interfering links are operating on distinct channels, allowing interference-free parallel transmissions on the backhaul [START_REF] Aoun | Gateway Placement Optimization in Wireless Mesh Networks with QoS Constraints[END_REF].

Traffic-We model data traffic as bidirectional symmetric flows between two UEs. We only consider intra-cellular flows, where both UEs of a flow belong to the same network. Let F be the set of flows, and f = {u, v} ∈ F a bidirectional flow between UEs u and v. A flow exists between two UEs with a given probability p ∈ [0, 1]. A single UE can have several simultaneous flows with different UEs.

We denote by d f the requested data rate of a flow f , in bits/second, in each direction. Each flow f is accompanied by signaling traffic: between the MME and the BS to which the UE is associated, and between the MME and the S-GW to which the UE is attached.

Routing-Two BSs may or may not be directly connected via a backhaul link. Traffic transported on the backhaul between the entities is routed either directly, if the two endentities are at one hop from each other, or through the interconnected BSs in a multi-hop fashion. In the latter case, we adopt a minimum-hop routing policy, where the shortest path in terms of number of hops is selected for routing between two BSs. We define Z l j,j as a boolean, such that Z l j,j = 1 if link l ∈ L belongs to the shortest path between BSs j and j , and Z l j,j = 0, otherwise. RAN-We consider a time-frequency system (e.g., OFDMA) with a total of K j orthogonal channels allocated to each BS j. The system is in Frequency Division Duplexing (FDD) mode, such that distinct channels are used for DL and UL, with an FDD ratio α ∈ (0, 1), such that

K DL j = α • K j and K U L j = (1 -α) • K j ,
respectively. We assume that all BSs are identical in terms of transmit power and antenna gain. We adopt a physical layer model similar to the one used in [START_REF] Fooladivanda | Joint Resource Allocation and User Association for Heterogeneous Wireless Cellular Networks[END_REF]. We denote by R DL u,j and R U L u,j the maximum per channel physical rate UE u can get from BS j, in bits/second, on the DL and the UL, respectively. We define θ(•) as a function mapping a given SINR to the corresponding physical per channel rate, such that R [START_REF] Fooladivanda | Joint Resource Allocation and User Association for Heterogeneous Wireless Cellular Networks[END_REF]. Each flow is granted exactly the data rate it requests. For each of its flows, a UE is granted a fraction of the available channels on the BS it is associated to, depending on the physical per channel data rate it gets from that BS. The sum of channel fractions allocated to all users associated to a BS cannot exceed the maximum number of channels allocated to that BS.

DL/U L u,j = θ SIN R DL/U L u,j

IV. OPTIMIZING USER ASSOCIATION

We first propose a network-aware user association policy that takes into consideration the RAN, the backhaul, and the flow properties. Our goal is to determine to which BS each UE must associate in such a way that the bandwidth consumption on the backhaul is minimized, in order to avoid backhaul saturation. We determine, in the same problem, the optimal position of the MME, i.e., with which BS the MME must be co-located. An optimal MME placement is key, since all signaling traffic passes through that MME [START_REF] Oueis | Core Network Function Placement in Mobile Networks[END_REF].

Each BS of the network must be served by the MME colocated with one of the BSs. Each UE must be associated to one and only one BS, and attached to at least one S-GW. In this work, we study three attachment policies, leading to three different problem formulations:

P1: user attachment follows association. A UE is attached to the S-GW co-located with the BS it is associated to.

P2: user attachment does not necessarily follow association. A UE can be attached to any S-GW co-located with any BS, even if different from the BS it is associated to. In this case, we optimize attachment in addition to the association.

P3: attachment per flow. A UE is attached to one S-GW per flow. A UE can attach to different S-GWs for its different flows. In other words, UEs at both ends of a flow are attached to the same S-GW. The attachment is optimized on a per-flow basis in addition to the association.

Each of these problems is formulated as a mixed integer quadratic optimization problems (MIQP). We limit this work to the offline problem, where UEs are already in the network, with known positions, flows and respective data rates. We first formulate problem P1, in which attachment follows association. Fig. 1 shows the data and signaling traffic paths for a bidirectional flow between UEs u and v, respectively associated to BSs j 1 and j 2 . If u (resp. v) is associated to BS j 1 (resp. j 2 ), then u (resp. v) is attached to S-GW j 1 (resp. j 2 ). Hence, when two UEs are associated to the same BS, the data they exchange is not routed on the backhaul.

A. P1: user association optimization

P1 : min W,X l∈L C d l + C S1 l + C S2 l + C S3 l + C S4 l (1) j∈J W j = 1 (2) j∈J X u,j = 1 ; ∀u ∈ U (3) u∈U X u,j K DL j • R DL u,j f ∈F /u∈f d f ≤ 1 ; ∀j ∈ J (4) u∈U X u,j K U L j • R U L u,j f ∈F /u∈f d f ≤ 1 ; ∀j ∈ J (5)
C d l = f ∈F j1∈v X u,j1 j2∈J X v,j2 • Z l j1,j2 • 2d f ; ∀l ∈ L (6)
C S1 l = f ∈F j1∈J X u,j1 j0∈J
W j0 • Z l j1,j0 • S1 f ; ∀l ∈ L (7)
C S2 l = f ∈F j2∈J X v,j2 j0∈J
W j0 • Z l j2,j0 • S2 f ; ∀l ∈ L (8)
C S3 l = f ∈F j1∈J X u,j1 j0∈J W j0 • Z l j0,j1 • S3 f ; ∀l ∈ L (9)
C S4 l = f ∈F j2∈J X v,j2 j0∈J
W j0 • Z l j0,j2 • S4 f ; ∀l ∈ L (10)
We define association vector X, with X u,j a boolean, such that X u,j = 1 if UE u associates to BS j. We define vector W , such that W j = 1 if the MME is co-located with BS j. As constraints, there is only one MME in the network (Eq. 2), and a UE is associated to one BS (Eq. 3). For the RAN, the total flows received from UEs associated to a BS on the DL should not exceed the DL BS capacity (Eq. 4), and the total flows sent by UEs associated to a BS on the UL should not exceed the UL BS capacity (Eq. 5). If, for a given set of users, flows and data rates, there are no sufficient resources on the RAN to support all the flows (i.e., Eq. 4 or Eq. 5 not satisfied), then the problem is unfeasible. In practice, this corresponds to rejecting a new flow request due to insufficient RAN resources.

The data path of the bidirectional flow f , with rate d f in each direction, goes from j 1 to j 2 , and vice-versa (Fig. 1). In this case, a data rate 2 • d f (in Mb/s) is consumed by f on each link l on the shortest path between j 1 and j 2 , that is on each link l with Z l j1,j2 = 1. In Eq. 6 we compute C d l for each backhaul link l, which is the total bandwidth consumed by the data traffic of all the flows f ∈ F on the given link l. Signaling traffic exists for each flow f between MME j 0 and BS j 1 , MME j0 and BS j 2 , MME j 0 and S-GW j 1 , and MME j 0 and S-GW j 2 . The corresponding signaling bit rates consumed on each link l, belonging to each of those respective paths, are denoted as S1 f , S2 f , S3 f , and S4 f , respectively. From Eq. 7 to Eq. 10, we compute C S1 l , C S2 l , C S3 l , and C S4 l , respectively representing the total bandwidth consumed by the corresponding signaling traffic of all the flows f ∈ F on a single link l . Eventually, the bandwidth consumed on each backhaul link l by all the flows is the sum of the bandwidth consumed by both the data and the signaling traffic. Our objective is to minimize the total bandwidth consumed on the backhaul, as formulated in Eq. 1. We formulate P2 as an extension of P1, where user attachment is jointly optimized in addition to user association. The MME placement is also optimized.

With S-GWs distributed in the network and co-located with the BSs, the closer the S-GW of a UE is to the MME, the less signaling traffic is consumed on the backhaul. If the S-GW and the MME are co-located, the signaling traffic between them is not routed on the backhaul at all. However, the data traffic must always traverse the S-GW, which is not necessarily placed on the shortest backhaul path anymore.

Fig. 2 shows the updated data and signaling paths for a bidirectional flow between u and v, respectively associated to j 1 and j 2 . The objective function formulated in Eq. 1 remains the same. Likewise, the constraints in Eq. 2, Eq. 3, Eq. 4, and Eq. 5 remain unchanged. However, there are a few key differences with the problem formulated in P1. In P2, we define the attachment vector Y , with Y u,j a boolean such that Y u,j = 1 if UE u is attached to S-GW j. We add a constraint stating that a UE is attached to only one S-GW, such that:

j∈J Y u,j = 1 ; ∀u ∈ U (11)
As the BS and the S-GW are not necessarily co-located, the data path is now as follows: BS j 1 , S-GW j 3 , S-GW j 4 , BS j 2 , and vice-versa. This prompts a change in the C d l computation from Eq. 6, which becomes:

C d l = f ∈F 2d f j1∈J X u,j1 j3∈J Y u,j3 • Z l j1,j3 + j4∈J Y v,j4 j3∈J Y u,j3 • Z l j3,j4 + j2∈J X v,j2 • Z l j4,j2 ; ∀l ∈ L (12)
Following the same reasoning for the signaling paths, Eq. 7, and Eq. 8 remain unchanged from P1. However, Eq. 9 and Eq. 10, computing C S3 l and C S4 l in P1, are replaced by Eq. 13 and Eq. 14, respectively. Usually, each UE is attached to a default S-GW, and all flows of that UE are forwarded to that S-GW to handle their routing locally. For each flow, there is signaling traffic between the MME and the default S-GWs of each UE.

C S3 l = f ∈F j3∈J Y u,j3 j0∈J W j0 • Z l j0,j3 • S3 f ; ∀l ∈ L (13) C S4 l = f ∈F j4∈J Y v,j4 j0∈J
W j0 • Z l j0,j4 • S4 f ; ∀l ∈ L (
In this section, we propose an attachment policy that handles attachment flow by flow. For each flow, both UEs are attached to the same S-GW. The notion of a default S-GW for each UE no longer stands, since a UE can attach to different S-GWs for its different flows. Adding more flexibility to the attachment by allowing UEs to attach to multiple S-GWs at a time, in addition to each flow being handled by only one S-GW, reduces the backhaul consumption caused by signaling.

We formulate P3, the joint user association and attachment per flow optimization problem. Fig. 3 shows the updated data and signaling paths for a bidirectional flow between u and v, respectively associated to j 1 and j 2 . The objective function in Eq. 1 remains the same, as well as the constraints in Eq. 2, Eq. 3, Eq. 4, and Eq. 5. The key differences in P3 with respect to P1 and P2, is the fact that each flow must be attached to one S-GW. We define flow attachment vector T , with T f,j a boolean such that T f,j = 1 if flow f is attached to S-GW j. A constraint stating that a flow is attached to only one S-GW replaces the constraint in Eq. 11, such that:

j∈J T f,j = 1 ; ∀f ∈ F (15)
The data path of the bidirectional flow f is as follows: BS j 1 , S-GW j 5 , BS j 2 , and vice-versa. This prompts a change in the computation of C d l in Eq. 6, which becomes:

C d l = f ∈F 2d f j5∈J T f,j5 ( j1∈J X u,j1 • Z l j1,j5 + j2∈J X v,j2 • Z l j5,j2 ) ; ∀l ∈ L (16)
Following the same reasoning for the signaling paths, Eq. 7, and Eq. 8 remain unchanged from P1. However, Eq. 9 and Eq. 10 are replaced by Eq. 17, a single equation, since there is one S-GW per flow. The signaling bit rate between the MME and this S-GW is denoted S5 f . In Eq. 17, we compute C S5 l as the total bandwidth consumed by the signaling traffic of all the flows f ∈ F on a given link l belonging to the signaling path between MME j 0 and S-GW j 5 .

C S5 l = f ∈F j5∈J T f,j5 j0∈J W j0 • Z l j0,j5 • S5 f ; ∀l ∈ L (17)
V. NUMERICAL RESULTS

A. Network setup

We base our study on a setup well-suited for PS networks deployed in disaster relief scenarios. We consider a random network topology of 5 BSs randomly distributed in a square area of 1 km 2 , as shown in Fig. 4. The network is modeled as a connected random geometric graph, such that a backhaul link exists between 2 BSs if and only if the distance between them is smaller than a given radius η = 0.4 km. We suppose there are 35 randomly distributed UEs, with intra-cellular flows of average data rate d = 1 Mb/s.

As the volume of the signaling traffic and its bit rate are highly dependent on the service in question, and may differ from one particular flow to another, we do not limit our study to pre-defined values of the signaling bit rates. Instead, we evaluate each of our proposals function of different signaling bit rates, in order to emphasize their impact. To that end, we consider the signaling bit rate to be a linear function of the flow data rate, such that Si f = β • d f , ∀i ∈ [START_REF] Manoj | Communication Challenges in Emergency Response[END_REF][START_REF]Google Loon project[END_REF], with β given as a percentage. We set K j = 200 channels, equally divided between DL and UL, with an FDD ratio α = 0.5.

B. Backhaul bandwidth consumption

We set as benchmark the traditional RAN-based association policy, in which the UE associates to the BS from which it gets the maximum SINR and the attachment follows the association, and compare it to each of the proposed association and attachment schemes in P1, P2, and P3.

Each of the optimization problems is solved using the commercial solver CPLEX, despite the problems complexity. This is possible because of the small sizes of the problems in question, a direct consequence of the limited size of PS networks in terms of number of BSs and UEs. Each solution returns user association, user attachment, and MME placement. As our goal is to reduce the backhaul bandwidth consumption, we use as evaluation metric the relative backhaul bandwidth consumption reduction with respect to the best SINR policy, denoted δ, and expressed as a percentage. If C SIN R is the total backhaul bandwidth consumption with a best SINR policy, and C Pi is the total backhaul bandwidth consumption in Pi, then:

δ = 100 • C SIN R -C Pi C SIN R (18)
Fig. 5 shows the relative backhaul bandwidth consumption reduction with respect to the best SINR policy δ (Eq. 18), for P1, P2, and P3. Metric δ is shown function of the signaling bit rate, represented by the percentage β. For β = 0, there is no signaling traffic. We note that, for the 4 scenarios in question, when the topology shown in Fig. 4 is studied, the optimal position of the MME returned by each of the optimization problems is BS 4. Let us first evaluate the results of P1. We notice that, for β = 0, P1 reduces the backhaul bandwidth consumption by 40%. In other words, a gain of 40% in backhaul capacity is achieved when UEs are optimally associated, which is a relatively important gain. If we take the signaling traffic into consideration, we notice that, as the signaling traffic increases (β), the gain does not increase significantly. Indeed, P1 does not optimize attachment, and the results suggest that signaling traffic on the backhaul is not sufficiently reduced when only association is optimized. In other words, the gain achieved by optimizing association in P1 is mainly due to reducing data traffic on the backhaul, and not signaling.

Moving to P2, where attachment is also optimized, it is clear that, for β = 0, the results are exactly the same as in P1. This is expected because when signaling traffic is not accounted for, the only traffic on the backhaul comes from data following this path: BS j 1 , S-GW j 3 , S-GW j 4 , BS j 2 , and vice-versa (See Fig. 2). In this case, the optimal solution is clearly for each UE to attach to the BS it is associated to, similarly to what happens in P1, meaning no need for j 1 and j 3 (resp. j 2 and j 4 ) to be different. However, when signaling is accounted for, the previous statement does not hold anymore, since signaling between S-GW and MME is further routed on the backhaul. We notice that, as the signaling traffic increases, the backhaul consumption reduction also increases, achieving higher gains than in P1 once the signaling bit rate is more than 5% of the flow data rate. This proves that, in case the signaling traffic is significant, optimizing attachment further reduces the overall traffic on the backhaul by reducing both signaling and data traffic, leading to improved gains in backhaul capacity.

Finally, we evaluate P3, where we apply an optimized attachment per flow policy, rather than per user. Similarly to P1 and P2, for β = 0, the backhaul consumption reduction is at 40 % with respect to the best SINR case, proving once more that, when signaling is not accounted for or very low, attachment optimization is not necessary. Nevertheless, the backhaul consumption reduction increases with the increase of signaling traffic. The achieved gains on the backhaul capacity are higher than both P1 and P2 for the same signaling bit rates. For instance, even with signaling rates at β = 1%, there is a slight gain on backhaul capacity in comparison with P1. For β = 10%, the gain is 50% with respect to a best SINR strategy. Thus, the attachment per flow concept proves itself to be interesting in terms of backhaul bandwidth consumption reduction, notably when signaling traffic is important in the network. In Fig. 6, we show the user association distribution, as well as the attachment distribution among the BSs for the best SINR association policy and each of the proposed policies. The shown results correspond to a signaling traffic at β = 5% of the data traffic. We first note that user association distribution is the same in P1, P2 and P3. This is expected, as the difference between these policies mainly lies in the attachment criteria and not the association. In comparison with the best SINR policy, we notice that more users are associated to BS 4 than any other BS. This is one of the reasons of the achieved backhaul bandwidth consumption reduction observed in Fig. 5, since BS 4 is the BS co-located with the MME, as returned by the optimal solution. For the user attachment, the observation for P1 is redundant with user association, since there is no difference between association and attachment in this case. However, it is clear that when attachment is optimized in P2, more users are attached to the S-GW of BS 4, which is also co-located with the MME. Similarly, this is the case in P3, where the majority of the flows are also attached to BS4.

C. Association and attachment distribution

These observations indicate that, for most UEs, it is more beneficial to associate and/or attach to the BS co-located with the MME, if this is an option, as long as that BS can handle all the users. While this could raise questions on the achieved load balancing, we remind that RAN constraints are also accounted for, meaning no BS can take more users than allowed by its capacity.

VI. CONCLUSION

In conclusion, we revisited in this paper the user association problem, in the context of PS rapidly deployable networks. We proposed an optimal user association that minimizes the bandwidth consumption on the backhaul, while respecting the stringent user guaranteed bit rate requirements, and accounting for RAN constraints. This association significantly reduces traffic on the backhaul in comparison with a traditional RANbased association, achieving 40% less backhaul bandwidth consumption. Moreover, we showed that jointly optimizing user association and user attachment further reduces bandwidth consumption on the backhaul when signaling traffic is significant. While this study is limited to the offline problem, it can serve as a basis for more practical online user association schemes, in which a backhaul-aware optimal association decision is made in real-time for each user.

Fig. 1 .

 1 Fig. 1. Data and signaling traffic between BSs for a bidirectional flow in problem P1.

Fig. 2 .

 2 Fig. 2. Data and signaling traffic between BSs for a bidirectional flow in problem P2.

Fig. 3 .

 3 Fig. 3. Data and signaling traffic between BSs for a bidirectional flow in problem P3.

Fig. 4 .

 4 Fig. 4. Network topology.

Fig. 5 .

 5 Fig. 5. Relative backhaul bandwidth consumption reduction with respect to the best SINR policy for P1, P2, and P3, function of the signaling traffic.

Fig. 6 .

 6 Fig. 6. User association and attachment distribution among the BSs for the different association/attachment policies, for signaling traffic at β = 5%.


Isidora Stojanovic

Context and Disagreement

Keywords: faultless disagreement, contextualism, relativism faute, contextualisme, relativisme

This paper is an occasion to take stock of the place that the argument from faultless disagreement has occupied in philosophy of language in the last fifteen years, in particular in the debate between contextualism and relativism. The survey offered in the first part of the paper appears to show that the phenomenon of disagreement fails to provide any strong motivation for adopting any novel semantic framework, contrary to relativists' claims. But, on a more positive note, the interest in disagreement has allowed us to better understand how language works. The second part of the paper explains how the fine-grained structure of meaning -at the level of words, sentences and even entire discourse -reveals a variety of sources that may lead discourse participants to disagree.

delicious to Kathy, and it tastes awful to Rob, it seems that they are both right, and that they are both saying something correct, or even true. At any rate, neither of them seems to be wrong in the way one would be in making a false claim, such as "São Paulo is to the North of Rio de Janeiro". Secondly, it also seems that they are in disagreement, which is indicated by Rob's use of the negation particle 'no', as well as his asserting the negation of the sentence asserted by Kathy. Thirdly, if disagreement is to be genuine, it seems that this should preclude the possibility that both parties may be right. While each of the three intuitions looks plausible when considered on its own, taken together, they are in tension (or even in contradiction). I suggest that the term "faultless disagreement" be used to describe the real phenomenon that arises when we have dialogues that trigger those three intuitions. Granted that there is solid empirical evidence that there is such a phenomenon (and I don't think that anyone in the debate disputes this), the theoretical question that arises is how one should account for those seemingly inconsistent intuitions. The early relativist literature yields the following picture of the repartition between the possible theoretical positions. Invariantism would be the view which seeks to explain away the first intuition: it may seem that both parties are right, but they really aren't. Contextualism would be the view that seeks to explain away the second intuition: it may seem that there is disagreement, but there really isn't. Finally, relativism would be the view that does away with the third intuition, and seeks to demonstrate that there can be genuine disagreement even when both parties are right.

We'll shortly see that this picture is not completely accurate, and in particular, that contextualism encompasses several views that accept that there can be disagreement and are perfectly able to account for it. In the remainder of this section, I will first look at the way in which certain relativists have attempted to account for faultless disagreement, and explain why their attempt has failed. Then I will go through some more successful contextualist attempts to account for disagreement.

The argument from disagreement as an argument for relativism

The argument from faultless disagreement to semantic relativism may be seen as taking the form of an inference to the best explanation. Caricaturing perhaps a bit, a relativist would argue along the following lines. 3 Step one. The three intuitions that we are confronted with (faultlessness, disagreement, and disagreement-precludes-faultlessness) are not on a par. The first two are more robust and both of them ought to be upheld. (This is why they think that neither invariantism nor contextualism are viable positions.) Hence we must give up the third intuition, and make room for a notion of disagreement that does not preclude that both parties may be right.

Step two. The best way to make room for such a notion is by allowing for contents whose truth depends on an agent (or assessor, or judge). What it takes for two parties to disagree is that one party asserts some content, and the other party rejects that same content. This is compatible with the idea that both parties are right -provided, of course, that the content over which they disagree is true when assessed from (or evaluated at) the one party, and false when assessed from/evaluated at the other party. The relativist semantic framework, in which contents are defined as mappings from agents (also called assessors or judges) and other parameters, such as worlds and times, to truth values, would then yield a straightforward account of faultless disagreement.

I will focus here on only one line of criticism, which is the one that I advanced in [START_REF] Stojanovic | Talking about taste: Disagreement, implicit arguments, and relative truth[END_REF]. 4 It goes as follows. Assume, for the sake of the argument, that we are operating with a relativist semantics, on which contents are mappings from agents (and other parameters) to truth values. Assume furthermore that speakers are semantically competent, in the sense that they are aware that a statement of the form "This is delicious" is apt to bear a truth value only when it is evaluated at an agent (or whatever other suitable parameter). Then, looking at the example in (1), Kathy knows that the content that she is asserting is true or false depending not only on what the world is like, but also on the judge. The same goes for Rob when he denies the content asserted by Kathy. Now, if Kathy intends the content that she is asserting to be evaluated for truth at herself, and if Rob intends the denial of that content to be evaluated for truth at himself, then it is no longer clear why they should be seen as disagreeing. For both of them know that one and the same content may take different truth values when evaluated at different agents, and they also know that the one's assertion and the other's denial of the same content are inconsistent only when evaluated with respect to the same agent. Hence if each party intends the asserted content to be evaluated at himself or herself, and if this is mutually clear between them, then they must realize that there is no clash in truth value between their respective claims (when evaluated for truth as they each intend them to be), and that their apparent disagreement must be driven by something else than aiming at truth. The rebuttal of the relativist's argument that I have just sketched is formulated for a simple version of the relativist framework, namely, the one that defines contents as mappings from parameters that include agents (judges, assessors) to truth values, and that does not stipulate that there is a determinate way in which the context of utterance would fix the values at which the truth of the content is to be evaluated. This is the framework of [START_REF] Kölbel | Truth Without Objectivity[END_REF] and [START_REF] Lasersohn | Context dependence, disagreement, and predicates of personal taste[END_REF], but not that of MacFarlane (2014), who, in the formal framework, introduces a distinction between contexts of utterance and contexts of assessment. While there are genuine formal differences between the simpler framework and MacFarlane's, that does not make the latter better suited to account for the puzzle. For assume Kathy and Rob to be competent speakers; they must be aware, then, that their claims can only be evaluated for truth with respect to a context of assessment. If Kathy intends her claim to be evaluated with respect to her own context of assessment, and Rob intends his denial of Kathy's claim to be evaluated with respect to his own context, and if this is mutually clear between them, then we have hardly made any progress towards an explanation of their presumed disagreement.

MacFarlane is aware that the formal framework does not by itself provide any account of disagreement. He does offer such an account, though, by positing two norms of assertion, a truth norm (2014: 102-103), and a retraction norm (2014: 108). Regardless of the problems and/or merits of MacFarlane's proposal, what matters for our present purposes is that, although the two norms are formulated by presupposing a distinction between contexts of utterance and contexts of assessment, the gist of his explanation is not at all bound up with relativism qua semantic framework.5

The argument from disagreement as an argument against contextualism

The argument from disagreement has triggered a large number of responses. In what follows, I will focus on five, which I take to be the most important. All five have been made (unless I am mistaken) on behalf of contextualism, though some responses work equally well on behalf of invariantist approaches. 6 Let me stress from the outset that these approaches should not be seen as competing with each other but, rather, as complementing each other, and sometimes even as overlapping. I label them as follows, and will discuss them in this order: (i) the underdetermination approach; (ii) the metasemantic approach; (iii) the metalinguistic approach; (iv) the presuppositional approach; (v) the attitudinal approach.

The underdetermination approach. I start with this one not only because it is the one that I proposed in [START_REF] Stojanovic | Talking about taste: Disagreement, implicit arguments, and relative truth[END_REF] 7 but also because it was one among the first to have been put forward. It goes as follows. The intuitions of faultlessness and of disagreement that dialogues such as (1) trigger are not to be taken at face value. At a first glance, such a dialogue may well trigger those two intuitions, but in order to know whether we have a case of genuine disagreement (i.e. disagreement over the truth of a statement), or rather, a case in which the two parties are expressing their own preferences, we need more information about the context, and in particular, on how such a dialogue may evolve. I speculated that the meaning of the claims under consideration can be made more specific, and receive different readings. For example:

2. Kathy (talking about parsley): "This is delicious". Rob: "No, it isn't." Kathy: "Well, look, all I mean is that to me it is delicious." Rob: "OK, fair enough. But to me, it tastes like a bitter, dry and rough piece of rubbish, and I just can't understand how anyone can like it." 3. Kathy (talking about parsley): "This is delicious". Rob: "No, it isn't." Kathy: "Yes it is. And I don't just mean that I like it. It is delicious, to anyone." Rob: "You are completely wrong. It isn't delicious, it tastes like a bitter, dry and rough piece of rubbish."

The way in which the dialogue in (2) evolves suggests that the intended reading for Kathy's initial claim is one on which she occupies the relevant experiencer argument, while the way in which it evolves in (3) suggests that the intended reading is a generic one, that is to say, that the experiencer argument is bound by a covert generic operator (see e.g. [START_REF] Moltmann | Relative Truth and the First Person[END_REF] and [START_REF] Pearson | A judge-free semantics for predicates of personal taste[END_REF] for the idea that taste predicates are covertly generic). Consequently, (2) provides a case in which the faultlessness intuition wins, so to speak, whereas (3) provides a case in which Kathy and Rob disagree, pretty much in the way in which they might disagree over the truth of some general descriptive claim, such as, say, the claim that parsley contains more iron than cilantro does.

One issue that is important and that I did not address in [START_REF] Stojanovic | Talking about taste: Disagreement, implicit arguments, and relative truth[END_REF], but did so in Stojanovic (2012a), is the question of what kind of evidence could ultimately settle a disagreement such as the one in (3). In this respect, the underdetermination approach goes only part of the way towards accounting for the general phenomenon.8

The metasemantic approach. [START_REF] Glanzberg | Context, Content and Relativism[END_REF] provides another early response to the argument from disagreement, similar in spirit to the underdetermination approach.

Glanzberg's focus, though, is on the nature of adjectives and, in particular, the fact that, qua gradable adjectives, their semantics requires scales and thresholds at which sentences containing such adjectives are to be evaluated. Relying on the significant semantic literature on adjectives, including [START_REF] Bierwisch | The Semantics of gradation[END_REF] work on multidimensional adjectives, 9 Glanzberg sets out to propose a contextualist account of predicates of personal taste, in line with the semantics of other gradable adjectives. To be sure, adjectives such as 'tasty' and 'fun' are not as simple as adjectives such as 'tall'. While 'tall' has a single conventionally associated scale, namely, height, 'fun' and 'tasty' may requires multiple scales. But, as he notes, "this is not a feature specific to adjectives of personal taste. Many gradable adjectives can be associated with multiple scales. For instance, someone can be smart as in 'book smart' or 'street smart', a large city can be large in population, geography, etc." (2007: 10). Secondly, predicates of personal taste involve response-dependent properties. It makes little sense to think of tastiness as a property that an object can possess in itself, independently of there being some individual who could potentially experience its taste (and similarly for 'fun'). [START_REF] Glanzberg | Context, Content and Relativism[END_REF] is relatively uncommital regarding the status of the experiencer argument. He does not posit it as a bona fide hidden argument, but writes: "To take response dependence into account, we will need to see the scales associated with tasty and fun to be experiencer-involving scales" (2007: 13). Finally, the gist of his rebuttal of the argument from disagreement is to point out that fixing all the different values of all those different parameters, in a context, is no straightforward matter and requires what he calls "indirect metasemantics." He similarly believes that whether there is genuine disagreement or not may depend on the context: if all the relevant parameters, that is to say, scales, experiencers and thresholds, are the same for Kathy's and Rob's utterances, we do have disagreement; but if the scale that is relevant to interpreting Kathy's utterance differs from the one relevant to interpreting Rob's utterance (as will happen, for example, if the experiencers relevant to fixing her scale are, say, food connaisseurs, and the ones relevant to fixing his scale are people in general), then it is no longer clear that they are disagreeing -or rather, it is no longer clear what it is that they are disagreeing about. For, in a sense, their disagreement turns on the question of how to fix the scale relevant for interpreting 'tasty' and, in this respect, the proposed account anticipates the gist of the metalinguistic approach, to which I now turn.

The metalinguistic approach. Sundell (2011) may be seen as the most fierce defender of the metalinguistic approach. There is some overlap between his proposal and both the underdetermination and the semantic approach, since all three hold that a dialogue that at a first glance may look like a disagreement in which the two parties disagree about whether some object has a certain property (e.g. whether tastiness is a property of parsley) may turn out, upon scrutiny, to be a disagreement about questions such as what counts, in a given context, as "tasty". The negotiation of scales and standards is thus seen, in the metalinguistic approach, as what often drives our disagreements not only on matters of taste, but also on aesthetic matters (see [START_REF] Sundell | Aesthetic Negotiations[END_REF] or on moral matters (see [START_REF] Plunkett | Disagreement and the semantics of normative and evaluative terms[END_REF]. One of the key points of this approach is to argue that even though disagreement very often turns out to be a metalinguistic disagreement, this does not make it less significant than other kinds of disagreements. The authors also point out that in ethics and aesthetics, disagreements are often about the very concepts themselves. Thus in disagreeing, say, whether discussions in analytic philosophy are agressive, we may agree on which criteria make a discussion agressive, and disagree whether the discussions in analytic philosophy are such, but we may also disagree about the very criteria that make a discussion count as an agressive one. (This is my example, not theirs; but I take it that it illustrates their general point.)

The presuppositional approach. Presupposition is one of the most central phenomena in language, and we will shortly see that there is more than one way in which this notion is relevant to understanding, at least from a linguistic point of view, why one may be led to Isidora Stojanovic, "Context and Disagreement" disagree with a statement made by somebody else. However, in the present context, by the presuppositional approach I mean the approach that Dan López de Sa has been pursuing since the beginning of the debate (see López de Sa ( 2008), ( 2015)), also discussed in [START_REF] Marques | Disagreement about taste: commonality presuppositions and coordination[END_REF]. What the presuppositional approach shares with the first two approaches is the idea that, taken at face value, a dialogue such as (1) may turn out to be a genuine case of disagreement, but it need not be. The way the presuppositional approach accounts for this idea is that we start from the assumption that there may be different standards of taste, which hardly anyone disputes. But while we know that tastes do differ, when we use a predicate of personal taste, we normally presuppose that our interlocutors share our taste. If I take you to my favorite restaurant, and I tell you that a certain dish is delicious, that may help you decide what to order partly because we presuppose that our gustatory tastes are alike. This kind of presupposition is what López de Sa calls a presupposition of commonality. Now when we enter into a disagreement, and the presupposition is satisfied -that is to say, we do have a similar taste, then we disagree indeed, although it is no longer a faultless disagreement. For if the two interlocutors share the same standard of taste, and the standard is determinate enough, then relative to that standard, either a sentence or its negation can be true, but not both. On the other hand, if our standards of taste diverge significantly, then the presupposition fails, and a linguistic exchange of the from "This is delicious -No, it isn't" becomes deficient in a similar way in which (adapting a famous example from David Kaplan) if I presuppose that the person at whom I am pointing is Rudolf Carnap, and you presuppose that it is Spiro Agnew, and I say "He is a famous philosopher" and you reply "No, he isn't", we are not really disagreeing.

The attitudinal approach. The last line of response to the relativists' argument from Isidora Stojanovic, "Context and Disagreement" disagreement that I want to mention takes inspiration from expressivism (see e.g. [START_REF] Gibbard | Wise Choices, Apt Feelings: a Theory of Normative Judgement[END_REF]). As is well known, for an expressivist, an evaluative statement is not in the business of stating facts, but rather, it aims at expressing the speaker's attitude. When Rob and Kathy disagree over the deliciousness of parsley, they are not trying to determine what parsley is factually like, but rather, Kathy is expressing her positive attitude towards parsley and Rob, his negative attitude. This clash of attitudes constitutes a genuine disagreement (or so the idea goes). If such a disagreement in attitude is already able to account for the disagreement intuition in cases such as (1), then the semantic interpretation of what Kathy and Rob are saying is, in a way, beside the point. Even if they stated their preferences using the first person pronoun, as in (4) below, they would still be disagreeing in the relevant sense: 4. Kathy: "I like parsley".

Rob: "I dislike it."

Although the idea derives from expressivism, an expressivist semantics is not required to deploy this kind of mechanism as an explanation of why we perceive disagreement in cases such as (1). The same strategy becomes available to contextualists, or even invariantists. For a development of this line of reply, see, inter alia, [START_REF] Huvenes | Varieties of disagreement and predicates of taste[END_REF] and [START_REF] Marques | Doxastic disagreement[END_REF][START_REF] Marques | Disagreeing in Context[END_REF].

With this, I close the survey of the argument from disagreement and the role that it has played in the contextualism-relativism debate. To be sure, the survey does not claim to be exhaustive, and there are other strategies that have been proposed. In the next section, I will draw some lessons regarding the relationship between theory of meaning and theory of disagreement, and will argue that these explanations of what is going on are not mutually exclusive but, to the contrary, often work together, as I will show on a concrete case.

The linguistic complexity of disagreement: a case-study

Based on the discussion from the first part of the paper, and in general, on a critical assessment of the place that the argument from disagreement used to occupy but gradually lost, it is tempting to draw a negative conclusion about the relationship between disagreement and semantics. On the one hand, it is widely agreed nowadays that relativist semantics per se, be it some simpler version as in [START_REF] Kölbel | Truth Without Objectivity[END_REF] or [START_REF] Lasersohn | Context dependence, disagreement, and predicates of personal taste[END_REF], or a more cumbersome version as in MacFarlane (2014), does not yield a straightforward account of disagreement. This is conceded even by the proponents of relativism, as witnessed by the need in MacFarlane ( 2014) to develop a heavy normative machinery to handle disagreement. On the other hand, as revealed through the various responses to the argument from disagreement, non-relativists have a range of different mechanisms (semantic, pragmatic, cognitive) to which they can appeal in order to shed light on what is happening in various cases of disagreement over matters of taste. Several of these mechanisms are not tied to a contextualist semantics, but are available to almost equal degree to contextualists, relativists, invariantists and even expressivists.

Based on this, one may be tempted to think that semantics, that is, the theory of meaning, and the theory of disagreement, have nothing to do with each other. The intended take-home message of this paper is that we should resist such a pessimistic conclusion. The study of disagreement has, to the contrary, been a fruitful and constructive enterprise that has made it possible to reach a better understanding of the fine-grained meaning structure that the expressions and constructions at stake possess. Looking at disagreement does teach us stuff about semantics -although not quite the lesson that the relativists wanted us to draw.

Conversely, understanding the different aspects of meaning provides valuable insight into the Isidora Stojanovic, "Context and Disagreement" reasons that may drive people into disagreeing.

The remainder of the paper is expands on this optimistic conclusion by looking at a real life case of a disagreement regarding hipsters. My case study is based on an online discussion about hipsters, under the title "Why do so many people hate "hipsters"?" I have selected from it a series of excerpts, listed below, that are meant to help me illustrate some of the previous theoretical observations regarding disagreements. 10 8. I see a lot of hate for the hipster crowd and I can't really understand why. I myself am not a hipster. But I do know a LOT of people who could be considered to be hipsters and they are all really nice, well educated people. Usually very friendly people who would give you the shirt off their back if you needed it. And when it comes to music, politics, whatever.... I have never gotten the music snob vibe from them, more so awesome suggestions of some music I might not of heard. 9. I don't hate hipsters as people, I hate the hipster aesthetic because it is insincere. As I see it, hipsterdom is based on the notion that individualistic authenticity can be bought and displayed as a piece of fashion. Obviously, this is self-contradictory, and it pisses me off to no end. 10. The insincerity aesthetic is a little irritating, but I find the accompanying pretentiousness to be the most annoying part.

11. "Hipsters" are trend-eating, fad-mongering, consumer-whores that dress up like each other, while blindly reinforcing and building the corporatocracy they ostensibly revile.

It doesn't involve any sort of creativity or intellectualism to be a hipster.

12. I don't understand why some people, myself included, are automatically "trend 10 I have perhpas included more excerpts that I need to make my points, but they provide a more complete background for the discussion of the specific examples.The details of the discussion may be consulted here: https://www.reddit.com/r/AskReddit/comments/fppf1/why_do_so_many_people_hate_hipsters/ whores" when all we do is buy clothes we think make us look nice.

13. It is socially acceptable to hate them. Take as fact that most people crave acceptance.

A way to feel a part of a group is to extol views and ideas that are already widely accepted. Given that reddit is a place where it is already popular to hate on hipsters, simply agreeing or propagating that sentiment will result in acceptance. (…) This is similar to the way that everyone seems to hate on socks and sandals. There is nothing inherently wrong with this, and in fact, it's very comfortable.

14. What bugs me is that there is this tacit assertion that it DOES take creativity and intellectualism to be a hipster. It's this completely hollow, passive-aggressive sense of superiority that bugs me. I actually sort of like the hipster look to be honest with you.

15. Because they're hypocritical. They try to be individual yet they're conforming to the same aesthetic. I don't dislike hipsters as people. I dislike hipsters as a persona.

They're often pompous, arrogant, and snobbish; hating on me for my "mainstream" likes.

16. I always kinda saw your type of generalization and stereotyping as a tad bit ignorant and clueless. (as a reply to 15) 17. I always kinda sorta thought that passive aggressiveness and nonchalance were the trademarks of a hipster. (as a reply to 16) 18. I can't be a hipster because I'm fat; I can't fit in those skinny jeans and I look like an idiot in those flourescent raybans. That's why I hate hipsters.

19. They're a commercialized and consumption-driven version of the "back to nature" movement, which is insulting to everyone who is genuinely trying to encourage a lifestyle that is basic and honest. 20. My main beef with hipsters is that they are, ostensibly, the type of people I would love Isidora Stojanovic, "Context and Disagreement" to be good friends with. For the most part, they have a lot of good tastes, are more intelligent than the average human, are artsy, politically active, and individualistic.

They are the people I hung out with, before they became hipsters.

21. When I think of hipsters I think of arrogant gits who are all snobby and elitist, and yet, also ignorant. If someone is that nice they're not really a hipster, by definition, because being kind is too mainstream.

22. I dress like how most would describe a "hipster" and get insulted almost every day for it. I dress like this because I care about fashion and I believe that I look nice in these clothes. I don't do it to be different or because I think it will make me "cool", I just feel good in these clothes. I don't hate on or think I'm better than people that dress other ways, yet it's always assumed I do. I typically just have to ignore the barrage of driveby insults I get daily because I know I'm happy how I am.

23. I think there's a difference between alternative lifestyles and being a hipster. Hipsters, to me, are all about devouring meaningful things and reducing them to their most consumerist, vapid incarnation. (…) It's a reactionary thing, experience something good in the world and then make it your own without actually adopting the principles.

That's why it's something to be scorned.

The first thing that strikes one in this discussion is that it is, to a large extent, a disagreement in attitude. It is a disagreement between pro-hipsters and anti-hipsters, between people who like hipsters and those who dislike them, or even hate them. Interestingly, even though the leading question of the post is "Why so many people hate "hipsters"?", the nature of the replies and comments does not address that descriptive question (with (13) being a possible exception), but rather, it addresses something akin to a normative question along the lines of "Do "hipsters" deserve to be hated, and if so, why?"

The second striking observation is that, to a large extent, the discussion is meta-linguistic.

An early indication of this metalinguistic character is the use of quotation marks with the word 'hipster' in the leading question itself, and quotes are used in several posts (e.g. ( 11), ( 22)). Other clear indications of the metalinguistic character may be seen in posts whose speakers explicitly address the question of what makes a hipster a "hipster", a nice example of which is (21), repeated below as (24): 24.

When I think of hipsters I think of arrogant gits who are all snobby and elitist, and yet, also ignorant. If someone is that nice they're not really a hipster, by definition, because being kind is too mainstream.

The first sentence may be interpreted as a metalinguistic statement about which group of people the term 'hipster' refers to. Note also the use of the "by definition", a clearly metalinguistic device. Other neat illustrations of the metalinguistic nature of the disagreement are ( 14), ( 17), ( 22), and especially (23), in which the speaker contrasts the concept of leading an "alternative lifestyle" (presumably positively valued) and "being a hipster" (negatively valued). In "Hipsters, to me, are all about devouring meaningful things and reducing them to their most consumerist, vapid incarnation", the appositive "to me" works as a metalinguistic hedge that means something along the lines "the way I understand the term 'hipster'".

I now turn to a third observation that percolates from this case study, and has to do with something fairly similar to López de Sa's presupposition of commonality. The kind of presupposition that lies in the background of the discussion over hipsters is certainly not the presupposition that the different participants in the debate share the same taste. To the contrary, it is taken for granted from the start that the tastes are likely to depart considerably: the anti-hipsters will, in general, dislike those things that are highly valued according to the Isidora Stojanovic, "Context and Disagreement" hipster taste, while the pro-hipsters will include many people who endorse the hipster taste.

(Of course, there are exceptions, as in ( 14), in which the speaker expresses an anti-hipster stance, while admitting that he or she likes the hipster look, hence shares the hipster taste.)

The reason why López de Sa's explanation does not apply squarely onto the present case study is that the disagreement over hipsters is much more complex than, say, a disagreement over parsley. It is not, or at least, not exclusively, about taste. (Though taste, in a broad sense, is involved, such as music taste and fashion taste.) Some of the disagreement is aesthetic (as stressed e.g. in (9): "I don't hate hipsters as people, I hate the hipster aesthetic"), but a lot of the disagreement turns on issues that arguably belong to the moral realm. This is not surprising, given that the underlying normative question is whether a group of people deserves to be hated, which calls for ethics-related justifications. Hating somebody just because of the way they look is perceived, in our society, as wrong, hence, even if de facto some of the hipster-haters hate them because of the way they look, they will likely try to back up their claims with arguments having to do with some moral qualities that they ascribe to hipsters. And this is indeed what we see in many posts, where hipsters are described as insincere (9), pretentious (10), hypocritical (15), pompous (15), arrogant (15, 21), snobbish, snobby (15, 21), or elitist (21), all of which are thick terms that are used to convey negative value-judgements.11 Consumerism is another characteristic that various speakers appeal to (e.g. ( 11), ( 19), ( 23)) in order to justify their dislike for hipsters. Conversely, in pro-hipster posts, we can also pinpoint terms that have a positive valence: really nice, well educated, friendly (8), intelligent, artsy, politically active, individualistic (20). 12Turning back to the idea of a presupposition of commonality, we can see it at work in our case study in the following way. Although it is agreed from the start that the pro-hipsters and the anti-hipsters need not share their tastes, both sides presuppose that they share some more general values. For instance, they mutually take it for granted that the qualities of arrogance and insincerity are bad qualities -and then, some anti-hipsters claim that these are, in general, qualities possessed by hipsters, while pro-hipsters balk at this kind of generalization. As a general pattern, the two sides in a dispute often agree on some more basic set of values -or, more precisely, they presuppose that they share some more basic set of values -, which in turn makes it possible for them to rationally disagree over partially normative issues, such as whether hipsters are dislikeable.

Just as this case study illustrates some presuppositions of commonality that are in place, it also serves to illustrate what happens when such a presupposition breaks down. Thus a couple of anti-hipster posts, e.g. ( 9), (11), or (19), aim to back up their dislike of hipsters by describing them as fashion-followers who care about trends, and, importantly, by assuming that to have this sort of property is bad, and that its badness must be mutually acknowledged.

In ( 12) and ( 22), however, the speakers explicitly address -and reject -the presupposition that dressing like a hipster and caring about fashion is in any way bad. The clash between the two sides in this case is, then, one in which the relevant presupposition of commonality no longer holds: one side values interest in fashion negatively, while the other side does not value it negatively. There still is a disagreement, but one which is now about the sets of values that the two disagreeing parties endorse respectively.

To take stock, we see several disagreement patterns:

(i) a metalinguistic disagreement over who counts as a "hipster": people who are nice, well-educated, art-lovers etc. vs. people who have distorted the original idea and have turned it into an elitist and consumerist fashion trend;

(ii) a factual disagreement over the properties that are attributed to a group: whether hipsters are, generally speaking, arrogant, pretentious and insincere or, to the contrary, really nice and friendly; in this case, the two sides converge in valuing arrogance, pretentiousness and insincerity negatively, and niceness and friendliness positively;

(iii) a disagreement in values: the two parties may agree on a property that they attribute to hipsters as a group, for instance, that they like to dress in a certain fashion, yet they disagree whether having this property has any bad implications or not.

By way of wrapping up this case study, let me note that here, we did not see any support for either the metasemantic or the underdetermination approach. This should come as no surprise, because those two specifically aim at explaining why predicates of personal taste create dialogues that trigger intuitions of faultless disagreement. 13 *** My aim in this paper has been to discuss the role that considerations about disagreements over matters of taste (and similar subjective matters) have played in shaping the landscape of natural language semantics. I have argued that adopting a relativist semantic framework is neither necessary nor sufficient in order to understand what happens in the alleged cases of faultless disagreement. I have not argued against relativism per se -indeed, there are areas, such as metaethics, in which relativism constitutes an important and respectable tradition (see [START_REF] Stojanovic | Metaethical Relativism[END_REF] for discussion). My claim is, rather, that the phenomenon of disagreement does not straightforwardly motivate relativist semantics, and that, conversely, contextualist semantics has a variety of mecanisms at its disposal to account for the phenomenon. The take-13 This being said, there is one respect in which the underdetermination proposal may be relevant. For even in this case study, we can notice a contrast between expressing a purely first-personal attitude (like or dislike) towards hipsters vs. arguing that people in general ought to have a certain attitude (like or dislike) towards them. The contrast is illustrated, for example, by the emphasized used of the first person pronoun in (18): "That's why I hate hipsters" as opposed to the generic construction "That's why it's something to be scorned" in (23). See also Stojanovic (2012a) for a related point concerning expressions of emotion. home message of this paper is that the various contextualist strategies that arose in reply to the argument from disagreement actually reveal a variety of language-related sources that may lead people to disagree. These contextualist replies do not compete with each other but, rather, complement each other. Disagreement is a complex phenomenon, in which context intervenes at many stages, as I have illustrated with a case-study.

For the sake of convenience, I will be mainly talking about predicates of personal taste, and will leave aside epistemic modals. I hope that nothing crucial hinges on that.

Isidora Stojanovic, "Context and Disagreement"

I think that it is fair to attribute this line of argument to[START_REF] Kölbel | Truth Without Objectivity[END_REF],[START_REF] Lasersohn | Context dependence, disagreement, and predicates of personal taste[END_REF], and[START_REF] Egan | Epistemic Modals in Context[END_REF],[START_REF] Stephenson | Judge-Dependence, Epistemic Modals, and Predicates of Personal Taste[END_REF],[START_REF] Richard | When Truth Gives Out[END_REF]. Shortly we will see that the view in MacFarlane (2014) is more elaborate.

I think that the same line of criticism has been noted by other people as well, which comes as no surprise, since it is quite straightforward.Isidora Stojanovic, "Context and Disagreement"

This is admittedly a bit quick, but I will not go into further elaboration in this paper in part of lack of space, and in part because I believe that MacFarlane's explanation is on the wrong track. In particular, it has been shown in[START_REF] Kneer | Perspective in Language[END_REF] that almost no ordinary speaker subscribes to the norm of retraction either in the case of taste statements or in the epistemic case. Kneer tested both for retraction and for reassessment of truth value regarding claims such as "Fishsticks are tasty" that a person made at an earlier time (when they used to find them tasty) and was asked to reassess from a later time (when they no longer found them tasty). Ordinary speakers do not think that the change of taste makes the earlier claim false, nor do they think that a person is required to retract their claim. I am also skeptical that MacFarlane's formal account presents any advantage over the simple relativist account; seeStojanovic (2012b) for further details.

Invariantist semantics, which would be a semantics that analyses a predicate such as 'tasty' or 'fun' as a predicate that either applies to an object or doesn't, is not plausible from a linguistic point of view. Such predicates are gradable adjectives, and if they are to be such that their application conditions are context-insensitive, then they should correspond to so-called absolute gradable adjectives, such as 'open' or 'straight' (see[START_REF] Kennedy | Scale structure, degree modification and the semantics of gradable predicates[END_REF]. At the very least, predicates of taste have thresholds that may vary with the context, which already requires a contextualist semantics.Isidora Stojanovic, "Context and Disagreement"

[START_REF] Stojanovic | Talking about taste: Disagreement, implicit arguments, and relative truth[END_REF], I did not use the term "underdetermination"; I only did so inStojanovic (2012a).Isidora Stojanovic, "Context and Disagreement"

A contextualist semantics for predicates of personal taste in the same spirit of the one I sketched in[START_REF] Stojanovic | Talking about taste: Disagreement, implicit arguments, and relative truth[END_REF], albeit more elaborate, is defended e.g. in[START_REF] Saebø | Judgement ascriptions[END_REF] or[START_REF] Bylinina | The Grammar of Standards: Judge-Dependence, Purpose-Relativity, and Comparison Classes in Degree Constructions[END_REF], although these authors are not particularly concerned with disagreement.

For a more up-to-date study of multidimensional adjectives, see[START_REF] Sassoon | A typology of multidimensional adjectives[END_REF].Isidora Stojanovic, "Context and Disagreement"

[START_REF] Cepollaro | Hybrid Evaluatives[END_REF], we propose a presuppositional account of thick terms and slurs. We analyze them as having a certain descriptive content while at the same time triggering an evaluative presupposition. For example, the term 'arrogant' would refer to people who behave in a certain way, and at the same time, it would trigger the presupposition that people who behave in that way are bad because of that. We also discuss what happens when the interlocutor does not endorse the evaluative presupposition (as in the case of objectionable thick terms; see e.g.[START_REF] Väyrynen | Objectionable Thick Concepts in Denials[END_REF]).

It is at least controversial whether 'artsy', 'politically active', or 'individualistic' should be considered as thick terms, and my own view would be that there are not, to the extent that no positive (or, for that matter, negative) valence is associated with those terms as a matter of their meaning. But in the present context, they are clearly used by the speaker of (20) in order to convey a positive value-judgement.Isidora Stojanovic, "Context and Disagreement"

Acknowledgments

Earlier versions of this work were presented at the conference Faces of Disagreement in Montreal, Canada, on 27 May 2017, and at the University of Taiyuán, China, on 22 August 2017. I would like to thank the audiences at these events for helpful feedback, in particular Ethan Jerzak, Michele Palmira, Sarah Stroud, Christine Tappolet and Sandy Goldberg. I have also benefited from discussions with Julia Zakkou, Neftalí Villanueva, Teresa Marques and Dan Zeman. I am particularly grateful to Edwiges Maria Morato and Anna Christina Bentes for their invitation to contribute to the present issue. Finally, I acknowledge institutional support from the following grants: ANR-10-LABX-0087 IEC, ANR-10-IDEX-0001-02 PSL, MINECO FFI2016-80636-P, and European Union's Horizon 2020 Marie Skłodowska-Curie grant agreement n. 675415.