G Manson

J Norwood

A Marabelle

H Kohrt

R Houot
email: roch.houot@chu-rennes.fr

Prof Roch Houot

Biomarkers Associated with Checkpoint Inhibitors

Keywords: Biomarkers, checkpoint inhibitors, cancer, immunotherapy

Checkpoint Inhibitors (CPI), namely anti-CTLA4 and anti-PD1/PD-L1 antibodies, demonstrated efficacy across multiple types of cancer. However, only subgroups of patients respond to these therapies.

Additionally, CPI can induce severe immune-related adverse events (irAE). Biomarkers that predict efficacy and toxicity may help define the patients who may benefit the most from these costly and potentially toxic therapies. In this study, we review the main biomarkers that have been associated with the efficacy (pharmacodynamics and clinical benefit) and the toxicity (irAE) of CPIs in patients.

Introduction

Checkpoint Inhibitors (CPI) are a new class of anti-cancer agents. These antibodies (Ab) target normal immune cells in order to stimulate the anti-tumor response. They work by blocking interactions between inhibitory receptors expressed on T cells and their ligands. In oncology, the two main classes of CPI which are the most advanced in clinical development are the anti-CTLA-4 and anti-PD-1/PD-L1 Abs. Three of these Abs have been approved by the FDA for clinical use (Table 1). CPI can have efficacy across several types of cancer. However, only subgroups of patients respond to these drugs. Additionally, CPI can induce "autoimmune-like" toxicities. These findings raise several questions.

What is the impact of CPI on the immune system? Are there biological markers related to their efficacy or toxicity? After a brief review of the mechanisms of action of CPI, we will present the biomarkers that have been associated with pharmacodynamics changes, therapeutic efficacy and toxicity of these treatments in clinic.

CTLA-4 pathway

T-cell activation following the stimulation of its receptor (T cell receptor [TCR]) requires a second signal which results from the interaction between the activating receptor CD28 located on the T cell surface and the CD80 (B7.1) and CD86 (B7.2) molecules expressed by the antigen-presenting cells (APC). Secondly, the activated T cell expresses CTLA-4 (cytotoxic T-lymphocyte-associated protein 4) on its surface, an inhibitory receptor which also recognizes the CD80 and CD86 molecules, but with a much stronger affinity than CD28. The binding of CD80/CD86 to CTLA-4 then inhibits T cells. Anti-CTLA-4 Abs block this interaction and prevent T cell inhibition [START_REF] Pardoll | The blockade of immune checkpoints in cancer immunotherapy[END_REF] . They could also work by eliminating regulatory T cells (Tregs) that constitutively express this receptor [START_REF] Selby | Anti-CTLA-4 antibodies of IgG2a isotype enhance antitumor activity through reduction of intratumoral regulatory T cells[END_REF] . PD-1/PD-L1 pathway PD-1 or "programmed-death 1" is a surface protein which, once bound to its ligand, inhibits the proliferation and function of T cells. PD-1 receptor is expressed by T cells after activation. PD-1 possesses two ligands, PD-L1 and PD-L2. PD-L1 is expressed on the surface of APC (mainly dendritic cells and macrophages) and a broad variety of tissues such as epithelial and endothelial tissues, in response to a stimulation by pro-inflammatory cytokines [START_REF] Mcdermott | PD-1 as a potential target in cancer therapy[END_REF] . Expression of PD-L1 inhibits the proliferation of activated T cells and is responsible for negative feedback control of inflammation. The other PD-1 ligand, PD-L2, is expressed mainly by APC [START_REF] Mcdermott | PD-1 as a potential target in cancer therapy[END_REF] . Expression of PD-L1 and/or PD-L2 by tumor cells or cells in the microenvironment allows the tumor to protect itself from the immune system.

Blocking monoclonal Abs directed against PD-1 and PD-L1 have been developed in order to prevent PD-1/PD-L1 and PD-1/PD-L2 binding and so to restore the activity of anti-tumor T cells [START_REF] Pardoll | The blockade of immune checkpoints in cancer immunotherapy[END_REF] .

Biomarkers associated with pharmacodynamics and clinical responses to CPI

The main biological markers associated with pharmacodynamics and/or clinical responses to CPI are listed in Table 2. A multitude of biomarkers has been studied, predominantly involving indices from the patient's tumor (tumor cells or cells from the microenvironment) or blood (circulating cells or serum). The following section provides a brief summary of each biomarker most advanced in study.

Circulating lymphocytes, neutrophils, eosinophils, and monocytes

Several studies have shown that treatment with anti-CTLA-4 Ab increased the level of circulating lymphocytes [START_REF] Wolchok | Ipilimumab monotherapy in patients with pretreated advanced melanoma: a randomised, double-blind, multicentre, phase 2, dose-ranging study[END_REF] . This increase seems to be associated with a better clinical efficacy [START_REF] Ku | Single-institution experience with ipilimumab in advanced melanoma patients in the compassionate use setting[END_REF][START_REF] Delyon | Experience in daily practice with ipilimumab for the treatment of patients with metastatic melanoma: an early increase in lymphocyte and eosinophil counts is associated with improved survival[END_REF][START_REF] Nj | Association of peripheral blood absolute lymphocyte count (ALC) and clinical activity in patients (pts) with advanced melanoma treated with ipilimumab[END_REF] . More recently, a study conducted in a 'real world' population of melanoma patients treated with ipilimumab found a correlation between baseline absolute lymphocyte count (ALC) and overall survival (OS was greater in patients with increased ALC at baseline) [START_REF] Kelderman | Lactate dehydrogenase as a selection criterion for ipilimumab treatment in metastatic melanoma[END_REF] .

Two studies evaluating an anti-PD-L1 Ab (MPDL3280A) in different cancers showed transient increase of CD8+ HLA-DR+ Ki-67+ cells early during treatment, but there was no correlation with clinical activity [START_REF] Herbst | Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients[END_REF][START_REF] Powles | MPDL3280A (anti-PD-L1) treatment leads to clinical activity in metastatic bladder cancer[END_REF] .

A study showed that the ratio between neutrophils and lymphocytes (N/L) during treatment with Ipilimumab correlated with clinical efficacy. A N/L ratio below normal limits after 7 and 10 weeks of treatment was significantly associated with a better survival [START_REF] Di Giacomo | Long-term survival and immunological parameters in metastatic melanoma patients who responded to ipilimumab 10 mg/kg within an expanded access programme[END_REF] .

A low level of eosinophils at baseline before treatment was associated with a better overall survival in patients treated with anti-CTLA-4 Ab (Ipilimumab) for a metastatic melanoma [START_REF] Schindler | Pretreatment levels of absolute and relative eosinophil count to improve overall survival (OS) in patients with metastatic melanoma under treatment with ipilimumab, an anti CTLA-4 antibody[END_REF] .

Finally, a high level of CD16-expressing monocytes at baseline was found to be associated with higher response rate and lower Tregs counts in the tumor microenvironment of responding patients [START_REF] Romano | Ipilimumab-dependent cell-mediated cytotoxicity of regulatory T cells ex vivo by nonclassical monocytes in melanoma patients[END_REF] .

CD4+ ICOS hi T cells

ICOS is a co-stimulatory receptor expressed on the surface of T cells after activation. In murine models, it has been shown that expression of ICOS is necessary for the efficacy of anti-CTLA-4 Ab. Indeed, mice lacking ICOS or its ligand have a lower response to anti-CTLA-4 Ab than wild-type mice [START_REF] Fu | The ICOS/ICOSL pathway is required for optimal antitumor responses mediated by anti-CTLA-4 therapy[END_REF] .

In patients, it has been described that anti-CTLA-4 Ab increased the number of CD4+ ICOS hi T cells (producing IFNγ) in the blood [START_REF] Vonderheide | Tremelimumab in combination with exemestane in patients with advanced breast cancer and treatment-associated modulation of inducible costimulator expression on patient T cells[END_REF][START_REF] Liakou | CTLA-4 blockade increases IFNgamma-producing CD4+ICOShi cells to shift the ratio of effector to regulatory T cells in cancer patients[END_REF] and in the tumor [START_REF] Liakou | CTLA-4 blockade increases IFNgamma-producing CD4+ICOShi cells to shift the ratio of effector to regulatory T cells in cancer patients[END_REF][START_REF] Chen | Anti-CTLA-4 therapy results in higher CD4+ICOShi T cell frequency and IFNlevels in both nonmalignant and malignant prostate tissues[END_REF][START_REF] Carthon | Preoperative CTLA-4 blockade: tolerability and immune monitoring in the setting of a presurgical clinical trial[END_REF] . For example, in patients receiving neoadjuvant therapy with anti-CTLA-4 Ab (Ipilimumab) for bladder cancer before cystoprostatectomy, CD4+ ICOS hi T-Lymphocytes count was significantly increased in prostatic tissue, whether they were healthy or invaded by adenocarcinoma [START_REF] Chen | Anti-CTLA-4 therapy results in higher CD4+ICOShi T cell frequency and IFNlevels in both nonmalignant and malignant prostate tissues[END_REF] . Moreover, a persistent increase of CD4+ ICOS hi T cells in blood after 12 weeks of treatment with anti-CTLA-4 Ab was associated with an improved clinical outcome (defined as stable disease or objective response) and a better overall survival [START_REF] Carthon | Preoperative CTLA-4 blockade: tolerability and immune monitoring in the setting of a presurgical clinical trial[END_REF] .

Diversity of T cell repertoire

Anti-CTLA-4 therapy may amplify a pre-existing antitumor T cells response and/or generate T cells against new tumor antigens ("epitope spreading").

A retrospective study including 12 patients harbouring metastatic melanoma evaluated the diversity of the circulating T cell repertoire before treatment with anti-CTLA-4 Ab (Ipilimumab). In this study, response rate was higher in patients presenting with a more diverse T cell repertoire [START_REF] Postow | Peripheral T cell receptor diversity is associated with clinical outcomes following ipilimumab treatment in metastatic melanoma[END_REF] .

Cha et al. assessed TCR diversity during CTLA-4 blockade in patients with castration-resistant metastatic prostate cancer and metastatic melanoma, and found that clonotype stability after treatment was associated with a better clinical outcome [START_REF] Cha | Improved survival with T cell clonotype stability after anti-CTLA-4 treatment in cancer patients[END_REF] . Kvistborg et al. showed that anti-CTLA-4 therapy broadened the repertoire of melanoma-reactive CD8+ T cells but did not amplify pre-existing T cells. There was no correlation with clinical outcome [START_REF] Kvistborg | Anti-CTLA-4 therapy broadens the melanoma-reactive CD8+ T cell response[END_REF] .

In patients with metastatic melanoma, Tumeh et al found that clinical response to anti-PD1 therapy (pembrolizumab) correlated with i) a more clonal (i.e. more restricted, less diverse) TCR repertoire in pre-treatment tumor samples and ii) an increased clonal expansion of T cells in the tumor after anti-PD1 therapy [START_REF] Tumeh | PD-1 blockade induces responses by inhibiting adaptive immune resistance[END_REF] .

Immune response against tumor-associated antigens

In patients with melanoma, the presence of Ab targeting NY-ESO-1 (a tumor antigen found in several solid tumors) before treatment and under treatment with Ipilimumab was associated with a better clinical outcome (defined as stable disease or partial/complete response) [START_REF] Yuan | Integrated NY-ESO-1 antibody and CD8+ T-cell responses correlate with clinical benefit in advanced melanoma patients treated with ipilimumab[END_REF] . Among patients seropositive for NY-ESO-1, overall survival was higher in those harbouring CD8 T cells directed against NY-ESO-1 [START_REF] Yuan | Integrated NY-ESO-1 antibody and CD8+ T-cell responses correlate with clinical benefit in advanced melanoma patients treated with ipilimumab[END_REF] . Interestingly, Kvistborg et al. demonstrated that anti-CTLA-4 treatment induced new melanoma-specific CD8 T cells (in blood) but did not significantly expand melanoma-specific T cell responses that were already detected before start of therapy, suggesting that anti-CTLA-4 therapy enhances T cell priming [START_REF] Kvistborg | Anti-CTLA-4 therapy broadens the melanoma-reactive CD8+ T cell response[END_REF] .

Regulatory T cells (Tregs)

Tregs express CTLA-4 constitutively and therefore can be targeted directly by anti-CTLA-4 Abs [START_REF] Sojka | Mechanisms of regulatory T-cell suppression -a diverse arsenal for a moving target[END_REF] .

Studies have found a decrease in the number of circulating [START_REF] Attia | Autoimmunity Correlates With Tumor Regression in Patients With Metastatic Melanoma Treated With Anti-Cytotoxic T-Lymphocyte Antigen-4[END_REF] or intratumoral [START_REF] Liakou | CTLA-4 blockade increases IFNgamma-producing CD4+ICOShi cells to shift the ratio of effector to regulatory T cells in cancer patients[END_REF][START_REF] Chen | Anti-CTLA-4 therapy results in higher CD4+ICOShi T cell frequency and IFNlevels in both nonmalignant and malignant prostate tissues[END_REF] Tregs after Ipilimumab treatment while other studies did not find such depletion [START_REF] Carthon | Preoperative CTLA-4 blockade: tolerability and immune monitoring in the setting of a presurgical clinical trial[END_REF][START_REF] Weber | Ipilimumab Increases Activated T Cells and Enhances Humoral Immunity in Patients With Advanced Melanoma[END_REF][START_REF] Maker | Tumor regression and autoimmunity in patients treated with cytotoxic T lymphocyte-associated antigen 4 blockade and interleukin 2: a phase I/II study[END_REF] . Data regarding the correlation between the variation of Tregs and clinical efficacy are likewise contradictory [START_REF] Simeone | Immunological and biological changes during ipilimumab treatment and their potential correlation with clinical response and survival in patients with advanced melanoma[END_REF][START_REF] Tarhini | Immune monitoring of the circulation and the tumor microenvironment in patients with regionally advanced melanoma receiving neoadjuvant ipilimumab[END_REF][START_REF] Weide | Immunologic Correlates in the Course of Treatment With Immunomodulating Antibodies[END_REF] .

Myeloid-Derived Suppressor Cells (MDSCs)

MDSCs are an heterogeneous population of cells that exists at basal state and expands under pathological conditions such as infection, inflammation or cancer, and exert suppressive activities, notably on T cells [START_REF] Gabrilovich | Myeloid-derived suppressor cells as regulators of the immune system[END_REF] . In certain types of cancer, circulating MDSCs have been found to correlate with tumor stage, tumor volume, and even prognosis [START_REF] Diaz-Montero | Myeloid-derived suppressor cells in cancer: therapeutic, predictive, and prognostic implications[END_REF] . A recent study by Martens et al. showed a correlation between a low baseline count of MDSCs and better overall survival in melanoma patients treated with anti-CTLA-4 [START_REF] Martens | Baseline peripheral blood biomarkers associated with clinical outcome of advanced melanoma patients treated with ipilimumab[END_REF] . Several studies found a decrease in the number of MDSCs following Ipilimumab therapy [START_REF] Tarhini | Immune monitoring of the circulation and the tumor microenvironment in patients with regionally advanced melanoma receiving neoadjuvant ipilimumab[END_REF][START_REF] Pico De Coaña | Ipilimumab treatment results in an early decrease in the frequency of circulating granulocytic myeloid-derived suppressor cells as well as their Arginase1 production[END_REF] . In one study, the decrease of certain types of MDSCs under Ipilimumab treatment (given in a neo-adjuvant setting) was associated with higher progression-free survival in patients with melanoma [START_REF] Tarhini | Immune monitoring of the circulation and the tumor microenvironment in patients with regionally advanced melanoma receiving neoadjuvant ipilimumab[END_REF] . Similarly, Kitano et al. showed that a low monocytic MDSCs count at week 6 after Ipilimumab treatment was associated with prolonged overall survival [START_REF] Kitano | Computational algorithm-driven evaluation of monocytic myeloid-derived suppressor cell frequency for prediction of clinical outcomes[END_REF] .

Soluble CD25 (sCD25)

Anti-tumor activity of anti-CTLA-4 Ab seems highly dependent on IL-2, a cytokine involved in the activation of T cells. In murine models, neutralization of IL-2 or blockade of the α and β subunits of its receptor (CD25 and CD122, respectively) precluded the anti-tumor effect as well as the increase in the ratio of intratumoral effector/regulatory T cells usually found during anti-CTLA-4 Ab therapy [START_REF] Hannani | Anticancer immunotherapy by CTLA-4 blockade: obligatory contribution of IL-2 receptors and negative prognostic impact of soluble CD25[END_REF] .

The soluble form of CD25 (sCD25), capable of capturing IL-2, decreases anti-CTLA-4 Ab efficacy in murine models [START_REF] Hannani | Anticancer immunotherapy by CTLA-4 blockade: obligatory contribution of IL-2 receptors and negative prognostic impact of soluble CD25[END_REF] . In patients presenting with metastatic melanoma, a high level of sCD25 before treatment with Ipilimumab was associated with treatment resistance [START_REF] Hannani | Anticancer immunotherapy by CTLA-4 blockade: obligatory contribution of IL-2 receptors and negative prognostic impact of soluble CD25[END_REF] .

Cytokines/chemokines

Treatment with anti-PD-L1 Ab (MPDL3280A) was associated with increased circulating IFN-γ, IL-18 and ITAC (an IFN-γ inducible chemokine which is chemotactic for activated T cells) and decreased IL-6. No correlation was found with clinical efficacy [START_REF] Herbst | Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients[END_REF][START_REF] Powles | MPDL3280A (anti-PD-L1) treatment leads to clinical activity in metastatic bladder cancer[END_REF] .

Lactate dehydrogenase (LDH)

In some solid tumors and hematologic malignancies, a high level of LDH at baseline is frequently associated with poor prognosis. In advanced melanoma, the site(s) of metastasis and a high level of LDH at baseline are the two most significant prognostic factors [START_REF] Balch | Final version of 2009 AJCC melanoma staging and classification[END_REF] . Increased LDH at baseline seems to be associated with resistance to anti-CTLA-4 Ab therapy in advanced melanoma [START_REF] Delyon | Experience in daily practice with ipilimumab for the treatment of patients with metastatic melanoma: an early increase in lymphocyte and eosinophil counts is associated with improved survival[END_REF][START_REF] Kelderman | Lactate dehydrogenase as a selection criterion for ipilimumab treatment in metastatic melanoma[END_REF][START_REF] Wilgenhof | Single-center experience with ipilimumab in an expanded access program for patients with pretreated advanced melanoma[END_REF] .

Tumor-infiltrating lymphocytes (TIL)

The presence of lymphocytes within the tumor is a favorable prognostic factor in numerous cancers [START_REF] Ruffini | Clinical significance of tumor-infiltrating lymphocytes in lung neoplasms[END_REF] . The lymphocyte infiltrate also seems to be a predictive factor of response to CPI. In patients with metastatic melanoma treated with anti-CTLA-4 Ab (Ipilimumab), an increase in lymphocyte infiltrate in the tumor between baseline and at three weeks after treatment initiation correlated with clinical response [START_REF] Hamid | A prospective phase II trial exploring the association between tumor microenvironment biomarkers and clinical activity of ipilimumab in advanced melanoma[END_REF] . Moreover, in melanoma patients treated with anti-PD-1 Ab (Pembrolizumab), response rate was better in patients with high numbers of peri-and intra-tumoral CD8 T cells in their pre-treatment samples [START_REF] Tumeh | PD-1 blockade induces responses by inhibiting adaptive immune resistance[END_REF] . Analysis of biopsies after treatment with anti-CTLA-4 Ab (Ipilimumab) showed a correlation between a high ratio of intratumoral CD8/regulatory T cells and tumor necrosis [START_REF] Liakou | CTLA-4 blockade increases IFNgamma-producing CD4+ICOShi cells to shift the ratio of effector to regulatory T cells in cancer patients[END_REF][START_REF] Hodi | Immunologic and clinical effects of antibody blockade of cytotoxic T lymphocyte-associated antigen 4 in previously vaccinated cancer patients[END_REF] . Granzyme B is a cytotoxic granule reflective of CD8 effector function. In the tumor, its expression seems to be increased after anti-PD-1 [START_REF] Beavis | CD73: A potential biomarker for anti-PD-1 therapy[END_REF] , anti-CTLA-4 [START_REF] Hamid | A prospective phase II trial exploring the association between tumor microenvironment biomarkers and clinical activity of ipilimumab in advanced melanoma[END_REF] or anti-PD-L1 Ab therapy [START_REF] Herbst | Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients[END_REF] . Sample analysis from patients with metastatic melanoma obtained before and after anti-PD-1 therapy showed a significant increase in granzyme B expressing CD8+ cells in post-dosing biopsies in the responding patients [START_REF] Tumeh | PD-1 blockade induces responses by inhibiting adaptive immune resistance[END_REF] .

Mutational load CPI work by amplifying pre-existing anti-tumor responses. Several studies aimed to determine if "immunogenic" tumors, i.e. tumors that can be recognized by the immune system, were more sensitive to CPI. Immunogenicity is associated with the mutational load, in other words with the number of somatic mutations present in the tumor cells [START_REF] Alexandrov | Signatures of mutational processes in human cancer[END_REF] . Indeed, the presence of mutations in the tumor generates neo-antigens (not expressed by normal cells) that are likely to be recognized by the immune system. The more mutations there are, the more the tumor is likely to be immunogenic.

A study actually found a significant relationship between cytolytic activity in the tumor (defined by a greater perforin/granzyme B transcript level) and total mutation count in eight tumor types including colorectal and lung cancer [START_REF] Rooney | Molecular and Genetic Properties of Tumors Associated with Local Immune Cytolytic Activity[END_REF] . Indeed, clinical studies showed that patients treated with anti-CTLA-4 Ab (Ipilimumab) for melanoma [START_REF] Snyder | Genetic Basis for Clinical Response to CTLA-4 Blockade in Melanoma[END_REF][START_REF] Van Allen | Genomic correlates of response to CTLA-4 blockade in metastatic melanoma[END_REF] or with anti-PD-1 Ab (Pembrolizumab) for non-small cell lung carcinoma [START_REF] Rizvi | Mutational landscape determines sensitivity to PD-1 blockade in non-small cell lung cancer[END_REF] had better clinical benefit if the mutational load of their tumor was high. Likewise, patients treated with anti-PD-1 Ab (Pembrolizumab) for colorectal cancer had a significantly better response rate and overall survival if they had a mismatch repair deficiency (involved in the repair of DNA replication errors) [START_REF] Le | PD-1 Blockade in Tumors with Mismatch-Repair Deficiency[END_REF] .

PD-L1 expression within the tumor

Given the mechanism of action of anti-PD-1 and anti-PD-L1 Abs, several studies have tried to determine if the efficacy of these Abs correlated with PD-L1 ligand expression in the tumor. The first studies provided evidence that there was indeed a strong link between PD-L1 expression by tumor cells and the response to anti-PD-1 Ab. Topalian et al. showed that all the responses to Nivolumab were observed in patients whose tumors expressed PD-L1 [START_REF] Topalian | Activity, and Immune Correlates of Anti-PD-1 Antibody in Cancer[END_REF] . Likewise, in the KEYNOTE-001 trial, responses to Pembrolizumab correlated with PD-L1 expression by tumor cells [START_REF] Garon | Pembrolizumab for the treatment of non-small-cell lung cancer[END_REF] . A trial assessing the effect of an anti-PD-L1 (MPDL3280A) on different types of cancer found a correlation between the level of PD-L1 present in the intratumoral immune infiltrate (but not by the tumor cells themselves) and clinical response [START_REF] Herbst | Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients[END_REF] . However, other studies did not confirm this correlation [START_REF] Robert | Nivolumab in previously untreated melanoma without BRAF mutation[END_REF][START_REF] Robert | Pembrolizumab versus Ipilimumab in Advanced Melanoma[END_REF][START_REF] Postow | Peripheral and tumor immune correlates in patients with advanced melanoma treated with nivolumab (anti-PD-1, BMS-936558, ONO-4538) monotherapy or in combination with ipilimumab[END_REF][START_REF] Kefford | Clinical efficacy and correlation with tumor PD-L1 expression in patients (pts) with melanoma (MEL) treated with the anti-PD-1 monoclonal antibody MK-3475[END_REF][START_REF] Daud | Long-term efficacy of pembrolizumab (pembro; MK-3475) in a pooled analysis of 655 patients (pts) with advanced melanoma (MEL) enrolled in KEYNOTE-001[END_REF] . In a meta-analysis including 1475 patients treated with Nivolumab, Pembrolizumab or MPDL3280A, response rates were significantly higher in PD-L1 positive tumors (34% versus 19.9%) [START_REF] Carbognin | Differential Activity of Nivolumab, Pembrolizumab and MPDL3280A according to the Tumor Expression of Programmed Death-Ligand-1 (PD-L1): Sensitivity Analysis of Trials in Melanoma, Lung and Genitourinary Cancers[END_REF] .

These differences regarding the predictive value of PD-L1 may have multiple explanations. First, the analysis of PD-L1 expression within tumors is not standardized. Different staining techniques are available, using different Abs for immunohistochemistry and different levels of positivity. Efforts are currently being made to harmonize the assessment of PD-ligand expression. Also, some studies looked at PD-L1 expression by tumor cells whereas others also included its expression by cells of the microenvironment. These differences could also be explained by the dynamic nature of PD-L1 expression. In fact, PD-L1 is inducible, notably by IFN-γ exposure [START_REF] Pardoll | The blockade of immune checkpoints in cancer immunotherapy[END_REF] . Therefore, a tumor which does not express PD-L1 at baseline may become PD-L1 positive in an inflammatory background. This could explain why basal expression of PD-L1 does not have a predictive value on response when anti-PD-1 is combined with anti-CTLA-4 Ab in melanoma patients [START_REF] Larkin | Combined Nivolumab and Ipilimumab or Monotherapy in Untreated Melanoma[END_REF] . Inflammation induced by anti-CTLA-4 Abs could indeed induce PD-L1 in tumors formerly negative for this marker [START_REF] Postow | Peripheral and tumor immune correlates in patients with advanced melanoma treated with nivolumab (anti-PD-1, BMS-936558, ONO-4538) monotherapy or in combination with ipilimumab[END_REF] . Lastly, a significant percentage of patients negative for PD-L1 respond to anti-PD-1/PD-L1 therapy.

Indoleamine 2,3-dioxygenase (IDO)

IDO is an enzyme which degrades tryptophan, an essential amino-acid. Its presence lowers tryptophan availability in the tumor microenvironment and increases the concentration of its catabolite. IDO has an immunosuppressive effect by decreasing proliferation, function and survival of T cells [START_REF] Mbongue | The Role of Indoleamine 2, 3-Dioxygenase in Immune Suppression and Autoimmunity[END_REF] . Expression of IDO by some tumors contributes to immune escape. Hamid et al. found a positive correlation between a high expression of IDO at baseline and the clinical activity of Ipilimumab in metastatic melanoma [START_REF] Hamid | A prospective phase II trial exploring the association between tumor microenvironment biomarkers and clinical activity of ipilimumab in advanced melanoma[END_REF] . The presence of IDO could indicate a pre-existing inflammatory/immune response (IDO could be induced by pro-inflammatory cytokines like IFN-γ) which would promote the response to CPI [START_REF] Jung | Differential regulation of indoleamine 2,3-dioxygenase by lipopolysaccharide and interferon gamma in murine bone marrow derived dendritic cells[END_REF][START_REF] Robinson | The role of IFN-gamma and TNF-alpha-responsive regulatory elements in the synergistic induction of indoleamine dioxygenase[END_REF] .

Gene expression profile (GEP)

In blood, transcriptome analysis has shown that treatment with an anti-CTLA-4 Ab induces a gene expression profile related to proliferation of T cells, mainly of memory phenotype [START_REF] Das | Combination Therapy with Anti-CTLA-4 and Anti-PD-1 Leads to Distinct Immunologic Changes In Vivo[END_REF] . Anti-PD-1 Abs are responsible for the expression of genes implicated in cytolysis and NK cell function [START_REF] Das | Combination Therapy with Anti-CTLA-4 and Anti-PD-1 Leads to Distinct Immunologic Changes In Vivo[END_REF] . Combination of anti-PD-1 and anti-CTLA-4 Abs induces higher gene expression compared to monotherapy, notably for genes involved in proliferation and coding of cytokines. Some genes can only be induced by the combination of both anti-PD-1 and anti-CTLA-4 Abs 61 .

In the tumor, transcriptome analysis performed on biopsies from 45 patients with melanoma before treatment found gene expression profiles (increased expression of immunity-related genes) predictive of response to anti-CTLA-4 Ab (Ipilimumab) therapy [START_REF] Ji | An immune-active tumor microenvironment favors clinical response to ipilimumab[END_REF] . Similarly, GEP performed in melanoma tumors before anti-PD1 treatment (pembrolizumab and nivolumab) revealed a transcriptional signature related to innate anti-PD-1 resistance (IPRES) [START_REF] Hugo | Genomic and Transcriptomic Features of Response to Anti-PD-1 Therapy in Metastatic Melanoma[END_REF] . Interestingly, IPRES signatures was not associated with resistance to anti-CTLA-4 suggesting that mechanisms of innate resistance to anti-PD-1 and anti-CTLA-4 may be different.

Melanoma patients responding to MPDL3280A (anti-PD-L1) had an increased expression of IFN-γ and IFN-γ-inducible genes (i.e. IDO1 and CXCL9) on pre-treatment tumours [START_REF] Herbst | Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients[END_REF] .

Biomarkers associated with toxicity of CPIs

CPI, by stimulating the immune system non-specifically, can trigger side effects called Immune-Related Adverse Events (irAEs). Most frequent irAEs may affect the skin (pruritus, rash, vitiligo), the intestinal tract (colitis), the liver (hepatitis) and the endocrine system. They are usually more pronounced with anti-CTLA-4 Abs than with anti-PD-1 or anti-PD-L1 Abs [START_REF] Michot | Immune-related adverse events with immune checkpoint blockade: A comprehensive review[END_REF] . Notably, anti-CTLA-4 Abs can cause serious colitis. Some of these irAEs can be life-threatening. IrAEs may require discontinuation of CPI therapy and immunosuppressive treatment. Several studies looked for predictive biomarkers of toxicity. Main results are summarized in Table 3.

Eosinophils

In 156 patients presenting with metastatic melanoma, the circulating eosinophils count before and during treatment with anti-CTLA-4 Ab (Ipilimumab) was associated with irAEs occurence [START_REF] Schindler | Correlation of absolute and relative eosinophil counts with immune-related adverse events in melanoma patients treated with ipilimumab[END_REF] .

IL-17

In 52 patients treated with anti-CTLA-4 Ab (Ipilimumab) for metastatic melanoma, increase followed by decrease of blood IL-17 levels were respectively associated with the settling and the resolution of colitis [START_REF] Callahan | Evaluation of serum IL-17 levels during ipilimumab therapy: Correlation with colitis[END_REF] .

Gene expression profile (GEP)

Gene expression profiling performed on blood from patients treated with anti-CTLA-4 Ab (Ipilimumab) showed that, out of 10,000 probe sets tested, the increased expression of CD177 and CEACAM1 genes, two markers of neutrophil activation, was associated with digestive toxicity [START_REF] Shahabi | Gene expression profiling of whole blood in ipilimumab-treated patients for identification of potential biomarkers of immune-related gastrointestinal adverse events[END_REF] .

Digestive infiltrate by neutrophils

A study of melanoma patients treated with anti-CTLA-4 Ab (Ipilimumab) showed that, on colon biopsies performed just before treatment initiation, lamina propria infiltration by neutrophils as well as other markers of inflammation (cryptic abscess, gland destruction, mucosal erosion) were associated with the occurrence of digestive toxicity [START_REF] Berman | Blockade of cytotoxic T-lymphocyte antigen-4 by ipilimumab results in dysregulation of gastrointestinal immunity in patients with advanced melanoma[END_REF] .

Lastly, several studies suggest that the occurrence of irAEs could correlate with better efficacy of anti-CTLA-4 Ab (Ipilimumab) [START_REF] Attia | Autoimmunity Correlates With Tumor Regression in Patients With Metastatic Melanoma Treated With Anti-Cytotoxic T-Lymphocyte Antigen-4[END_REF][START_REF] Downey | Prognostic factors related to clinical response in patients with metastatic melanoma treated by CTL-associated antigen-4 blockade[END_REF][START_REF] Tarhini | Releasing the brake on the immune system: ipilimumab in melanoma and other tumors[END_REF][START_REF] Weber | Ipilimumab: controversies in its development, utility and autoimmune adverse events[END_REF] . However, association between toxicity and efficacy is not entirely clear [START_REF] Ascierto | Clinical experience with ipilimumab 3 mg/kg: real-world efficacy and safety data from an expanded access programme cohort[END_REF] and numerous patients respond to CPI therapy without experiencing irAEs.

Conclusions

Numerous biomarkers may reflect the pharmacodynamics of CPIs and predict their efficacy and/or their toxicity in patients. However, the relevance of these biomarkers to clinical practice and their potential for routine application remains ill-defined, and will have to be clarified in larger, prospective studies. A subset of biomarkers seem relevant and accessible enough to be part of our practices (e.g. LDH level, absolute lymphocytes count variation); others look promising but need standardisation of current practices (e.g. measure of PD-L1 expression) and finally, some biomarkers are not yet accessible to daily practice (e.g. transcriptional analysis, mutational load). In addition, most of the biomarkers described so far have been tested in melanoma patients and therefore require validation in other cancer types and immunotherapeutic agents.

Patients who seem to benefit most from CPIs are those presenting with immunogenic tumors (i.e. with a high mutational load), pre-existing immune response (intratumoral immune infiltrate) and the immune escape ligands being targeted (i.e. PD-L1 for patients treated with anti-PD-1/PD-L1 Abs).

Nevertheless, these biomarkers are not perfect. In the future, better knowledge of the mechanisms of action of CPIs in vivo should help us identify other biomarkers in order to define patients who will benefit most from these effective but costly and potentially toxic drugs.  Increased lymphocytes count during treatment associated with better clinical efficacy [START_REF] Ku | Single-institution experience with ipilimumab in advanced melanoma patients in the compassionate use setting[END_REF][START_REF] Delyon | Experience in daily practice with ipilimumab for the treatment of patients with metastatic melanoma: an early increase in lymphocyte and eosinophil counts is associated with improved survival[END_REF][START_REF] Nj | Association of peripheral blood absolute lymphocyte count (ALC) and clinical activity in patients (pts) with advanced melanoma treated with ipilimumab[END_REF]  Decreased neutrophils/lymphocytes ratio during treatment associated with higher survival [START_REF] Di Giacomo | Long-term survival and immunological parameters in metastatic melanoma patients who responded to ipilimumab 10 mg/kg within an expanded access programme[END_REF]  Low eosinophil baseline level associated with better survival [START_REF] Schindler | Pretreatment levels of absolute and relative eosinophil count to improve overall survival (OS) in patients with metastatic melanoma under treatment with ipilimumab, an anti CTLA-4 antibody[END_REF]  High CD16-expressing monocyte level at baseline associated with higher response rate [START_REF] Romano | Ipilimumab-dependent cell-mediated cytotoxicity of regulatory T cells ex vivo by nonclassical monocytes in melanoma patients[END_REF] Anti-PD-L1

 Transient increase of CD8+ HLA-DR+ Ki-67+ lymphocytes [START_REF] Herbst | Predictive correlates of response to the anti-PD-L1 antibody MPDL3280A in cancer patients[END_REF][START_REF] Powles | MPDL3280A (anti-PD-L1) treatment leads to clinical activity in metastatic bladder cancer[END_REF] CD4+ ICOS hi T cells Anti-CTLA-4  Increase of CD4+ ICOS hi T cell count in blood, tumor and healthy tissues [START_REF] Liakou | CTLA-4 blockade increases IFNgamma-producing CD4+ICOShi cells to shift the ratio of effector to regulatory T cells in cancer patients[END_REF][START_REF] Chen | Anti-CTLA-4 therapy results in higher CD4+ICOShi T cell frequency and IFNlevels in both nonmalignant and malignant prostate tissues[END_REF][START_REF] Carthon | Preoperative CTLA-4 blockade: tolerability and immune monitoring in the setting of a presurgical clinical trial[END_REF]  Persistent increase of circulating CD4+ ICOS hi T cell count under treatment associated with better

4  21  4  23 in melanoma 23 TregsAnti-CTLA- 4  25  30 MDSCsAnti-CTLA- 4 , 34  33  29 Anti-CTLA- 4  10 LDHAnti-CTLA- 4  4 cells, mostly of memory subtype 61 Anti-PD- 1  61 TUMOR 4  40  41  40 Anti-PD- 1  22  1  22  4  46 Anti-PD- 1  4  73 Anti-PD- 1 

 421423234253043433294104461161440414012212244614731 Increase of TCR diversity 20,Diversity of T cell repertoire associated with higher Presence of Ab directed against NY-ESO-1 antigen associated with higher clinical benefit in melanoma Presence of NY-ESO-1 specific T CD8 cells in NY-ESO-1-seropositive patients associated with better survival Decrease of circulating Tregs count after Ipilimumab treatment in some studies Contradictory data concerning variation of circulating Tregs count and clinical response 24-Decrease of MDSCs count upon Ipilimumab treatment 29Low baseline MDSCs count associated with better overall survival Decrease in several subtypes of MDSCs associated with higher progression-free survival Decrease in monocytic MDSCs during treatment associated with prolonged overall survival 35 Soluble CD25 High basal serum level of soluble CD25 associated with treatment resistance 36 Cytokines/chemokines Anti-PD-L1 Increased level of IFN-γ, IL-18, ITAC and decreased level of IL-6 9,High basal serum level of LDH associated with treatment resistance 6,8,38 Gene expression Anti-CTLA- Expression of genes involved in proliferation of T profile Expression of genes involved in cytolysis and NK cells proliferation Presence of intratumoral lymphocytes associated with better clinical efficacy Increased CD4 T cells/Tregs ratio associated with tumor necrosis 16,Increase of Granzyme B lymphocytes in the tumor after anti-CTLA-4 Ab Presence of peri-and intratumoral CD8 T cells associated with higher response rates Increase of granzyme B lymphocytes in the tumor after anti-PD-1 42 and anti-PD-L1 Ab 9 . Increase in granzyme B CD8+ T cells after anti-PD1 Ab associated with clinical efficacy in melanoma patients 22 . More clonal (i.e. more restricted, less diverse) TCR repertoire in pre-treatment tumor samples associated with clinical response Increased clonal expansion of T cells after treatment associated with clinical response 22 Mutational load Anti-CTLA-High mutational load associated with better efficacy in melanoma 45,High mutational load associated with better efficacy in NSCLC 47 Mismatch-repair deficiency associated with better efficacy in Transcriptomic signature associated with better clinical efficacy in melanoma 62,Transcriptomic signature associated with innate anti-PD-1 resistance (IPRES) in melanoma and other types of cancer 63 Anti-PD-L1  Increased IFN-γ genes expression on pretreatment tumor biopsies associated with response to anti-PDL1 in melanoma patients 9

Table 1 . CPIs FDA-approved for the treatment of cancer

 1

						Indication (date of approval)
	Target	Antibody	Isotype Company	Melanoma	Non-small cell lung carcinoma	Renal cell carcinoma
					• Unresectable or
					metastatic
					melanoma
					(2011)
					• Adjuvant
					treatment of
					patients with
					cutaneous
					melanoma with
					pathologic
					involvement of
					regional lymph
					nodes of more
	CTLA-4	Ipilimumab	IgG1	BMS	than 1 mm who complete have undergone	-	-
					resection,
					including total
					lymphadenecto
					my (2015)
					• Patients with
					BRAF V600 wild-
					type,
					unresectable or
					metastatic
					melanoma, in
					combination
					with nivolumab
					(2015)
	PD-1 Pembrolizumab	IgG4	Merck	• Unresectable or metastatic melanoma with disease progression following ipilimumab and, if BRAF V600 melanoma metastatic unresectable or of patients with • Initial treatment inhibitor (2014) positive, a BRAF mutation	• Metastatic non-small cell lung cancer (NSCLC) whose tumors express programmed death ligand 1 (PD-L1) as (2015) chemotherapy containing after platinum-progression on or with disease FDA-approved test, determined by an	-

Table 2 . Biomarkers associated with pharmacodynamics and clinical response to CPI

 2

	Biomarker	Ab	Result

Table 3 . Biomarkers associated with CPI toxicity

 3

		Biomarkers	Drugs	Association
				 Increased eosinophils before and after treatment
		Eosinophils	Anti-CTLA-4
				associated with irAEs occurence 65
				 Increased circulating IL-17 level during treatment
		IL-17	Anti-CTLA-4
				associated with digestive toxicity 66
		Gene expression		 Increased expression of CD177 and CEACAM1 genes
	BLOOD	profile	Anti-CTLA-4	associated with digestive toxicity 67
		Digestive
		Neutrophils	Anti-CTLA-4
	TISSUE	infiltrate

 Infiltration of lamina propria by neutrophils in colon during treatment associated with digestive toxicity

[START_REF] Berman | Blockade of cytotoxic T-lymphocyte antigen-4 by ipilimumab results in dysregulation of gastrointestinal immunity in patients with advanced melanoma[END_REF]

Disclosure

The authors did not receive funding for this study. The authors have declared no conflicts of interest.

Nivolumab

IgG4 BMS


Célia Da Costa

Andrea G B Pereira
email: celia.pereira@unice.fr

Serena Tettamanzi
email: andrea.tettamanzi@unice.fr

Villata

A Belief-Based Approach to Measuring Message Acceptability

We propose a formal framework to support belief revision based on a cognitive model of credibility and trust. In this framework, the acceptance of information coming from a source depends on (i) the agent's goals and beliefs about the source's goals, (ii) the credibility, for the agent, of incoming information, and (iii) the agent's beliefs about the context in which it operates. This makes it possible to approach belief revision in a setting where new incoming information is associated with an acceptance degree. In particular, such degree may be used as input weight for any possibilistic conditioning operator with uncertain input (i.e., weighted belief revision operator).

Introduction

Fulfilling its goals is an important concern for an agent. The agent's perceptions about its environment highly influences this process. Such perceptions dynamically enrich the agent's beliefs, namely thanks to new more or less credible/trusted information. According to the principle of primacy update, in belief revision new information is generally accepted. However, as pointed out by several authors [START_REF] Delgrande | Iterated revision as prioritized merging[END_REF][START_REF] Dragoni | Belief revision through the belief-function formalism in a multiagent environment[END_REF][START_REF] Gabbay | Controlled revision-an algorithmic approach for belief revision[END_REF], in real-world situations it is often the case that new information is not fully considered or simply not accepted due to an insufficient amount of plausibility [START_REF] Booth | Credibility-limited revision operators in propositional logic[END_REF]. The extent to which new information will be accepted (i.e., really considered) by the agent directly depends on these credibility and trust values. A key factor for the agent's success in fulfilling its goals is then its ability to compute both the credibility of new information and its trust in the source providing information. Recently, Adali [START_REF] Adali | Modeling Trust Context in Networks[END_REF] has proposed to define information trust as a computational concept whose value depends on the trustworthiness of the information source, 1 and on the credibility of the information content. Adali's approach also agrees with the one proposed by Sparks [START_REF] Sparks | Unreliable and anomalous: How the credibility of data affects belief revision[END_REF]. However, to the best of our knowledge, a formal framework for measuring the acceptability of a message which takes into account the agent's goals and the agent's beliefs about the source's goals, the credibility of the message with respect to its content and with respect to both the agent's competence and the source's competence, and the agent's beliefs about the source's nature (malicious or not) is still missing.

The research question of how to provide such a framework breaks down into the following subquestions:

-How do we take the nature of the information source into account? -How do we take the agent's and source's goals into account? -How do we measure the credibility of information based on the agent's and the source's competences?

We answer these questions by proposing a possibilistic model whereby the cognitive notions of trust and credibility can be formalized and the acceptability of the pieces of information can be computed. Our framework makes it possible to:

represent the fact that the agent's beliefs may include the "nature" of a source, which may be categorized as malicious, rational, etc.-each evaluation of a component of trust should consider this fact; somehow measure the source's willingness to cooperate thanks to the agent's perceptions about the source's goals-a source sharing my goals should (implicitly or explicitly) act/help for the achievement of these goals, unless, perhaps, it is not rational; compute the credibility of information coming from a given source with respect to:

• the agent's competence-the agent may be able to evaluate the information content regardless of how trustworthy it considers the information source; • the source's competence-we suppose that (1) each piece of information belongs to a domain of competence and (2) the agent has beliefs about the domains of competence of the sources. It is then possible to evaluate the credibility of such a new piece of information with respect to the source's competence;

Our approach is cast within the framework of possibility theory in order to cover cases when not enough data to compute probabilities are available.

The paper is organized as follows: first, we present some related work and we compare them to the proposed approach. Then, we provide some basic notions of possibility theory, upon which our model is built. Our proposal is put forth in Section 4, and its formal properties are discussed. Conclusions end the paper.

Related Work

In multi-agent systems, representing and making possible the evaluation of the credibility associated with a piece of information is important especially when the agents have their own beliefs and can obtain new information from other sources. In this case, assessing to which extent such new information should be integrated with the agents' beliefs depends on its credibility and on the trustworthiness of its source. Tamargo et al. [START_REF] Tamargo | Modeling knowledge dynamics in multiagent systems based on informants[END_REF] address this problem in a collaborative multi-agent system in which agents can receive new information from informant agents through communication. The authors consider a credibility order among the informant agents. A belief is then revised when new contradictory incoming information arrives from an informant that is highly credible. Unlike in Tamargo's approach, where credibility is associated to agents, here we propose to associate a (computed) credibility degree to the new piece of information.

Krümpelmann et al. [START_REF] Krümpelmann | Forwarding credible information in multi-agent systems[END_REF] propose to attach an agent identifier to each piece of information, representing the credibility of the transferred information. But still, credibility is associated to an agent. Besides, while our value of credibility together with the trust value will determine the extent to which the new piece of information will be accepted, in the above-mentioned approaches the aim of the credibility order is to help in the choice of which, of the old belief and the new piece of information, will be adopted/maintained.

On the other hand, there exist several works about trust in the literature and in different disciplines [START_REF] Pinyol | Computational trust and reputation models for open multi-agent systems: a review[END_REF][START_REF] Bies | Trust and distrust: New relationships and realities[END_REF][START_REF] Sparks | Unreliable and anomalous: How the credibility of data affects belief revision[END_REF][START_REF] Ullmann-Margalit | Trust out of distrust[END_REF]. Among the numerous and interesting contributions by Falcone et al., we can underline [START_REF] Falcone | From manifesta to krypta: The relevance of categories for trusting others[END_REF], in which the authors claim that an agent's decision about trusting an information source or not depends on the agent's representation of the source's nature. The principle according to which "only an agent endowed with goals and beliefs can trust another agent" has been pointed out by Castelfranchi and Falcone [START_REF] Castelfranchi | Social trust: A cognitive approach[END_REF]. Trust is thus considered as a matter of utility and a context-sensitive concept. All the above proposals lead us to argue that trust is a multidimensional concept. Sabater et al. [START_REF] Sabater | Regret: Reputation in gregarious societies[END_REF] share this point of view. Indeed, they proposed a model which deals with three dimensions of trust or reputation. The first dimension is based on an agent's own experiences. The second dimension is based on third-party information obtained thanks to the agent's social relationships, and the third dimension, also called the ontological dimension, helps to transfer trust information between related contexts. Sierra and Debenham [START_REF] Sierra | An information-based model for trust[END_REF] propose a trust-based decision model to be used in the context of negotiation. They propose a probabilistic method to represent and define trust as depending on the information gain caused by a piece of evidence-the more information an agent has about an event, the smaller its (probabilistic) uncertainty about that event. Probability theory is also used by Teacy et al. [START_REF] Teacy | Travos: Trust and reputation in the context of inaccurate information sources[END_REF] to represent trust by taking past interactions with other agents into account while possibility theory is used in [START_REF] Ben-Naim | Evaluating trustworthiness from past performances: Intervalbased approaches[END_REF] for proposing an interval-based representations of trust and distrust based on past performances by considering the fact that data are not necessarily numerous in practice.

Background

In this section, we provide basic notions of possibility theory and define how beliefs and goals are formalized in our framework to model cognitive agents. Finally, we propose a way to associate the information content of a message to domains of competence, by adopting implication in logical Information Retrieval models.

Language and Interpretations

A classical propositional language may be used to represent information for manipulation by a cognitive agent. Definition 1. (Language) Let Prop be a finite set of atomic propositions and let L be the propositional language such that Prop ∪ { , ⊥} ⊆ L, and, ∀φ,

ψ ∈ L, ¬φ ∈ L, φ ∧ ψ ∈ L, φ ∨ ψ ∈ L.
As usual, one may define additional logical connectives and consider them as useful shorthands for combinations of connectives of L, e.g., φ ⊃ ψ ≡ ¬φ∨ψ. We will denote by Ω = {0, 1} Prop the set of all interpretations on Prop. An interpretation I ∈ Ω is a function I : Prop → {0, 1} assigning a truth value p I to every atomic proposition p ∈ Prop and, by extension, a truth value φ I to all formulas φ ∈ L. 2 We will denote by [φ] the set of all models of φ, [φ] = {I : I |= φ}.

Possibility Theory

Fuzzy sets [START_REF] Zadeh | Fuzzy sets[END_REF] are sets whose elements have degrees of membership in [0, 1]. Possibility theory is a mathematical theory of uncertainty that relies upon fuzzy set theory, in that the (fuzzy) set of possible values for a variable of interest is used to describe the uncertainty as to its precise value. At the semantic level, the membership function of such set, π, is called a possibility distribution and its range is [0, 1]. A possibility distribution can represent the beliefs of an agent: π(I) represents the degree of compatibility of the interpretation I with the available evidence about the real world if we are representing uncertain beliefs. By convention, π(I) = 1 means that it is totally possible for I to be the real world, 1 > π(I) > 0 means that I is only somehow possible, while π(I) = 0 means that I is certainly not the real world.

A possibility distribution π is said to be normalized if there exists at least one interpretation I 0 s.t. π(I 0 ) = 1, i.e., there exists at least one possible situation which is consistent with the available knowledge.

Definition 2 (Fuzzy Measure). Let Ω be a universe of discourse; a function f :

2 Ω → [0, 1] is a fuzzy measure if 1. f (∅) = 0; 2. for all A, B ⊆ Ω, A ⊆ B ⇒ f (A) ≤ f (B). A fuzzy measure f is normalized if f (Ω) = 1.

Definition 3 (Possibility and Necessity Measures).

A possibility distribution π induces a possibility measure and its dual necessity measure, denoted by Π and N respectively. Both measures apply to a classical set S ⊆ Ω and are defined as follows:

Π(S) = max I∈S π(I); (1)
N (S) = 1 -Π( S) = min I∈ S {1 -π(I)}. (2)
A few properties of Π and N induced by a normalized possibility distribution on a finite universe of discourse Ω are the following. For all subsets S ⊆ Ω:

1. Π(A ∪ B) = max{Π(A), Π(B)}; N (A ∩ B) = min{N (A), N (B)}; 2. Π(A ∩ B) ≤ min{Π(A), Π(B)}; N (A ∪ B) ≥ max{N (A), N (B)}; 3. Π(∅) = N (∅) = 0; Π(Ω) = N (Ω) = 1; 4. Π(S) = 1 -N ( S) (duality); 5. N (S) > 0 ⇒ Π(S) = 1; Π(S) < 1 ⇒ N (S) = 0;
In case of complete ignorance on S, Π(S) = Π( S) = 1 and N (S) = N ( S) = 0.

Beliefs

We assume a possibilistic BDI model of agency like the one proposed in [START_REF] Da | Belief-goal relationships in possibilistic goal generation[END_REF]. In that model, the epistemic state of an agent is represented by a normalized possibility distribution π : Ω → [0, 1]. The degree to which a given arbitrary formula φ ∈ L is believed can, therefore, be calculated from it as

B(φ) = N ([φ]) = 1 -max I |=φ {π(I)}. (3)
Straightforward consequences of the properties of possibility and necessity measures are that B(φ) > 0 ⇒ B(¬φ) = 0, i.e., if the agent somehow believes φ then it cannot believe ¬φ at all; B(φ

∧ ψ) = min{B(φ), B(ψ)} and B(φ ∨ ψ) ≥ max{B(φ), B(ψ)}. Notice that B( ) = 1 and B(⊥) = 0.
The rationale for choosing possibility theory to represent beliefs is its ability to capture epistemic uncertainty. It is well known that possibility theory is suited to represent uncertainty by only using a notion of order (much easier to have with few data) between the possible outcomes. A viable alternative would be the Dempster-Shafer theory of evidence [START_REF] Shafer | A Mathematical Theory of Evidence[END_REF]; however, the use of that theory would be computationally much heavier, due to the need to maintain a probability mass assignment to every element of 2 Ω , as compared to a possibility assignment to every interpretation of Ω in possibility theory.

Goals

The goals of an agent may be represented as a set G of formulas from the same language L. The meaning of saying that ψ ∈ G is a goal for the agent is that the agent would be happy with any state of the world I ∈ Ω such that I |= ψ.

Domains of Competence

We propose to associate formulas to domains of competence. This is in line with what has been proposed by Paglieri et al. [START_REF] Paglieri | Trusting the messenger because of the message: feedback dynamics from information quality to source evaluation[END_REF], except that they referred to arguments instead of just formulas and they defined domains based on the propositions their truth depends on. We propose a more general definition inspired by the use of implication in logical Information Retrieval models [START_REF] Ughetto | Implication in information retrieval systems[END_REF]. More precisely, given a domain d described by a formula χ d (like a query in (fuzzy) set-based models of information retrieval) and a formula φ (like a document), we use implication to determine if φ is relevant to d i.e., if χ d |= φ. The intuitive meaning of this is that incoming information is relevant to a domain if the models of the formula describing the domain are included in the models of the formula describing incoming information. However, because entailment is too rigid a relation and cannot express partial relevance [START_REF] Lalmas | Logical models in information retrieval: Introduction and overview[END_REF], what we propose is in line with fuzzy set-based models in Information retrieval [START_REF] Ughetto | Different interpretations of fuzzy gradual-inclusion-based IR models[END_REF], where one resorts to a fuzzy measure of the χ d |= φ entailment. We define one such measure based on possibilistic conditioning [START_REF] Benferhat | A practical approach to revising prioritized knowledge bases[END_REF] of φ by χ d . Definition 4. Given language L and D the set of domains of competence, such that every d ∈ D is defined by a formula χ d ∈ L, the association between formulas and domains is represented by a fuzzy relation R :

L × D → [0, 1] such that, given φ ∈ L, d ∈ D, the membership degree of formula φ in domain d is R(φ, d) = 1, if χ d |= φ, Π([φ ∧ χ d ]), otherwise.
In addition, we may require that the domains D form a partition of the universe of discourse, i.e., that

d∈D χ d = , ∀d 1 , d 2 ∈ D, χ d1 ∧ χ d2 = ⊥. Proposition 1. Let φ, ψ ∈ L. For all domain d ∈ D, if φ |= ψ, R(φ, d) ≤ R(ψ, d).
Proof: Given a domain d, we may distinguish three cases:

1. χ d |= φ; in this case, it must also be that χ d |= ψ and, as a consequence, R(φ, d) = R(ψ, d) = 1, and the thesis holds; 2.

χ d |= φ and χ d |= ψ; in this case, R(φ, d) = Π([φ ∧ χ d ]) ≤ 1 and R(ψ, d) = 1,
and the thesis holds; 3.

χ d |= φ and χ d |= ψ; in this case, R(φ, d) = Π([φ ∧ χ d ]) and R(ψ, d) = Π([ψ ∧ χ d ]); now, φ |= ψ means [φ] ⊆ [ψ]; therefore, [φ] ∩ [χ d ] ⊆ [ψ] ∩ [χ d ], hence Π([φ ∧ χ d ]) ≤ Π([ψ ∧ χ d ])
, and the thesis holds.

4 A Formal Framework of Cognitive Trust

We are now ready to formalize the notion of trust, the nature of an information source, the relation between beliefs and goals, and credibility.

Trust as Belief

Some pieces of information can contribute to increase or decrease the trust that an agent has in a source, and others can contribute to increase or decrease distrust. Trust is also a matter of competences. 3 Indeed, we can have different evaluations of trust (distrust) in the same source relevant to different domains of competence.

Like in [START_REF] Mcknight | Trust and distrust definitions: One bite at a time[END_REF], we suppose that trust and distrust are not the opposite ends of a single continuum, but linked dimensions that can coexist and have different antecedents and consequences [START_REF] Bies | Trust and distrust: New relationships and realities[END_REF]. We consider the social-cognitive model of trust [START_REF] Castelfranchi | Social trust: A cognitive approach[END_REF][START_REF] Robinson | Measures of Personality and Social Psychological Attitudes. Measures of social psychological attitudes[END_REF], in which trust is defined as beliefs: an agent trusts a source s, in a domain d, if and only if it somehow believes that s will be able to somehow help it fulfill its goals. We will also define distrust as a belief: an agent distrusts a source s with respect to a domain of competence d if and only if it somehow believes that s might try to prevent it to reach its goals. Although in the next sections we will show how to compute trust and distrust in a source s, we should always keep in mind that trust and distrust in s are to be construed conceptually as if they were defined as follows: trust(s) ≡ B("s is trustworthy"), (4) distrust(s) ≡ B("s is untrustworthy").

(

) 5
Notice that proposition "s is untrustworthy" is the logical negation of "s is trustworthy". Some authors treat "distrust" as if it were defined as ¬B("s is trustworthy"), in which case distrust(s) = 1 -trust(s): trust is considered as the complement of distrust [START_REF] Ullmann-Margalit | Trust out of distrust[END_REF]. Here, we give distrust a stronger meaning: we distrust someone if we have valid reasons to believe he is lying, not if we do not have valid reasons to believe he is telling the truth. In other words, distrust is not the complement of trust.

A consequence of Equations 4 and 5, together with the properties of Π and N , is that trust and distrust, wrt a given domain, obey the following mutual constraints:

trust(s) > 0 ⇒ distrust(s) = 0, (6) distrust(s) > 0 ⇒ trust(s) = 0. (7)
In case of total ignorance, we have that trust(s) = distrust(s) = 0. Notice that if we consider trust as the complement of distrust, we cannot represent the situations of total ignorance in which the agent does not know anything which could lead it to trust or distrust the source; distrust(s) = 1 -trust(s) = 0.5 would not mean ignorance!

The Nature of a Source

Any judgment about the competence or willingness of a source to provide useful information must be, implicitly or explicitly, based on an agent's judgment (i.e., beliefs) about the source according to past interactions as well as recommendations or the source's reputations. We will refer to such assessment as the source's nature.

Without any claim of exhaustiveness and just to ground our presentation on an intuitive setting, we draw inspiration from the abstract model of a human agent's social behavior proposed by Italian economist Carlo Cipolla [START_REF] Cipolla | The basic laws of human stupidity[END_REF] as the backdrop on which his theory of human stupidity is expounded.

According to Cipolla's model, an agent's behavior may be summarized by two coordinates:

x the average gain (or loss) that an agent obtains as a result of his or her actions; y the average gain (or loss) that an agent produces to other agents or groups of agents.

As a result, agents can be plotted as points on a diagram like the one shown in Figure 1 based on their x, y behavior. Such a diagram divides the two-dimensional plane into four quadrants or eight sectors, corresponding to different natures of the agents.

For the sake of simplicity, let us represent an agent's position in one of the eight sectors by means of three propositional variables: r if agent s is rational (x > 0); m if agent s is malicious (y < 0); and e if |y| < |x|.

It is worth mentioning that this concept of source nature allows us to model the two kinds of beliefs, namely "willingness belief" and "persistence belief", proposed by Ramchurn [START_REF] Ramchurn | Trust in multi-agent systems[END_REF] to ensure that a certain task can be delegated by an agent to another one. More precisely, the eight sectors we identify are used by the agent to decide when it needs to maintain a suspicious attitude in dealing with malicious or irrational agents.

Trust and (Shareable) Goals

We make the assumption that the agent's beliefs about the source's goals may also influence its trust in the source. Indeed, regardless of the content of information, if, for example, a source s shares the same goal g with the agent, we may suppose that s will act to fulfill g. This should, at least in case of rational sources, prevent s from taking actions that could negatively influence the satisfaction of g.

The way beliefs about the source's goals, G s are taken into account is by comparing them with the agent's own goals, G. We distinguish four cases, which represent three possible situations. The four cases are schematically illustrated in Figure 2.

Trust in a Source

We assume that an agent has an internal reasoning mechanism allowing it to compute the trust/distrust, τ z /δ z , with z ∈ {(a), (b), (c), (d)} (the four cases in Section 4.3). Such degrees depend on the agent's beliefs about the source's position in the nature diagram and its beliefs about the source's goals with respect to its own goals. Figure 3 shows a minimal such mechanism based on look-up tables.

Computing trust can be seen as a set of material implications. Given a source's position in the nature diagram, "if the source's goals configuration is z, then the agent will associate a trust τ z to that source". However, the agent may not know precisely the source's position and it can just have a notion of order about which among the eight possible sectors the source could be in, some of them being more possible than others. If we consider a source s, the uncertainty is captured in our formalism trough the possibility distribution on the worlds (i.e., interpretations) I which are consistent with {0, 1} {rs,ms,es} . The above implication is then represented as a fuzzy implication. Among the existing definitions of fuzzy implications (see for example [START_REF] Mas | A survey on fuzzy implication functions[END_REF] for a survey) we adopt the Kleene-Dienes fuzzy implication. Other definitions might be used as well. The truth value of the fuzzy implication "If a source is somehow compatible with situation I, then the agent trusts that source to degree τ z (I)" quantifies to what extent "the agent trusts that source to degree τ z (I)" is at least as true as "that source is somehow compatible with situation I". Let us recall that we consider eight possible positions and that we have a possibility distribution on these positions. We have then eight fuzzy implications with their respective truth values. Therefore, for each goal configuration z, we define the trust and distrust that the agent has in source s as follows: 4trust z (s) = min

I∈{0,1} {rs,ms,es } max{τ z (I), 1 -π(I)}, (8)
distrust z (s) = min I∈{0,1} {rs,ms,es} max{δ z (I), 1 -π(I)}. (9)
Besides, we can also have uncertainty about the configuration of the source's goals. The overall trust/distrust of an agent in a source s depends then on (i) its judgment about a source defined by τ z /δ z , (ii) the uncertainty about the source's real nature, and (iii) the uncertainty about the source's goals. We thus define these trust and distrust values based on goals and nature as follows:

trust(s) = min z∈{a,b,c,d} max{trust z (s), 1 -π(z)}, (10)
distrust(s) = min z∈{a,b,c,d} max{distrust z (s), 1 -π(z)}. (11)
Proposition 2. If the two functions τ z (I) and δ z (I) are such that, for all z and I, τ z (I) > 0 ⇒ δ z (I) = 0 and δ z (I) > 0 ⇒ τ z (I) = 0, then, for all source s, trust(s) and distrust(s) satisfy the bipolar conditions of Equations 6 and 7.

Proof: Since π is normalized, ∃z 0 , I 0 such that π(z 0 ) = π(I 0 ) = 1. Then, trust(s) > 0 ⇒ ∀z max{trust z (s), 1 -π(z)} > 0 ⇒ trust z0 (s) > 0 ⇒ τ z0 (I 0 ) > 0 ⇒ δ z0 (I 0 ) = 0 and 1 -π(I 0 ) = 0 ⇒ max{δ z0 (I 0 ), 1 -π(I 0 )} = 0 ⇒ distrust(s) = 0. A similar reasoning proves that distrust(s) > 0 ⇒ trust(s) = 0. 2
A corollary of this proposition is that, for all source s, trust(s) + distrust(s) ≤ 1. We can notice that, in case of complete ignorance, trust(s) = distrust(s) = 0. Definition 5. (Trustworthiness order relation) Let s 1 and s 2 be two information sources. We consider that s 1 is less trustworthy than s 2 , s 1 s 2 , if and only if trust(s 1 ) ≤ trust(s 2 ) and distrust(s 1 ) ≥ distrust(s 2 ). Proposition 3. (Total order) The relation is a total order.

Proof:

The thesis is a direct consequence of Equations 6 and 7. 2

Credibility and Competence

Let D be the set of domains of competence considered for the agent and the sources. The agent's competences are represented through a vector κ, whose component κ d represents the extent to which the agent is competent with respect to domain d ∈ D. Moreover, we suppose that the agent may have beliefs about the competences of a source. To this aim, we assume that Prop contains propositions c s d , meaning "source s is competent about domain d"; B(c s d ) will thus be the extent to which the agent believes s is competent about d. Definition 6. Let φ ≡ ⊥ be new information provided by s. The extent to which the agent deems φ credible, given that φ is reported by source s, is

cr(φ, s) = max{B(φ), max d∈D min{cr d (φ, s), R(φ, d)}}, (12)
where

cr d (φ, s) = min{B(c s d ), 1 -κ d , Π([φ])}, if κ d > B(c s d ); B(c s d ), otherwise. (13)
For the sake of completeness, ∀s, cr(⊥, s) = 0.

Equation 12 may be paraphrased as "φ being reported by s is credible if there exists a domain to which φ is related and with respect to which it is credible". Taking a max with B(φ) accounts for the fact that the extent to which something is believable cannot be less than it is already believed, no matter which source is reporting it, since credibility is the quality of being believable. Besides, a message is believable if we deem it possible.

Formally, for all formula φ provided by a source s we have B(φ) ≤ cr(φ, s) ≤ Π ([φ]). This definition of credibility allows us to capture the notion of "competence belief" proposed in [START_REF] Ramchurn | Trust in multi-agent systems[END_REF], going even further by using both the receiving agent's own competence and the source's expected competences to assess the credibility of the information item. Equation 13involves two cases:

if the agent is not more competent about d than the source is (κ d ≤ B(c s d ), second case of Equation 13), then it will not try to filter the incoming message according to its own beliefs; this is a mandatory assumption if an agent is to be capable of learning from sources it believes to be more knowledgeable than it is; if, however, the agent believes to be more competent about d than the source (κ d > B(c s d ), first case of Equation 13), information supplied by the source should be evaluated by its internal credibility; in addition, the resulting credibility of supplied information should not be greater than the competence of the source providing it, otherwise an agent scarcely competent about a domain would incur the risk of accepting acritically anything that a source just a little more competent than it about that domain would say, which is not in conflict with its (admittedly very incomplete) beliefs. Furthermore, the first case in Equation 13 refers to an "internal" credibility of φ, which satisfies the following two intuitive properties:

1. if φ is completely relevant to d, cr d (φ) ≤ 1 -B(¬φ); 2. the more the agent's knowledge is complete on domain d (i.e., the agent is competent), the more cr d (φ) will approach its lower bound B(φ) and, vice versa, the more the agent is ignorant about d, the more it must be keen on heeding a φ that does not contradict its current beliefs.

Like in [START_REF] Booth | Credibility-limited improvement operators[END_REF], for example, the idea here is to capture the fact that a piece of information is accepted by the agent if and only if it is "credible" for the agent. "Our definition" of credibility is nevertheless different from the one used by Booth et al.. They consider the set of credible formulas as "an (explicit) part of an epistemic state, since it defines how easily an agent can accept very implausible new pieces of information". In our setting, the credibility of a piece of information represents the capability of the agent to evaluate the tenability of the piece of information with respect to its own competences and the ones of the sources. Obviously, if the agent is less competent or not competent at all with respect to a domain, this credibility degree must depend (be weighted), in a sense, by the source's competence. 2

Being the credibility cr(•, s) in an information content provided by a certain source a fuzzy measure, the following two properties hold: Proposition 5. Given a source s, ∀φ, ψ ∈ L, cr(φ ∨ ψ, s) ≥ max(cr(ψ, s), cr(ψ, s)) and cr(φ ∧ ψ, s) ≤ min(cr(ψ, s), cr(ψ, s)).

Proof: ∀φ, ψ ∈ L, (a) φ |= φ∨ψ, and ψ |= φ∨ψ; therefore, cr(φ, s) ≤ cr(φ∨ψ, s) and cr(ψ, s) ≤ cr(φ∨ψ, s); (b) φ∧ψ |= φ and φ∧ψ |= ψ; therefore, cr(φ∧ψ, s) ≤ cr(φ, s) and cr(φ ∧ ψ, s) ≤ cr(ψ, s). 2

Accepting Information

The extent to which a piece of information φ (provided by a source s) is accepted by an agent depends on the trust and distrust computed on the basis of the source's goals and nature (Equations 10 and 11) and the credibility of φ for the agent (Equation 12) which depends on the competences of the agent and the sources. We may be combined these values using the minimum triangular norm, to yield the extent to which φ provided by s is accepted by the agent: acc(φ, s) = min{cr(φ, s), trust(s)}.

The choice of min as the aggregation operator is motivated by the fact that an agent should accept information φ provided by source s to the extent to which it deems φ credible and s trustworthy according to its goals and nature. Proposition 6. ∀s, acc(•, s) is a fuzzy measure. It is normalized if trust(s) = 1.

Proof: Since acc(•, s) is the min of a normalized fuzzy measure and trust(s), which is a constant for a fixed s, acc(•, s) is a fuzzy measure, i.e., acc(⊥, s) = 0 and, for φ, ψ ∈ L such that φ |= ψ, acc(φ, s) = min{cr(φ, s), trust(s)} ≤ min{cr(ψ, s), trust(s)} = acc(ψ, s).

Finally, if trust(s) = 1, acc( , s) = min{cr( , s), 1} = min{1, 1} = 1. 2

A piece of information φ may be provided by more sources. In this case, the extent to which φ is accepted by the agent, accepted(φ) may be defined as accepted(φ) = max s∈src(φ) {acc(φ, s)}, [START_REF] Lalmas | Logical models in information retrieval: Introduction and overview[END_REF] where src(φ) denotes the sources of φ. Operators other than max might be used, e.g., operators with cumulative effects. The value accepted(φ) may be used as input weight for any weighted belief revision operator, like the ones studied in [START_REF] Benferhat | Syntactic computation of hybrid possibilistic conditioning under uncertain inputs[END_REF].

Experimental results obtained by Sparks in [START_REF] Sparks | Unreliable and anomalous: How the credibility of data affects belief revision[END_REF] shows that when untrustworthy sources provide non-credible information, individuals are less likely to revise their initial beliefs. Our formalism also captures the fact that the initial beliefs of an agent are not revised if new information is non-credible or is provided by untrustworthy sources.

Conclusion

The goal of this paper is to shed some light on a few fundamental formal aspects of credibility and trust as used by humans in view of their implementation on computers. More precisely, our contribution consists in providing a model for computing the acceptance of information provided by a source taking into account both trust in the source and credibility of the message.

Our model encompasses, but is not limited to, the four "kinds" of beliefs needed by an agent before delegating a task to another agent [START_REF] Ramchurn | Trust in multi-agent systems[END_REF], where the task is "to provide useful information". In particular, -"competence belief" is captured by "our" definition of credibility that goes even further by using also the receiving agent's own competence to assess information provided by another agent; -"willingness belief" and "persistence belief" are captured thanks to the concept of "source nature": we should always adopt and maintain a suspicious attitude with respect to an agent we believe to be irrational for example; and -"motivation belief" is captured by taking into account both the goals of the agent and the ones of the source: the agent believes that a source sharing its goals has some motivation to help it.

As for future work, we plan to apply our formalism towards a cognitive view of adversarial reasoning, and to analyze and reason over irrational behavior (i.e., stupid agents are dangerous because they act irrationally).

Fig. 1 .Fig. 2 .

 12 Fig. 1. The correspondence between the eight sectors of the source nature diagram and the truth assignments to the propositional variables r, m, and e.

Fig. 3 .

 3 Fig. 3. A definition of functions τz(I) and δz(I), for z ∈ {a, b, c, d} and I ∈ {0, 1} {r,m,s} .

Proposition 4 .

 4 Given a source s, cr(•, s) is a normalized fuzzy measure. Proof: We must prove that cr(⊥, s) = 0; cr( , s) = 1; and ∀φ, ψ ∈ L, φ |= ψ ⇒ cr(φ, s) ≤ cr(ψ, s) (monotonicity). Now, cr(⊥, s) = 0 holds by definition; cr( , s) = 1 holds because cr( , s) = max{B( ), max d∈D min{cr d ( , s), R( , d)}} ≥ B( ) = 1. To prove monotonicity, we observe that, for every domain d ∈ D, -B(φ) ≤ B(ψ), because B is a fuzzy measure; -R(φ, d) ≤ R(ψ, d) by Proposition 1; -Π([φ]) ≤ Π([ψ]), because Π is a fuzzy measure; -B(c s d ) and κ d do not depend on φ or ψ. Therefore, since max{a, b} ≤ max{c, d} and min{a, b} ≤ min{c, d} if a ≤ c and b ≤ d, cr(φ, s) ≤ cr(ψ, s).

In the rest of the paper we will also refer to the "trustworthiness of an information source" for an agent as the agent's "trust in a source".

When φ I = 1, i.e., I satisfies formula φ, in symbols I |= φ, I is called a model of φ.

Here, we name such a competence-based trust credibility.

For the the sake of readability, we restrict the interpretations I as if the language were built on atomic propositions rs, ms, and es only.