Measuring Ranks via the Complete Laws of Iterated Contraction

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper gives a complete axiomatization of that behavior, i.e., a complete set of laws of iterated contraction. It does so by showing how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multi-plicative constant and thus how to measure ranks on a ratio scale

Truth and rationality

This paper is about the pragmatic notion of truth, according to which what we believe in the ideal limit of inquiry is true. Hence, it refers to the dynamics of belief and thus to theoretical rationality. Thereby, truth and rationality are inexorably entangled; neither can be explained without the other. The paper intends to make plausible that this entanglement may be developed into rigorous and fruitful theory

Two-dimensional Truth

The paper identifies two major strands of truth theories, ontological and epistemological ones, and argues that both are of equal primacy and find their home within two-dimensional semantics. Contrary to received views, it argues further that epistemological truth theories operate on Lewisian possible worlds and ontological truth theories on Wittgensteinian possible worlds and that both are mediated by the so-called epistemic-ontic map the further specification of which is of utmost philosophical importance

Time Evolution of Spin Waves

A rigorous derivation of macroscopic spin-wave equations is demonstrated. We introduce a macroscopic mean-field limit and derive the so-called Landau-Lifshitz equations for spin waves. We first discuss the ferromagnetic Heisenberg model at T=0 and finally extend our analysis to general spin hamiltonians for the same class of ferromagnetic ground states.Comment: 4 pages, to appear in PR

Exchange on Spohn's Laws of Belief

The authors of the following discussion notes have been working on causation for about 40 years. Woodward’s work culminated in his book Making Things Happen (OUP 2003), Spohn’s work culminated in chapters 14 and 15 of his book The Laws of Belief (OUP 2012), which have almost book-length. Prima facie, their accounts look quite similar; the interventionist theory of causal Bayes nets seems to be their common ground. Therefore, it is important to also see their differences. These are explained in the notes, which mutually discuss their theories of causation. The exchange originates from an Author Meets Critic session at the APA meeting in Baltimore in January 2017

Ranking Theory

Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology

A Multi-Institutional Analysis of Prostate Cancer Patients With or Without 68Ga-PSMA PET/CT Prior to Salvage Radiotherapy of the Prostatic Fossa

Introduction: 68Ga-PSMA PET/CT is associated with unprecedented sensitivity for localization of biochemically recurrent prostate cancer at low PSA levels prior to radiotherapy. Aim of the present analysis is to examine whether patients undergoing postoperative, salvage radiotherapy (sRT) of the prostatic fossa with no known nodal or distant metastases on conventional imaging (CT and/or MRI) and on positron emission tomography/computed tomography (68Ga-PSMA PET/CT) will have an improved biochemical recurrence-free survival (BRFS) compared to patients with no known nodal or distant metastases on conventional imaging only. Material and Methods: This retrospective analysis is based on 459 patients (95 with and 364 without 68Ga-PSMA PET/CT). BRFS (PSA < post-sRT Nadir + 0.2 ng/ml) was the primary study endpoint. This was first analysed by Kaplan-Meier and uni- and multivariate Cox regression analysis for the entire cohort and then again after matched-pair analysis using tumor stage, Gleason score, PSA at time of sRT and radiation dose as matching parameters. Results: Median follow-up was 77.5 months for patients without and 33 months for patients with 68Ga-PSMA PET/CT. For the entire cohort, tumor stage (pT2 vs. pT3-4; p= <0.001), Gleason score (GS ≤ 7 vs. GS8-10; p=0.003), pre-sRT PSA (<0.5 vs. ≥0.5ng/ml; p<0.001) and sRT dose (<70 vs. ≥70Gy; p<0.001) were the only factors significantly associated with improved BRFS. This was not seen for the use of 68Ga-PSMA PET/CT prior to sRT (p=0.789). Matched-pair analysis consisted of 95 pairs of PCa patients with or without PET/CT and no significant difference in BRFS based on the use of PET/CT was evident (p=0.884). Conclusion: This analysis did not show an improvement in BRFS using 68Ga-PSMA PET/CT prior to sRT neither for the entire cohort nor after matched-pair analysis after excluding patients with PET-positive lymph node or distant metastases a priori. As no improved BRFS resulted with implementation of 68Ga-PSMA PET in sRT planning, sRT should not be deferred until the best “diagnostic window” for 68Ga-PSMA PET/CT

Whole pelvis vs. hemi pelvis elective nodal radiotherapy in patients with PSMA-positive nodal recurrence after radical prostatectomy - a retrospective multi-institutional propensity score analysis.

PURPOSE Despite growing evidence for bilateral pelvic radiotherapy (whole pelvis RT, WPRT) there is almost no data on unilateral RT (hemi pelvis RT, HPRT) in patients with nodal recurrent prostate cancer after prostatectomy. Nevertheless, in clinical practice HPRT is sometimes used with the intention to reduce side effects compared to WPRT. Prostate-specific membrane antigen positron emission tomography / computed tomography (PSMA-PET/CT) is currently the best imaging modality in this clinical situation. This analysis compares PSMA-PET/CT based WPRT and HPRT. METHODS A propensity score matching was performed in a multi-institutional retrospective dataset of 273 patients treated with pelvic RT due to nodal recurrence (214 WPRT, 59 HPRT). In total, 102 patients (51 in each group) were included in the final analysis. Biochemical recurrence-free survival (BRFS) defined as prostate specific antigen (PSA) < post-RT nadir + 0.2ng/ml, metastasis-free survival (MFS) and nodal recurrence-free survival (NRFS) were calculated using the Kaplan-Meier method and compared using the log rank test. RESULTS Median follow-up was 29 months. After propensity matching, both groups were mostly well balanced. However, in the WPRT group there were still significantly more patients with additional local recurrences and biochemical persistence after prostatectomy. There were no significant differences between both groups in BRFS (p = .97), MFS (p = .43) and NRFS (p = .43). After two years, BRFS, MFS and NRFS were 61%, 86% and 88% in the WPRT group and 57%, 90% and 82% in the HPRT group, respectively. Application of a boost to lymph node metastases, a higher RT dose to the lymphatic pathways (> 50 Gy EQD2α/β=1.5 Gy) and concomitant androgen deprivation therapy (ADT) were significantly associated with longer BRFS in uni- and multivariate analysis. CONCLUSIONS Overall, this analysis presents the outcome of HPRT in nodal recurrent prostate cancer patients and shows that it can result in a similar oncologic outcome compared to WPRT. Nevertheless, patients in the WPRT may have been at a higher risk for progression due to some persistent imbalances between the groups. Therefore, further research should prospectively evaluate which subgroups of patients are suitable for HPRT and if HPRT leads to a clinically significant reduction in toxicity