On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

Computation in Non-Classical Foundations?

The Church-Turing Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms (like "set", "function", and "number") are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare what they mean. We argue for some minimal conditions that must be met if two frameworks are to be compared; if frameworks are radical enough, comparison becomes hopeless. Our aim is to clarify the dialectical situation in this bourgeoning area of research, shedding light on the nature of non-classical logic and the notion of computation alike.

Classical and non-classical HLA molecules and p16(INK4a) expression in precursors lesions and invasive cervical cancer

Objectives: Viruses and turnout cells may regulate the expression of HLA molecules on the cell surface to escape immune system surveillance. Absence of classical HLA class I molecules may impair the action of specific cytotoxic cells, whereas non-classical HLA class I molecules may regulate innate and adaptive immune cells. We assess here the possible associations between classical/non-classical class I HLA and p16(INK4a) molecule expression in cervical biopsies of women infected with HPV, stratified according to grade of the lesion and HPV type. Study design: Cervical biopsies (N = 74) presenting cervical intraepithelial neoplasia grade 1 (CIN1) (n = 31), CIN2-3 (n = 19), and invasive cancer (n = 14) were evaluated alongside 10 normal cervical specimens. Results: HLA-A/B/C/G staining was observed in the early stages of HPV infection. A significant association was detected between HLA-A/B/C staining and HPV16/18 infection (OR = 0.12, 95%CI: 0.0163-0.7899; p = 0.04). HLA-E expression increased with the progression of the lesion (chi(2)-test for trend = 4.01; p = 0.05), and a significant association was found between HLA-E staining and HPV16/18 infection (OR = 11.25, 95%CI: 2.324-54.465; p = 0.003). Irrespective of the grade of the lesion, HLA-A/B/C staining and p16(INK4a) presented a good concordance (Kappa: 0.67). Conclusions: HLA-E overexpression seemed to be associated with invasive cancer and HPV16/18 infection. (C) 2008 Elsevier Ireland Ltd. All rights reserved.

Non-classical error bounds in the central limit theorem

The classical central limit theorem states the uniform convergence of the distribution functions of the standardized sums of independent and identically distributed square integrable real-valued random variables to the standard normal distribution function. While first versions of the central limit theorem are already due to Moivre (1730) and Laplace (1812), a systematic study of this topic started at the beginning of the last century with the fundamental work of Lyapunov (1900, 1901). Meanwhile, extensions of the central limit theorem are available for a multitude of settings. This includes, e.g., Banach space valued random variables as well as substantial relaxations of the assumptions of independence and identical distributions. Furthermore, explicit error bounds are established and asymptotic expansions are employed to obtain better approximations. Classical error estimates like the famous bound of Berry and Esseen are stated in terms of absolute moments of the random summands and therefore do not reflect a potential closeness of the distributions of the single random summands to a normal distribution. Non-classical approaches take this issue into account by providing error estimates based on, e.g., pseudomoments. The latter field of investigation was initiated by work of Zolotarev in the 1960's and is still in its infancy compared to the development of the classical theory. For example, non-classical error bounds for asymptotic expansions seem not to be available up to now ...

Cross-sectional observational study of 208 patients with non-classical urea cycle disorders.

Urea cycle disorders (UCDs) are inherited disorders of ammonia detoxification often regarded as mainly of relevance to pediatricians. Based on an increasing number of case studies it has become obvious that a significant number of UCD patients are affected by their disease in a non-classical way: presenting outside the newborn period, following a mild course, presenting with unusual clinical features, or asymptomatic patients with only biochemical signs of a UCD. These patients are surviving into adolescence and adulthood, rendering this group of diseases clinically relevant to adult physicians as well as pediatricians. In preparation for an international workshop we collected data on all patients with non-classical UCDs treated by the participants in 20 European metabolic centres. Information was collected on a cohort of 208 patients 50% of which were ≥ 16 years old. The largest subgroup (121 patients) had X-linked ornithine transcarbamylase deficiency (OTCD) of whom 83 were female and 29% of these were asymptomatic. In index patients, there was a mean delay from first symptoms to diagnosis of 1.6 years. Cognitive impairment was present in 36% of all patients including female OTCD patients (in 31%) and those 41 patients identified presymptomatically following positive newborn screening (in 12%). In conclusion, UCD patients with non-classical clinical presentations require the interest and care of adult physicians and have a high risk of neurological complications. To improve the outcome of UCDs, a greater awareness by health professionals of the importance of hyperammonemia and UCDs, and ultimately avoidance of the still long delay to correctly diagnose the patients, is crucial.

Non-classical karyotypic features in relapsed childhood B-cell precursor acute lymphoblastic leukemia.

Karyotype analysis of acute lymphoblastic leukemia (ALL) at diagnosis has provided valuable prognostic markers for treatment stratification. However, reports of cytogenetic studies of relapsed ALL samples are limited. We compared the karyotypes from 436 nonselected B-cell precursor ALL patients at initial diagnosis and of 76 patients at first relapse. We noticed a relative increase of karyotypes that did not fall into the classic ALL cytogenetic subgroups (high hyperdiploidy, t(12;21), t(9;22), 11q23, t(1;19), <45 chromosomes) in a group of 29 patients at relapse (38%) compared to 130 patients at presentation (30%). Non-classical cytogenetic aberrations in these 29 patients were mostly found on chromosomes 1, 2, 7, 9, 13, 14, and 17. We also describe six rare reciprocal translocations, three of which involved 14q32. The most frequent abnormalities were found in 9p (12/29 cases) and were associated with a marked decrease in the duration of the second remission, but not of the probability of 10-year event-free survival after relapse treatment. From 29 patients with non-classical cytogenetic aberrations, only 8 (28%) had been stratified to a high risk-arm on the first treatment protocol, suggesting that this subgroup might benefit from the identification of new prognostic markers in future studies.

TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY

Abstract In this paper we present a philosophical motivation for the logics of formal inconsistency , a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC , a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence.

Multi-Prover and parallel repetition in non-classical interactive games

Depuis l’introduction de la mécanique quantique, plusieurs mystères de la nature ont trouvé leurs explications. De plus en plus, les concepts de la mécanique quantique se sont entremêlés avec d’autres de la théorie de la complexité du calcul. De nouvelles idées et solutions ont été découvertes et élaborées dans le but de résoudre ces problèmes informatiques. En particulier, la mécanique quantique a secoué plusieurs preuves de sécurité de protocoles classiques. Dans ce m´emoire, nous faisons un étalage de résultats récents de l’implication de la mécanique quantique sur la complexité du calcul, et cela plus précisément dans le cas de classes avec interaction. Nous présentons ces travaux de recherches avec la nomenclature des jeux à information imparfaite avec coopération. Nous exposons les différences entre les théories classiques, quantiques et non-signalantes et les démontrons par l’exemple du jeu à cycle impair. Nous centralisons notre attention autour de deux grands thèmes : l’effet sur un jeu de l’ajout de joueurs et de la répétition parallèle. Nous observons que l’effet de ces modifications a des conséquences très différentes en fonction de la théorie physique considérée.

Transreal arithmetic as a consistent basis for paraconsistent logics

Paraconsistent logics are non-classical logics which allow non-trivial and consistent reasoning about inconsistent axioms. They have been pro- posed as a formal basis for handling inconsistent data, as commonly arise in human enterprises, and as methods for fuzzy reasoning, with applica- tions in Artificial Intelligence and the control of complex systems. Formalisations of paraconsistent logics usually require heroic mathe- matical efforts to provide a consistent axiomatisation of an inconsistent system. Here we use transreal arithmetic, which is known to be consis- tent, to arithmetise a paraconsistent logic. This is theoretically simple and should lead to efficient computer implementations. We introduce the metalogical principle of monotonicity which is a very simple way of making logics paraconsistent. Our logic has dialetheaic truth values which are both False and True. It allows contradictory propositions, allows variable contradictions, but blocks literal contradictions. Thus literal reasoning, in this logic, forms an on-the- y, syntactic partition of the propositions into internally consistent sets. We show how the set of all paraconsistent, possible worlds can be represented in a transreal space. During the development of our logic we discuss how other paraconsistent logics could be arithmetised in transreal arithmetic.

On the geometry of non-classical curves

In this paper we relate the numerical invariants attached to a projective curve, called the order sequence of the curve, to the geometry of the varieties of tangent linear spaces to the curve and to the Gauss maps of the curve. © 1992 Sociedade Brasileira de Matemática.

Non-classical HLA-E gene variability in Brazilians: a nearly invariable locus surrounded by the most variable genes in the human genome

The non-classical human leukocyte antigen (HLA) class I genes present a very low rate of variation. So far, only 10 HLA-E alleles encoding three proteins have been described, but only two are frequently found in worldwide populations. Because of its historical background, Brazilians are very suitable for population genetic studies. Therefore, 104 bone marrow donors from Brazil were evaluated for HLA-E exons 14. Seven variation sites were found, including two known single nucleotide polymorphisms (SNPs) at positions +424 and +756 and five new SNPs at positions +170 (intron 1), +1294 (intron 3), +1625, +1645 and +1857 (exon 4). Haplotyping analysis did show eight haplotypes, three of them known as E*01:01:01, E*01:03:01 and E*01:03:02:01 and five HLA-E new alleles that carry the new variation sites. The HLA-E*01:01:01 allele was the predominant haplotype (62.50%), followed by E*01:03:02:01 (24.52%). Selective neutrality tests have disclosed an interesting pattern of selective pressures in which balancing selection is probably shaping allele frequency distributions at an SNP at exon 3 (codon 107), sequence diversity at exon 4 and the non-coding regions is facing significant purifying pressure. Even in an admixed population such as the Brazilian one, the HLA-E locus is very conserved, presenting few polymorphic SNPs in the coding region.

Cross-sectional observational study of 208 patients with non-classical urea cycle disorders

Urea cycle disorders (UCDs) are inherited disorders of ammonia detoxification often regarded as mainly of relevance to pediatricians. Based on an increasing number of case studies it has become obvious that a significant number of UCD patients are affected by their disease in a non-classical way: presenting outside the newborn period, following a mild course, presenting with unusual clinical features, or asymptomatic patients with only biochemical signs of a UCD. These patients are surviving into adolescence and adulthood, rendering this group of diseases clinically relevant to adult physicians as well as pediatricians. In preparation for an international workshop we collected data on all patients with non-classical UCDs treated by the participants in 20 European metabolic centres. Information was collected on a cohort of 208 patients 50% of which were ≥ 16 years old. The largest subgroup (121 patients) had X-linked ornithine transcarbamylase deficiency (OTCD) of whom 83 were female and 29% of these were asymptomatic. In index patients, there was a mean delay from first symptoms to diagnosis of 1.6 years. Cognitive impairment was present in 36% of all patients including female OTCD patients (in 31%) and those 41 patients identified presymptomatically following positive newborn screening (in 12%). In conclusion, UCD patients with non-classical clinical presentations require the interest and care of adult physicians and have a high risk of neurological complications. To improve the outcome of UCDs, a greater awareness by health professionals of the importance of hyperammonemia and UCDs, and ultimately avoidance of the still long delay to correctly diagnose the patients, is crucial.

Non-classical karyotypic features in relapsed childhood B-cell precursor acute lymphoblastic leukemia

Karyotype analysis of acute lymphoblastic leukemia (ALL) at diagnosis has provided valuable prognostic markers for treatment stratification. However, reports of cytogenetic studies of relapsed ALL samples are limited. We compared the karyotypes from 436 nonselected B-cell precursor ALL patients at initial diagnosis and of 76 patients at first relapse. We noticed a relative increase of karyotypes that did not fall into the classic ALL cytogenetic subgroups (high hyperdiploidy, t(12;21), t(9;22), 11q23, t(1;19), <45 chromosomes) in a group of 29 patients at relapse (38%) compared to 130 patients at presentation (30%). Non-classical cytogenetic aberrations in these 29 patients were mostly found on chromosomes 1, 2, 7, 9, 13, 14, and 17. We also describe six rare reciprocal translocations, three of which involved 14q32. The most frequent abnormalities were found in 9p (12/29 cases) and were associated with a marked decrease in the duration of the second remission, but not of the probability of 10-year event-free survival after relapse treatment. From 29 patients with non-classical cytogenetic aberrations, only 8 (28%) had been stratified to a high risk-arm on the first treatment protocol, suggesting that this subgroup might benefit from the identification of new prognostic markers in future studies.

Regulation of peripheral classical and non-classical monocytes on infliximab treatment in patients with rheumatoid arthritis and ankylosing spondylitis.

OBJECTIVE To investigate the regulatory effect of tumour necrosis factor (TNF) blockade with infliximab on the distribution of peripheral blood monocyte subpopulations in patients with rheumatoid arthritis (RA) and ankylosing spondylitis (AS). METHODS Purified CD11b+CD14+ monocytes from 5 patients with RA and 5 AS were analysed ex vivo before and after infliximab treatment by flow cytometry for CD16, CD163, CD11b, C-C chemokine receptor type 2 (CCR2) and CXC chemokine receptor 4 (CXCR4) at baseline and at days 2, 14, 84 and 168 after the first infliximab administration. Serum levels of the stromal cell-derived factor (SDF)-1 and monocyte chemotactic peptide (MCP)-1 at different time points were measured in either patient group before and on infliximab treatment. RESULTS Anti-TNF treatment with infliximab led to a significant increase of circulating CD11b+ non-classical and a concomitantly decrease of CD11b+ classical monocytes, to a decline in SDF-1 levels and reduced expression of CCR2 and CXCR4 on non-classical monocyte subpopulation. CONCLUSIONS Our study shows, that TNFα blockade by infliximab resulted in a dichotomy of the regulation of classical and non-classical monocytes that might have substantial impact on inhibition of osteoclastogenesis and of subsequent juxta-articular bone destruction and systemic bone loss in RA and AS.