A Tableaux Calculus for Reducing Proof Size

A tableau calculus is proposed, based on a compressed representation of clauses, where literals sharing a similar shape may be merged. The inferences applied on these literals are fused when possible, which reduces the size of the proof. It is shown that the obtained proof procedure is sound, refutationally complete and allows to reduce the size of the tableau by an exponential factor. The approach is compatible with all usual refinements of tableaux.Comment: Technical Repor

Proof-Pattern Recognition and Lemma Discovery in ACL2

We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition to pre-processes data from libraries, and then suggests auxiliary lemmas in new proofs by analogy with already seen examples. This paper presents the implementation of ACL2(ml) alongside theoretical descriptions of the proof-pattern recognition and lemma discovery methods involved in it

Integrating a Global Induction Mechanism into a Sequent Calculus

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.Comment: 16 page

System Description: The Proof Transformation System CERES

The original publication is available at www.springerlink.comInternational audienceCut-elimination is the most prominent form of proof trans- formation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolu- tion) works by extracting a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of an ACNF, an LK-proof with only atomic cuts. The system CERES, an implementation of the CERES-method has been used successfully in analyzing nontrivial mathematical proofs (see [4]).In this paper we describe the main features of the CERES system with spe- cial emphasis on the extraction of Herbrand sequents and simplification methods on these sequents. We demonstrate the Herbrand sequent ex- traction and simplification by a mathematical example

siRNA–Mediated Methylation of Arabidopsis Telomeres

Chromosome termini form a specialized type of heterochromatin that is important for chromosome stability. The recent discovery of telomeric RNA transcripts in yeast and vertebrates raised the question of whether RNA–based mechanisms are involved in the formation of telomeric heterochromatin. In this study, we performed detailed analysis of chromatin structure and RNA transcription at chromosome termini in Arabidopsis. Arabidopsis telomeres display features of intermediate heterochromatin that does not extensively spread to subtelomeric regions which encode transcriptionally active genes. We also found telomeric repeat–containing transcripts arising from telomeres and centromeric loci, a portion of which are processed into small interfering RNAs. These telomeric siRNAs contribute to the maintenance of telomeric chromatin through promoting methylation of asymmetric cytosines in telomeric (CCCTAAA)n repeats. The formation of telomeric siRNAs and methylation of telomeres relies on the RNA–dependent DNA methylation pathway. The loss of telomeric DNA methylation in rdr2 mutants is accompanied by only a modest effect on histone heterochromatic marks, indicating that maintenance of telomeric heterochromatin in Arabidopsis is reinforced by several independent mechanisms. In conclusion, this study provides evidence for an siRNA–directed mechanism of chromatin maintenance at telomeres in Arabidopsis

Genetic Rearrangements Can Modify Chromatin Features at Epialleles

Analogous to genetically distinct alleles, epialleles represent heritable states of different gene expression from sequence-identical genes. Alleles and epialleles both contribute to phenotypic heterogeneity. While alleles originate from mutation and recombination, the source of epialleles is less well understood. We analyze active and inactive epialleles that were found at a transgenic insert with a selectable marker gene in Arabidopsis. Both converse expression states are stably transmitted to progeny. The silent epiallele was previously shown to change its state upon loss-of-function of trans-acting regulators and drug treatments. We analyzed the composition of the epialleles, their chromatin features, their nuclear localization, transcripts, and homologous small RNA. After mutagenesis by T-DNA transformation of plants carrying the silent epiallele, we found new active alleles. These switches were associated with different, larger or smaller, and non-overlapping deletions or rearrangements in the 3′ regions of the epiallele. These cis-mutations caused different degrees of gene expression stability depending on the nature of the sequence alteration, the consequences for transcription and transcripts, and the resulting chromatin organization upstream. This illustrates a tight dependence of epigenetic regulation on local structures and indicates that sequence alterations can cause epigenetic changes at some distance in regions not directly affected by the mutation. Similar effects may also be involved in gene expression and chromatin changes in the vicinity of transposon insertions or excisions, recombination events, or DNA repair processes and could contribute to the origin of new epialleles

Derepression of the Plant Chromovirus LORE1 Induces Germline Transposition in Regenerated Plants

Transposable elements represent a large proportion of the eukaryotic genomes. Long Terminal Repeat (LTR) retrotransposons are very abundant and constitute the predominant family of transposable elements in plants. Recent studies have identified chromoviruses to be a widely distributed lineage of Gypsy elements. These elements contain chromodomains in their integrases, which suggests a preference for insertion into heterochromatin. In turn, this preference might have contributed to the patterning of heterochromatin observed in host genomes. Despite their potential importance for our understanding of plant genome dynamics and evolution, the regulatory mechanisms governing the behavior of chromoviruses and their activities remain largely uncharacterized. Here, we report a detailed analysis of the spatio-temporal activity of a plant chromovirus in the endogenous host. We examined LORE1a, a member of the endogenous chromovirus LORE1 family from the model legume Lotus japonicus. We found that this chromovirus is stochastically de-repressed in plant populations regenerated from de-differentiated cells and that LORE1a transposes in the male germline. Bisulfite sequencing of the 5′ LTR and its surrounding region suggests that tissue culture induces a loss of epigenetic silencing of LORE1a. Since LTR promoter activity is pollen specific, as shown by the analysis of transgenic plants containing an LTR::GUS fusion, we conclude that male germline-specific LORE1a transposition in pollen grains is controlled transcriptionally by its own cis-elements. New insertion sites of LORE1a copies were frequently found in genic regions and show no strong insertional preferences. These distinctive novel features of LORE1 indicate that this chromovirus has considerable potential for generating genetic and epigenetic diversity in the host plant population. Our results also define conditions for the use of LORE1a as a genetic tool

Salt Stress Induced Variation in DNA Methylation Pattern and Its Influence on Gene Expression in Contrasting Rice Genotypes

BACKGROUND: Salinity is a major environmental factor limiting productivity of crop plants including rice in which wide range of natural variability exists. Although recent evidences implicate epigenetic mechanisms for modulating the gene expression in plants under environmental stresses, epigenetic changes and their functional consequences under salinity stress in rice are underexplored. DNA methylation is one of the epigenetic mechanisms regulating gene expression in plant's responses to environmental stresses. Better understanding of epigenetic regulation of plant growth and response to environmental stresses may create novel heritable variation for crop improvement. METHODOLOGY/PRINCIPAL FINDINGS: Methylation sensitive amplification polymorphism (MSAP) technique was used to assess the effect of salt stress on extent and patterns of DNA methylation in four genotypes of rice differing in the degree of salinity tolerance. Overall, the amount of DNA methylation was more in shoot compared to root and the contribution of fully methylated loci was always more than hemi-methylated loci. Sequencing of ten randomly selected MSAP fragments indicated gene-body specific DNA methylation of retrotransposons, stress responsive genes, and chromatin modification genes, distributed on different rice chromosomes. Bisulphite sequencing and quantitative RT-PCR analysis of selected MSAP loci showed that cytosine methylation changes under salinity as well as gene expression varied with genotypes and tissue types irrespective of the level of salinity tolerance of rice genotypes. CONCLUSIONS/SIGNIFICANCE: The gene body methylation may have an important role in regulating gene expression in organ and genotype specific manner under salinity stress. Association between salt tolerance and methylation changes observed in some cases suggested that many methylation changes are not "directed". The natural genetic variation for salt tolerance observed in rice germplasm may be independent of the extent and pattern of DNA methylation which may have been induced by abiotic stress followed by accumulation through the natural selection process

DNA Methylation and Histone Modifications Regulate De Novo Shoot Regeneration in Arabidopsis by Modulating WUSCHEL Expression and Auxin Signaling

Plants have a profound capacity to regenerate organs from differentiated somatic tissues, based on which propagating plants in vitro was made possible. Beside its use in biotechnology, in vitro shoot regeneration is also an important system to study de novo organogenesis. Phytohormones and transcription factor WUSCHEL (WUS) play critical roles in this process but whether and how epigenetic modifications are involved is unknown. Here, we report that epigenetic marks of DNA methylation and histone modifications regulate de novo shoot regeneration of Arabidopsis through modulating WUS expression and auxin signaling. First, functional loss of key epigenetic genes—including METHYLTRANSFERASE1 (MET1) encoding for DNA methyltransferase, KRYPTONITE (KYP) for the histone 3 lysine 9 (H3K9) methyltransferase, JMJ14 for the histone 3 lysine 4 (H3K4) demethylase, and HAC1 for the histone acetyltransferase—resulted in altered WUS expression and developmental rates of regenerated shoots in vitro. Second, we showed that regulatory regions of WUS were developmentally regulated by both DNA methylation and histone modifications through bisulfite sequencing and chromatin immunoprecipitation. Third, DNA methylation in the regulatory regions of WUS was lost in the met1 mutant, thus leading to increased WUS expression and its localization. Fourth, we did a genome-wide transcriptional analysis and found out that some of differentially expressed genes between wild type and met1 were involved in signal transduction of the phytohormone auxin. We verified that the increased expression of AUXIN RESPONSE FACTOR3 (ARF3) in met1 indeed was due to DNA demethylation, suggesting DNA methylation regulates de novo shoot regeneration by modulating auxin signaling. We propose that DNA methylation and histone modifications regulate de novo shoot regeneration by modulating WUS expression and auxin signaling. The study demonstrates that, although molecular components involved in organogenesis are divergently evolved in plants and animals, epigenetic modifications play an evolutionarily convergent role in this process