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

Lemma and model caching in decision procedures for quantified boolean formulas

Abstract. The increasingrole of quantified Boolean logic in many applications calls for practically efficient decision procedures. One of the most promisingparadigms is the semantic tree format implemented in the style of the DPLL procedure. In this paper, so-called learningtechniques like intelligent backtrackingand cachingof lemmas which proved useful in the pure propositional case are generalised to the quantified Boolean case and the occuringdifferences are discussed. Due to the strongrestriction of the variable selection in semantic tree procedures for quantified Boolean formulas, learningmethods are more important than in the propositional case, as we demonstrate. Furthermore, in addition to the cachingof lemmas, significant advances can be achieved by techniques based on the caching of models, too. The theoretical effect of these improvements is illustrated by a comparison of the search spaces on pathological examples. We also describe the basic features of the system Semprop, which is an efficient implementation of (some of) the developed techniques, and give the results of an experimental evaluation of the system on a number of practical examples.

P-SETHEO: Strategy Parallel Automated Theorem Proving

One of the key issues in Automated Theorem Proving is the search for optimal proof strategies. Since there is not one uniform strategy which works optimal on all proof tasks, one is faced with the difficult problem of selecting a good strategy for a given task. In this paper, we discuss a way of circumventing this strategy selection problem by using strategy parallelism. In this approach, a proof task is attempted in parallel by a set of uniform strategies while distributing the given amount of computing resources according to a certain schedule. We discuss important issues of strategy parallelism like search space partitioning, schedule computation, and scalability. In order to evaluate the potential of the method experimentally, we have implemented the strategy parallel theorem prover p-SETHEO, which is also described in the paper. The experimental results obtained with the system justify our approach. 1 Introduction Automated Theorem Proving (ATP) is the subfield of theoretical co..

HIF-Prolyl Hydroxylases in the Rat Kidney : Physiologic Expression Patterns and Regulation in Acute Kidney Injury

Hypoxia-inducible transcription factors (HIFs) play important roles in the response of the kidney to systemic and regional hypoxia. Degradation of HIFs is mediated by three oxygen-dependent HIF-prolyl hydroxylases (PHDs), which have partially overlapping characteristics. Although PHD inhibitors, which can induce HIFs in the presence of oxygen, are already in clinical development, little is known about the expression and regulation of these enzymes in the kidney. Therefore, we investigated the expression levels of the three PHDs in both isolated tubular cells and rat kidneys. All three PHDs were present in the kidney and were expressed predominantly in three different cell populations: (a) in distal convoluted tubules and collecting ducts (PHD1,2,3), (b) in glomerular podocytes (PHD1,3), and (c) in interstitial fibroblasts (PHD1,3). Higher levels of PHDs were found in tubular segments of the inner medulla where oxygen tensions are known to be physiologically low. PHD expression levels were unchanged in HIF-positive tubular and interstitial cells after induction by systemic hypoxia. In rat models of acute renal injury, changes in PHD expression levels were variable; while cisplatin and ischemia/reperfusion led to significant decreases in PHD2 and 3 expression levels, no changes were seen in a model of contrast media-induced nephropathy. These results implicate the non-uniform expression of HIF-regulating enzymes that modify the hypoxic response in the kidney under both regional and temporal conditions