No abstract

Guarded fragments of first-order logic were recently introduced by Andréka, van Benthem and Németi; they consist of relational first-order formulae whose quantifiers are appropriately relativized by atoms. These fragments are interesting because they extend in a natural way many propositional modal logics, because they have useful model-theoretic properties and especially because they are decidable classes that avoid the usual syntactic restrictions (on the arity of relation symbols, the quantifier pattern or the number of variables) of almost all other known decidable fragments of first-order logic.Here, we investigate the computational complexity of these fragments. We prove that the satisfiability problems for the guarded fragment (GF) and the loosely guarded fragment (LGF) of first-order logic are complete for deterministic double exponential time. For the subfragments that have only a bounded number of variables or only relation symbols of bounded arity, satisfiability is Exptime-complete. We further establish a tree model property for both the guarded fragment and the loosely guarded fragment, and give a proof of the finite model property of the guarded fragment.It is also shown that some natural, modest extensions of the guarded fragments are undecidable.

No abstract

We introduce an atomic formula y ⊥ x z intuitively saying that the variables y are independent from the variables z if the variables x are kept constant. We contrast this with dependence logic D [7] based on the atomic formula =( x, y), actually equivalent to y ⊥ x y, saying that the variables y are totally determined by the variables x. We show that y ⊥ x z gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that y ⊥ x z can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using =( x, y) have.Of the numerous uses of the word "dependence" we focus on the concept of an attribute 1 depending on a number of other similar attributes when we observe the world. We call these attributes variables. We follow the approach of [7] and focus on the strongest form of dependence, namely functional dependence.

We identify the computational complexity of the satisfiability problem for FO2, the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO2 has the finite-model property, which means that if an FO2-sentence is satisiable, then it has a finite model. Moreover, Mortimer showed that every satisfiable FO2-sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO2 is NEXPTIME-complete.

Both the internal mammary artery and the saphenous vein are used to construct coronary-artery bypass grafts. We hypothesized that the release or production of endothelium-derived relaxing factor, which regulates blood flow and inhibits platelet function, may differ in venous and arterial grafts. We therefore studied endothelium-dependent relaxation in internal mammary arteries, internal mammary veins, and saphenous veins obtained from 58 patients undergoing coronary bypass surgery. Vascular rings with and without endothelium were suspended in organ chambers, and isometric tension was recorded. Acetylcholine (10(-8) to 10(-4) M), thrombin (1 U per milliliter), and adenosine diphosphate (10(-7) to 10(-4) M) evoked potent endothelium-dependent relaxation in the mammary artery but weak response in the saphenous vein (P less than 0.005; n = 6 to 27). In the mammary artery, relaxation was greatest in response to acetylcholine (86 +/- 4 percent reduction in norepinephrine-induced tension), followed by thrombin (44 +/- 7 percent) and adenosine diphosphate (39 +/- 8 percent). In the saphenous and mammary veins, relaxation was less than 25 percent. Relaxation was unaffected by indomethacin but was inhibited by methylene blue and hemoglobin (P less than 0.005 and 0.01, respectively), which suggests that endothelium-derived relaxing factor was the mediator. Endothelium-independent relaxation in response to sodium nitroprusside was similar in arteries and veins. We conclude that endothelium-dependent relaxation is greater in the mammary artery than in the saphenous vein. The possibility that this contributes to the higher patency rate among arterial grafts than among venous grafts will require further study.

Exercise testing with measurement of maximal oxygen uptake (VO2max) is increasingly used in the assessment of lung resection candidates, but its predictive value for postoperative complications remains controversial. We therefore sought to determine the prognostic value of VO2max compared with other pulmonary function tests. A consecutive group of 80 patients (mean age 61 yr; 57 males and 23 females) scheduled for lung resection (62 malignancies, 12 benign disorders, and 6 carcinoids) underwent pulmonary function tests and symptom-limited cycle ergometry. All patients underwent lung resections: 21 pneumonectomies, 45 lobectomies, and 14 segmental or wedge resections. Group A (64 patients, 80%) had an uneventful postoperative course, whereas Group B (16 patients, 20%) had complications; 3 of them died (4% overall mortality rate). In a stepwise logistic regression analysis used to determine independent risk factors for postoperative complications (within 30 d), VO2max expressed as a percentage of predicted (84 +/- 19 for Group A versus 61 +/- 11 for Group B) proved to be the best predictor (predictive value 85.5%). Although VO2max expressed in absolute values (ml/kg/min) was also highly predictive (79.5%), a ROC curve analysis proved the percentage predicted values to be significantly more sensitive. Of 9 patients with a VO2max < 60% of predicted, 8 had complications, including all 3 patients who died after resections of more than one lobe (sensitivity 50%, specificity 98%). The estimated probability (probit model SAS software package) of suffering no complication was 0.9 for VO2max > 75% of predicted and 0.1 for a VO2max < 43%.(ABSTRACT TRUNCATED AT 250 WORDS)

No abstract