Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus

Platelet activation and lipid peroxidation in patients with acute ischemic stroke

BACKGROUND AND PURPOSE: Both platelet activation and lipid peroxidation are potential sources of vasoactive eicosanoids that can be produced via the cyclooxygenase pathway, ie, thromboxane (TX) A2, or by free radical-catalyzed peroxidation of arachidonic acid, ie, isoprostanes. We investigated the biosynthesis of TXA2 and F2-isoprostanes, as reflected by the urinary excretion of 11-dehydro-TXB2 and 8-epi-prostaglandin (PG) F2 alpha respectively, in 62 consecutive patients (30 men, 32 women; mean age, 67 +/- 14 years) with acute ischemic stroke. METHODS: At least two consecutive 6-hour urine samples were obtained during the first 72 hours after onset of symptoms. Urinary eicosanoids were measured by previously described radioimmunoassays. RESULTS: Repeated periods of enhanced thromboxane biosynthesis were found in 52% of patients. Urinary 11-dehydro-TXB2 averaged 221 +/- 207 (mean +/- SD; n = 197; range, 13 to 967) pmol/mmol creatinine in 30 patients treated with cyclooxygenase inhibitors (mostly aspirin) at the time of study versus 392 +/- 392 (n = 186; range, 26 to 2533) in 32 untreated patients (P .05). The correlation between the two metabolites was moderate in both untreated patients (r = .41, P < .001) and patients with cyclooxygenase inhibitors (r = .31, P < .001). In a multiple regression analysis, increased thromboxane production was independently associated with severity of stroke on admission, atrial fibrillation, and treatment with cyclooxygenase-inhibiting drugs. CONCLUSIONS: We conclude that during the first few days after an acute ischemic stroke (1) platelet activation occurs repeatedly in a cyclooxygenase-dependent fashion; (2) platelet activation is not associated with concurrent changes in isoprostane biosynthesis; (3) platelet activation is independently associated with stroke severity and atrial fibrillation; and (4) isoprostane biosynthesis is largely independent of platelet cyclooxygenase activity

From Display to Labelled Proofs for Tense Logics

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt

Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate

Increased thromboxane biosynthesis is associated with poststroke dementia

BACKGROUND AND PURPOSE: It has been suggested that daily intake of aspirin is associated with a reduction of cognitive decline, both in normal and in demented subjects, but the mechanism is unclear. We have therefore studied the relationship between thromboxane (TX) A(2) biosynthesis, as reflected by the urinary excretion of 11-dehydro-TXB(2), and the presence of dementia in patients after acute stroke. METHODS: Patients from the Rotterdam Stroke Databank were screened for dementia between 3 and 9 months after stroke. Patients had a full neurological examination, neuropsychological screening, and, if indicated, extensive neuropsychological examination. Criteria used for the diagnosis of dementia were from the Diagnostic and Statistical Manual of Mental Disorders, Third Edition (Revised). Urine samples were taken at the time of screening. Urinary 11-dehydro-TXB(2) was measured by means of a previously validated radioimmunoassay. RESULTS: Dementia was diagnosed in 71 patients, and urine samples were available for 62. Median value (range) of 11-dehydro-TXB(2) was 399 (89 to 2105) pmol/mmol creatinine for demented patients versus 273 (80 to 1957) for 69 controls with stroke but without dementia (P=0.013). No difference was found between 44 patients with vascular dementia, 404 (89 to 2105) pmol/mmol creatinine, and 18 patients with Alzheimer's disease plus cerebrovascular disease, 399 (96 to 1467) pmol/mmol creatinine (P=0.68). In a stepwise logistic regression analysis, in which possible confounders such as use of antiplatelet medication, cardiovascular risk factors, and type of stroke were taken into account, increased urinary excretion of 11-dehydro-TXB(2) remained independently related to the presence of dementia (OR 1.12, 95% CI 1.03 to 1.22 per 100 pmol/mmol creatinine). The difference in metabolite excretion rates between demented and nondemented patients was most prominent within the subgroup of ischemic stroke patients who received aspirin (P<0.01). CONCLUSIONS: Increased thromboxane biosynthesis in the chronic phase after stroke is associated with the presence of but not the type of poststroke dementia. It is particularly apparent in patients on aspirin, thereby suggesting the involvement of extraplatelet sources of TXA(2) production in this setting

Generic Modal Cut Elimination Applied to Conditional Logics

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature

Towards a Proof Theory of G\"odel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish completeness and complexity results for these fragments