Cut-Elimination for SBL

2020 ◽  
pp. 265-298
Author(s):  
Toshiyasu Arai
Keyword(s):  
Cut Elimination

Risperidone-treated Children and Adolescents with Behavioral Disorders: Do Drug Dose and Patients’ Gender and Age Relate to Drug and Metabolite Plasma Levels?

2017 ◽  
Vol 41 (S1) ◽  
pp. S104-S104
Author(s):  
D. Piacentino ◽  
M. Grözinger ◽  
A. Saria ◽  
F. Scolati ◽  
D. Arcangeli ◽  
...  
Keyword(s):  
Regression Analysis ◽  
Children And Adolescents ◽  
Behavioral Disorders ◽  
Plasma Levels ◽  
Linear Models ◽  
Parent Drug ◽  
Drug Dose ◽  
Cut Elimination ◽  
Younger Patients ◽  
Gender And Age

IntroductionBehavioral disorders, such as conduct disorder, influence choice of treatment and its outcome. Less is known about other variables that may have an influence.Objectives/AimsWe aimed to measure the parent drug and metabolite plasma levels in risperidone-treated children and adolescents with behavioral disorders and investigate the role of drug dose and patients’ gender and age.MethodsWe recruited 115 children/adolescents with DSM-5 behavioral disorders (females = 24; age range: 5–18 years) at the Departments of Psychiatry of the Hospitals of Bolzano, Italy, and Innsbruck, Austria. We measured risperidone and its metabolite 9-hydroxyrisperidone plasma levels and the parent drug-to-metabolite ratio in the plasma of all patients by using LC-MS/MS. A subsample of 15 patients had their risperidone doses measured daily. We compared risperidone and 9-hydroxyrisperidone plasma levels, as well as risperidone/9-hydroxyrisperidone ratio, in males vs. females and in younger (≤ 14 years) vs. older (15–18 years) patients by using Mann-Whitney U test. We fitted linear models for the variables “age” and “daily risperidone dose” by using log-transformation, regression analysis and applying the R2 statistic.ResultsFemales had significantly higher median 9-hydroxyrisperidone plasma levels (P = 0.000). Younger patients had a slightly lower median risperidone/9-hydroxyrisperidone ratio (P = 0.052). At the regression analysis, daily risperidone doses and metabolite, rather than parent drug–plasma levels were correlated (R2 = 0.35).ConclusionsGender is significantly associated with plasma levels, with females being slower metabolizers than males. Concerning age, younger patients seem to be rapid metabolizers, possibly due to a higher activity of CYP2D6. R2 suggests a clear-cut elimination of the metabolite.Disclosure of interestThe authors have not supplied their declaration of competing interest.

A proof of the cut-elimination theorem in simple type theory

1973 ◽  
Vol 38 (2) ◽  
pp. 215-226
Author(s):  
Satoko Titani
Keyword(s):  
Boolean Algebra ◽  
Type Theory ◽  
Arbitrary Number ◽  
Formal System ◽  
Cut Elimination ◽  
Simple Type ◽  
Inductive Definition ◽  
Simple Type Theory ◽  
Maximal Ideals ◽  
Definition Of

In [4], I introduced a quasi-Boolean algebra, and showed that in a formal system of simple type theory, from which the cut rule is omitted, wffs form a quasi-Boolean algebra, and that the cut-elimination theorem can be formulated in algebraic language. In this paper we use the result of [4] to prove the cut-elimination theorem in simple type theory. The theorem was proved by M. Takahashi [2] in 1967 by using the concept of Schütte's semivaluation. We use maximal ideals of a quasi-Boolean algebra instead of semivaluations.The logical system we are concerned with is a modification of Schütte's formal system of simple type theory in [1] into Gentzen style.Inductive definition of types.0 and 1 are types.If τ1, …, τn are types, then (τ1, …, τn) is a type.Basic symbols.a1τ, a2τ, … for free variables of type τ.x1τ, x2τ, … for bound variables of type τ.An arbitrary number of constants of certain types.An arbitrary number of function symbols with certain argument places.

scholarly journals One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity

2020 ◽  
Author(s):  
Paweł Płaczek
Keyword(s):  
Analogous Result ◽  
Cut Elimination ◽  
Sequent Systems ◽  
Natural Symmetry ◽  
Sequent System

Bilinear Logic of Lambek [10] amounts to Noncommutative MALL of Abrusci [1]. Lambek [10] proves the cut–elimination theorem for a onesided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek [10], we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTIME complexity of the multiplicative fragment of NBL.

scholarly journals Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

2017 ◽  
Vol 46 (1/2) ◽  
Author(s):  
Wojciech Buszkowski
Keyword(s):  
Cut Elimination ◽  
Lambek Calculus ◽  
Double Negation ◽  
Sequent Systems ◽  
Sequent System

In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Grooté and Lamarche [10], is called Classical Non-Associative Lambek Calculus (CNL). Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is PTIME.

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