Cut elimination for S4 n and K4 n with the central agent axiom

2009 ◽  
Vol 49 (2) ◽  
pp. 123-139
Author(s):  
J. Andrikonis
Keyword(s):  
Cut Elimination ◽  
Central Agent

scholarly journals Cut-elimination for knowledge logics with interaction

2008 ◽  
Vol 48 ◽  
Author(s):  
Julius Andrikonis
Keyword(s):  
Cut Elimination ◽  
Multimodal Logics ◽  
Hilbert Type ◽  
Central Agent

In the article, multimodal logics K4n and S4n with the central agent axiom are analysed. The Hilbert type calculi are presented, then the Gentzen type calculi with cut are derived, and the proofs of thecut-eliminationtheorems are outlined. The work shows that it is possible to construct an analytical Gentzen type calculi for these logics.

scholarly journals Cut elimination for knowledge logic with interaction

2021 ◽  
Vol 47 ◽  
Author(s):  
Julius Andrikonis ◽  
Regimantas Pliuškevičius
Keyword(s):  
Cut Elimination ◽  
Knowledge Logic ◽  
Multimodal Logic ◽  
Agent Interaction ◽  
Interaction Axiom ◽  
Hilbert Type ◽  
Central Agent

In the article the multimodal logic Tn with central agent interaction axiom is analysed. The Hilbert type calculi is presented, then Gentzen type calculi with cut is derived and the proof of cutelimination theorem is outlined. The work shows that it is possible to construct a Gentzen type calculi without cut for this logic.

The Beginnings of Resistance

2018 ◽  
Author(s):  
Michael P. DeJonge
Keyword(s):  
Jewish Question ◽  
Political Thinking ◽  
The Church ◽  
Central Agent ◽  
Three Phases

With this chapter, the book transitions from a presentation of Bonhoeffer’s political thinking to an account of his resistance thinking in action. This chapter also begins the presentation of the first of the three phases of resistance, which lasts from 1932 until 1935. The chapter focuses on “The Church and the Jewish Question” (1933), the central text of this first phase, identifying in it the first two of Bonhoeffer’s six types of resistance: individual and humanitarian resistance to state injustice (type 1) and the church’s resistance through diaconal service to the victims of state injustice (type 2). These set the stage for Chapters 6–8’s considerations of resistance through the church’s preaching office, which is the central agent of resistance in the first phase.

scholarly journals Acting without Central Agent—Considerations for a Self-Model at the Cellular Level

2017 ◽  
Vol 11 ◽  
Author(s):  
Stefan Kippenberger ◽  
Johannes Kleemann ◽  
Roland Kaufmann ◽  
Markus Meissner
Keyword(s):  
Cellular Level ◽  
Central Agent

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.

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