A Cut-Elimination Proof in Positive Relevant Logic with Necessity

Studia Logica ◽  
2020 ◽  
Author(s):  
Mirjana Ilić
Keyword(s):  
Relevant Logic ◽  
Cut Elimination

CUT AND GAMMA I: PROPOSITIONAL AND CONSTANT DOMAIN R

2019 ◽  
Vol 13 (4) ◽  
pp. 887-909
Author(s):  
YALE WEISS
Keyword(s):  
Open Problem ◽  
Relevant Logic ◽  
Cut Elimination ◽  
Constant Domain ◽  
The Status

AbstractThe main object of this article is to give two novel proofs of the admissibility of Ackermann’s rule (γ) for the propositional relevant logic R. The results are established as corollaries of cut elimination for systems of tableaux for R. Cut elimination, in turn, is established both nonconstructively (as a corollary of completeness) and constructively (using Gentzen-like methods). The extensibility of the techniques is demonstrated by showing that (γ) is admissible for RQ* (R with constant domain quantifiers). The status of the admissibility of (γ) for RQ* was, to the best of the author’s knowledge, an open problem. Further extensions of these results will be explored in the sequel(s).

scholarly journals Why Intuitionistic Relevant Logic Cannot Be a Core Logic

2017 ◽  
Vol 58 (2) ◽  
pp. 241-248
Author(s):  
Joseph Vidal-Rosset
Keyword(s):  
Relevant Logic

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.

scholarly journals Reasoning-predicting Model based on Strong Relevant Logic in Road Traffic Forecasting

2012 ◽  
Vol 33 ◽  
pp. 1105-1110 ◽  
Author(s):  
Dancheng Li ◽  
Zhiliang Liu ◽  
Cheng Liu ◽  
Binsheng Liu ◽  
Wei Zhang
Keyword(s):  
Road Traffic ◽  
Relevant Logic ◽  
Predicting Model ◽  
Traffic Forecasting ◽  
Model Based

BILATERAL RELEVANT LOGIC

2014 ◽  
Vol 7 (2) ◽  
pp. 250-272
Author(s):  
NISSIM FRANCEZ
Keyword(s):  
Relevant Logic

Whither relevant arithmetic?

1992 ◽  
Vol 57 (3) ◽  
pp. 824-831 ◽  
Author(s):  
Harvey Friedman ◽  
Robert K. Meyer
Keyword(s):  
Relevant Logic ◽  
Peano Arithmetic ◽  
Central Question ◽  
Proof Methods ◽  
Classical Proof ◽  
Natural Way

AbstractBased on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. The reason is interesting: if PA is slightly weakened to a subtheory P+, it admits the complex ring C as a model; thus QRF is chosen to be a theorem of PA but false in C. Inasmuch as all strictly positive theorems of R# are already theorems of P+, this nonconservativity result shows that QRF is also a nontheorem of R#. As a consequence, Ackermann's rule γ is inadmissible in R#. Accordingly, an extension of R# which retains its good features is desired. The system R##, got by adding an omega-rule, is such an extension. Central question: is there an effectively axiomatizable system intermediate between R# and R#, which does formalize arithmetic on relevant principles, but also admits γ in a natural way?

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