An algebraic study of Diodorean modal systems

1965 ◽  
Vol 30 (1) ◽  
pp. 58-64 ◽  
Author(s):  
R. A. Bull
Keyword(s):  
Discrete Time ◽  
Decision Procedure ◽  
John Locke ◽  
Original Model ◽  
Completeness Proof ◽  
Semantic Tableaux ◽  
Algebraic Treatment ◽  
Algebraic Result ◽  
Modal Systems

Attention was directed to modal systems in which ‘necessarily α’ is interpreted as ‘α. is and always will be the case’ by Prior in his John Locke Lectures of 1956. The present paper shows that S4.3, the extension of S4 withALCLpLqLCLqLp,is complete with respect to this interpretation when time is taken to be continuous, and that D, the extension of S4.3 withALNLpLCLCLCpLpLpLp,is complete with respect to this interpretation when time is taken to be discrete. The method employed depends upon the application of an algebraic result of Garrett Birkhoff's to the models for these systems, in the sense of Tarski.A considerable amount of work on S4.3 and D precedes this paper. The original model with discrete time is given in Prior's [7] (p. 23, but note the correction in [8]); that taking time to be continuous yields a weaker system is pointed out by him in [9]. S4.3 and D are studied in [3] of Dummett and Lemmon, where it is shown that D includes S4.3 andCLCLCpLpLpCMLpLp.While in Oxford in 1963, Kripke proved that these were in fact sufficient for D, using semantic tableaux. A decision procedure for S4.3, using Birkhoff's result, is given in my [2]. Dummett conjectured, in a conversation, that taking time to be continuous yielded S4.3. Thus the originality of this paper lies in giving a suitable completeness proof for S4.3, and in the unified algebraic treatment of the systems. It should be emphasised that the credit for first axiomatising D belongs to Kripke.

Improved Bilinear Routh Approximation Method for Discrete-Time Systems

2000 ◽  
Vol 123 (1) ◽  
pp. 125-127 ◽  
Author(s):  
Younseok Choo
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Approximation Method ◽  
Original Model ◽  
Reduced Model ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

Hwang and Shieh proposed a bilinear Routh approximation method for reducing the order of discrete-time systems. A reduced model derived by the method is not only stable whenever an original model is stable, but also fits the first few time-moments of the original one. This paper addresses the possibility of improving the method by letting the impulse response energy of the original model also be conserved in the reduced model without destroying the stability preserving and time-moments matching properties.

scholarly journals A note on symmetry breaking in a non linear marketing model

2021 ◽  
Author(s):  
Andrea Caravaggio ◽  
Lorenzo Cerboni Baiardi ◽  
Mauro Sodini
Keyword(s):  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Original Model ◽  
Market Size ◽  
Multiple Attractors ◽  
Time Dynamic ◽  
Marketing Model ◽  
Adaptive Adjustment ◽  
Adjustment Mechanisms

AbstractIn this paper, we consider the nonlinear discrete-time dynamic model proposed by Bischi and Baiardi (Chaos Solitons Fractals 79:145-156, 2015a). The model considers players with adaptive adjustment mechanisms towards the best reply and a form of inertia in adopting such mechanism. Moreover, we formulate an extension of the original model, where endogenous market size is considered. Through numerical simulations, we show that multiple attractors may exist in the presence of homogeneous agents and the emergence of non-synchronized trajectories both in the short (on-off intermittency) and long (global riddling) run. Therefore, the article highlights that strategic contexts exist in which the players’ knowledge of the market and the adoption of the best reply do not always allow the use of the representative agent’s rhetoric to describe the dynamics of the model.

A Gentzen- or Beth-type system, a practical decision procedure and a constructive completeness proof for the counterfactual logics VC and VCS

1983 ◽  
Vol 48 (1) ◽  
pp. 1-20 ◽  
Author(s):  
H. C. M. de Swart
Keyword(s):  
Decision Procedure ◽  
Type System ◽  
Propositional Calculus ◽  
Axiom System ◽  
Completeness Proof ◽  
Counterfactual Conditional ◽  
System A ◽  
Counterfactual Logic ◽  
Classical Propositional Calculus

In [1] and [2] D. Lewis formulates his counterfactual logic VC as follows. The language contains the connectives ∧, ∨, ⊃, ¬ and the binary connective ≤. A ≤ B is read as “A is at least as possible as B”. The following connectives are defined in terms of ≤.A < B: = ¬(B ≤ A) (it is more possible that A than that B).◊ A ≔ ¬(⊥ ≤ A) (⊥ is the false formula; A is possible).□ A ≔ ⊥ ≤ ¬A (A is necessary). (if A were the case, then B would be the case). (if A were the case, then B might be the case). and are two counterfactual conditional operators. (AB) iff ¬(A ¬B).The following axiom system VC is presented by D. Lewis in [1] and [2]: V: (1) Truthfunctional classical propositional calculus.

scholarly journals On the quasi-sure superhedging duality with frictions

2019 ◽  
Vol 24 (1) ◽  
pp. 249-275
Author(s):  
Erhan Bayraktar ◽  
Matteo Burzoni
Keyword(s):  
Transaction Costs ◽  
Financial Market ◽  
Discrete Time ◽  
Natural Condition ◽  
Model Uncertainty ◽  
Original Model ◽  
Restrictive Assumption ◽  
Proportional Transaction Costs ◽  
No Arbitrage ◽  
Portfolio Constraints

AbstractWe prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modelled through solvency cones as in the original model of Kabanov (Finance Stoch. 3:237–248, 1999) adapted to the quasi-sure setup of Bouchard and Nutz (Ann. Appl. Probab. 25:823–859, 2015). Our approach allows removing the restrictive assumption of no arbitrage of the second kind considered in Bouchard et al. (Math. Finance 29:837–860, 2019) and showing the duality under the more natural condition of strict no arbitrage. In addition, we extend the results to models with portfolio constraints.

A New Consideration for Model Reduction Using Bilinear Schwarz Approximation for Discrete-Time Systems

2002 ◽  
Vol 124 (3) ◽  
pp. 475-477 ◽  
Author(s):  
Younseok Choo
Keyword(s):  
Model Reduction ◽  
Impulse Response ◽  
Discrete Time ◽  
Approximation Method ◽  
Original Model ◽  
Reduced Model ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

A bilinear Schwarz approximation method has been proposed in the literature for reducing the order of discrete-time systems. The reduced model derived by the method preserves the stability and first few time-moments of the original one. This paper shows that the method can be modified so that the impulse response energy of the original model is also conserved in the reduced model without destroying the stability and time-moments preserving properties.

Direct Observation of Monolayer Zones in Al-wt 4% Cu

1990 ◽  
Vol 48 (1) ◽  
pp. 14-15
Author(s):  
B. Jouffrey ◽  
D. Dorignac ◽  
A. Bourret
Keyword(s):  
Solid Solution ◽  
Synchrotron Radiation ◽  
Direct Observation ◽  
Supersaturated Solid Solution ◽  
Original Model ◽  
X Ray ◽  
Image Position

Since the early works on GP zones and the model independently proposed by Preston and Guinier on the first steps of precipitation in supersaturated solid solution of aluminium containing a few percent of copper, many works have been performed to understand the structure of different stages in the sequence of precipitation.The scheme which is generally admitted can be drawn from a work by Phillips.In their original model Guinier and Preston analysed a GP zone as composed of a single (100) copperrich plane surrounded by aluminum atomic planes with a slightly shorter distance from the original plane than in the solid solution.From X-ray measurements it has also been shown that GP1 zones were not only copper monolayer zones. They could be up to a few atomic planes thick. Different models were proposed by Guinier, Gerold, Toman. Using synchrotron radiation, proposals have been recently made.

The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽  
2017 ◽  
Vol 13 (2) ◽  
pp. 41-60
Author(s):  
Shahab Jolani ◽  
Maryam Safarkhani
Keyword(s):  
Randomized Controlled Trials ◽  
Discrete Time ◽  
Treatment Effect ◽  
Survival Data ◽  
Controlled Trials ◽  
Missing Covariates ◽  
Indicator Method ◽  
Imputation Methods ◽  
Randomized Controlled ◽  
Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

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