The consistency of some intuitionistic and constructive principles with a set theory

The main questions considered in this paper are the consistency of a variant of a set theory with intuitionistic logic, with Brouwer's principle and the investigation of the comparative power of the Church's Thesis' variants at the set theory level.     

Do the EPR correlations pose a problem for causal decision theory?

We argue that causal decision theory (CDT) is no worse off than evidential decision theory (EDT) in handling entanglement, regardless of one’s preferred interpretation of quantum mechanics. In recent works, Ahmed (Evidence, decision, and causality, Cambridge University Press, Cambridge, 2014) and Ahmed and Caulton (Synthese, 191(18): 4315–4352, 2014) have claimed the opposite; we argue that they are mistaken. Bell-type experiments are not instances of Newcomb problems, so CDT and EDT do not diverge in their recommendations. We highlight the fact that a Causal Decision Theorist should take all lawlike correlations into account, including potentially acausal entanglement correlations. This paper also provides a brief introduction to CDT with a motivating “small” Newcomb problem. The main point of our argument is that quantum theory does not provide grounds for favouring EDT over CDT.

     

On the Johnson-Neyman technique and some extensions thereof

The Johnson-Neyman technique is a statistical tool used most frequently in educational and psychological applications. This paper starts by briefly reviewing the Johnson-Neyman technique and suggesting when it should and should not be used; then several different modifications and extensions of the Johnson-Neyman technique, all of them conceptually simple, are proposed. The close relation between confidence intervals and regions of significance of the Johnson-Neyman type is pointed out. The problem of what to do when more than two groups are being compared is considered. The situation of more than one criterion variable is also considered.This research was supported in part by Educational Testing Service, and in part by the Mathematics Division of the Air Force Office of Scientific Research.     

The degrees of maximality of the intuitionistic propositional logic and of some of its fragments

Professor Ryszard Wójcicki once asked whether the degree of maximality of the consequence operationC determined by the theorems of the intuitionistic propositional logic and the detachment rule for the implication connective is equal to \(2^{2^\aleph 0} \) ? The aim of the present paper is to give the affirmative answer to the question. More exactly, it is proved here that the degree of maximality ofC _Ψ — theΨ — fragment ofC, is equal to \(2^{2^\aleph 0} \) , for every such that → εΨ.     

Completeness theorem for dummett's LC quantified and some of its extensions

Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame Q⁺, ,D, where Q⁺ is the set of non-negative rational numbers, is the numerical relation less or equal then and D is the domain function such that for all v, w Q⁺, D_v and if v w, then D _v . D _v D _w . Moreover, simple completeness proofs of extensions of Q-LC are given.     

The relative consistency of system RRC* and some of its extensions

We present a relative consistency proof for second order systemRRC* and for certain important extensions of this system. The proof proceeds as follows: we prove first the equiconsistency of the strongest of such extensions (viz., systemH RRC*+(/CP**)) with second order systemT ^* . Now, N. Cocchiarella has shown thatT ^* is relatively consistent to systemT*+Ext; clearly, it follows thatH RRC*+(/CP**) is relatively consistent toT*+E _xt. As an immediate consequence, the relative consistency ofRRC* and the other extensions also follows, being all of them subsystems ofH RRC*+(/CP**).I am grateful to the referee for some modifications suggested to an earlier draft of this paper.Presented byMelvin Fitting     

The finite inseparability of the first-order theory of diagonalisable algebras

In a recent paper, Montagna proved the undecidability of the first-order theory of diagonalisable algebras. This result is here refined — the set of finitely refutable sentences is shown effectively inseparable from the set of theorems. The proof is quite simple.     

The effects of context on the selection of decision strategies for the cost variance investigation problem

An important theme in research on behavioral decision making is that decision behavior is largely contingent on characteristics of the task and context. One variation on this theme is the appearance of contingency models that explain variation in decision behavior in terms of the effects that changes in task and context have on the relative net benefit of each available decision strategy. The L. R. Beach and T. R. Mitchell (1978, Academy of Management Review, July, 439–449) model is an example of such a model. In the present study, the Beach and Mitchell (1978) model is used as a framework for generating hypotheses about the effects of two contextual variables—state uncertainty and significance of the decision—on the selection of decision strategies for the management problem of whether to investigate the cause of a cost variance. The hypotheses are supported by an experimental test.     

The method of axiomatic rejection for the intuitionistic propositional logic

We prove that the intuitionistic sentential calculus is -decidable (decidable in the sense of ukasiewicz), i.e. the sets of theses of Int and of rejected formulas are disjoint and their union is equal to all formulas. A formula is rejected iff it is a sentential variable or is obtained from other formulas by means of three rejection rules. One of the rules is original, the remaining two are ukasiewicz's rejection rules: by detachement and by substitution. We extensively use the method of Beth's semantic tableaux.To the memory of Jerzy SupeckiTranslated from the Polish by Jan Zygmunt. Preparation of this paper was supported in part by C.P.B.P. 08-15.