Received (received date) Revised (revised date) Accepted (accepted date) We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant strategy of the adversary (the offering player), is investigated. It turns out that...

We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance significantly. We argue that the quantum model describes our spontaneously shown preferences more precisely than the classical model, as these preferences a...

The focus of the paper is on the logic of clarity and the problem of higherorder vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare different theories of vagueness understood as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s twodimensional semantics, and the system ...

We show that the transitivity of pointwise Turing reducibility on the recursively enumerable sets of integers cannot be proven in P− + IΣ1, first order arithmetic with induction limited to Σ1 predicates. We produce a example of intransitivity in a nonstandard model of P+IΣ1 by a finite injury priority construction.

We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance significantly. We argue that the quantum model describes our spontaneously shown preferences more precisely than the classical model, as these preferences a...