Related papers: Expected Utility from a Constructive Viewpoint

We provide and axiomatize a representation for preferences over lotteries that generalizes the expected utility model. Since the representation uses different utility functions to evaluate different lotteries, the preferences can be…

In this paper, we formulate a qualitative "linear" utility theory for lotteries in which uncertainty is expressed qualitatively using a Spohnian disbelief function. We argue that a rational decision maker facing an uncertain decision…

This article presents a computational semantics for classical logic using constructive type theory. Such semantics seems impossible because classical logic allows the Law of Excluded Middle (LEM), not accepted in constructive logic since it…

The constructive approach to mathematics has the advantage that witnesses can be extracted from statements of existence and theorems can be unwound to give algorithms. Even better, constructive theorems can be interpreted in any topos,…

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of…

We investigate different set-theoretic constructions in Residuated Logic based on Fitting's work on Intuitionistic Set Theory. We start by stating some results concerning constructible sets within valued models of Set Theory. We present two…

This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…

A theorem, usually attributed to Barr, yields that (A) geometric implications deduced in classical L_{\infty\omega} logic from geometric theories also have intuitionistic proofs. Barr's theorem is of a topos-theoretic nature and its proof…

We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic)…

An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…

The use of von Neumann -- Morgenstern utility is examined in the context of multiple choices between lotteries. Different conclusions are reached if the choices are simultaneous or sequential. It is demonstrated that utility cannot be…

This survey reviews recent developments in revealed preference theory. It discusses the testable implications of theories of choice that are germane to specific economic environments. The focus is on expected utility in risky environments;…

We present constructive provability logic, an intuitionstic modal logic that validates the L\"ob rule of G\"odel and L\"ob's provability logic by permitting logical reflection over provability. Two distinct variants of this logic, CPL and…

For most purposes, one can replace the use of Rolle's theorem and the mean value theorem, which are not constructively valid, by the law of bounded change. The proof of two basic results in numerical analysis, the error term for Lagrange…

In Chapter 3 of his Notes on constructive mathematics, Martin-L{\"o}f describes recursively constructed ordinals. He gives a constructively acceptable version of Kleene's computable ordinals. In fact, the Turing definition of computable…

Let $\succsim$ be a binary relation on the set of simple lotteries over a countable outcome set $Z$. We provide necessary and sufficient conditions on $\succsim$ to guarantee the existence of a set $U$ of von Neumann--Morgenstern utility…

We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…

Expected Utility: Algebraic Expected Utility In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von Neumann-Morgenstern setting, i.e. uncertainty…