The Stratiied Foundations are a restriction of naive set theory where the comprehension scheme is restricted to stratiiable propositions. It is known that this theory is consistent and that proofs strongly normalize in this theory. Deduction modulo is a formulation of rst-order logic with a general notion of cut. It is known that proofs normalize in a theory modulo if it has some kind of many-v...

§ 1. The Problem of consistency in axiomatics as a logical decision problem. The state of research in the field of foundations of mathematics, to which our presentation is related, is characterized by three kinds of investigations: 1. the development of the axiomatic method, especially with the help of the foundations of geometry, 2. the founding of analysis by today’s rigorous methods through ...

We provide a characterization of the symmetric and weighted versions of the Euclidean compromise solution for multiobjective optimization problems first proposed by P.L.Yu. These solutions minimize a measure of the distance between a feasible set and the utopia point of that set, and are closely related to solutions that have been proposed in the bargaining with claims literature. We provide ne...

Foundational work in game theory aims at making explicit the assumptions that underlie the basic concepts of the discipline. Non-cooperative game theory is the study of individual, rational decision making in situations of strategic interaction. This entry presents the epistemic foundations of non-cooperative game theory (this area of research is called epistemic game theory). Epistemic game th...

Where does morality come from? Why are moral judgments often so similar across cultures, yet sometimes so variable? Is morality one thing, or many? Moral Foundations Theory (MFT) was created to answer these questions. In this chapter we describe the origins, assumptions, and current conceptualization of the theory, and detail the empirical findings that MFT has made possible, both within social...

Jonathan Haidt's Moral Foundations Theory is an influential scientific account of morality incorporating psychological, developmental, and evolutionary perspectives. The theory proposes that morality is built upon five innate "foundations," each of which is believed to have been selected for during human evolution and, subsequently, tuned-up by learning during development. We argue here that al...