Related papers: Formal Power Series Representations in Probability…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
For Hilbert, the consistency of a formal theory T is an infinite series of statements "D is free of contradictions" for each derivation D and a consistency proof is i) an operation that, given D, yields a proof that D is free of…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
The theory of probability, based on very general rules referred to as the Cox-Polya-Jaynes Desiderata, can be used both as a theory of random mass phenomena and as a quantitative theory of plausible inference about the parameters of…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Various structured argumentation frameworks utilize preferences as part of their standard inference procedure to enable reasoning with preferences. In this paper, we consider an inverse of the standard reasoning problem, seeking to identify…
This paper axiomatizes, in a two-stage setup, a new theory for decision under risk and ambiguity. The axiomatized preference relation $\succeq$ on the space $\tilde{V}$ of random variables induces an ambiguity index $c$ on the space…
We give an extension of de Finetti's concept of coherence to unbounded (but real-valued) random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to…
Much has been written on reciprocity laws in number theory and their connections with group representations. In this paper we explore more on these connections. We prove a "reciprocity Law" for certain specific representations of semidirect…
A family of regularization functionals is said to admit a linear representer theorem if every member of the family admits minimizers that lie in a fixed finite dimensional subspace. A recent characterization states that a general class of…
We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear…
In the past, empirical evidence has been presented that Hilbert series of symplectic quotients of unitary representations obey a certain universal system of infinitely many constraints. Formal series with this property have been called…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
Monotonicity and recursivity are central assumptions in intertemporal consumption problems under ambiguity. We show that monotone recursive preferences admit both a recursive and an ex-ante representation, and that the certainty equivalent…
The Expansion property considered by researchers in Social Choice is shown to correspond to a logical property of nonmonotonic consequence relations that is the {\em pure}, i.e., not involving connectives, version of a previously known weak…
We prove a version of the completeness hypothesis that follows from the coexistence of symmetry and gravity: tree-level gravitational scattering mandates single-particle states in all possible irreducible representations of the symmetry…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from `probability' without recourse to indeterminism,…