Related papers: Gibbardian Collapse and Trivalent Conditionals
Consider an agent taking two successive decisions to maximize his expected utility under uncertainty. After his first decision, a signal is revealed that provides information about the state of nature. The observation of the signal allows…
The Ricardian model of world trade based on comparative advantage is not sufficient to justify equal trade relations.The existing model of trade relations does not explain the distribution of income among trading countries. This paper…
Relational verification encompasses research directions such as reasoning about data abstraction, reasoning about security and privacy, secure compilation, and functional specificaton of tensor programs, among others. Several relational…
In the field of categorical probability, one uses concepts and techniques from category theory, such as monads and monoidal categories, to study the structures of probability and statistics. In this paper, we connect some ideas from…
We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…
Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions -- hypothetical…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or…
Calibrated predictions are useful because their numerical values can be interpreted as probabilities. Calibration errors are therefore widely used to evaluate, compare, and tune probabilistic predictors. Recently, Haghtalab et al. (2024)…
A growing body of computational studies shows that simple machine learning agents converge to cooperative behaviors in social dilemmas, such as collusive price-setting in oligopoly markets, raising questions about what drives this outcome.…
The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic…
Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…
Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is…
We prove that the Thin Sandwich Conjecture in general relativity is valid, provided that the data $(g_{ab},\dot g_{ab})$ satisfy certain geometric conditions. These conditions define an open set in the class of possible data, but are not…
The paper is devoted to counterexamples involving the triviality of domains of products and/or adjoints of densely defined operators.
In this paper, we provide more evidence for the contention that logical consequence should be understood in normative terms. Hartry Field and John MacFarlane covered the classical case. We extend their work, examining what it means for an…
By Solovay's celebrated completeness result on formal provability we know that the provability logic $\mathrm GL$ describes exactly all provable structural properties for any sound and strong enough arithmetical theory with a decidable…
This paper is an original attempt to understand the foundations of economic reasoning. It endeavors to rigorously define the relationship between subjective interpretations and objective valuations of such interpretations in the context of…
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for…