Related papers: Complete Conditional Type Structures (Extended Abs…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory $T$ in which all partially recursive functions are representable, yet $T$…
Plausibility models are Kripke models that agents use to reason about knowledge and belief, both of themselves and of each other. Such models are used to interpret the notions of conditional belief, degrees of belief, and safe belief. The…
This paper studies distribution-free inference in settings where the data set has a hierarchical structure -- for example, groups of observations, or repeated measurements. In such settings, standard notions of exchangeability may not hold.…
The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players' beliefs. An assessment consisting of a strategy and a belief is a…
Human explanations of high-level decisions are often expressed in terms of key concepts the decisions are based on. In this paper, we study such concept-based explainability for Deep Neural Networks (DNNs). First, we define the notion of…
Infinite games with imperfect information are known to be undecidable unless the information flow is severely restricted. One fundamental decidable case occurs when there is a total ordering among players, such that each player has access…
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…
The combination of the Bayesian game and learning has a rich history, with the idea of controlling a single agent in a system composed of multiple agents with unknown behaviors given a set of types, each specifying a possible behavior for…
We introduce a model-complete theory which completely axiomatizes the structure $Z_{\alpha}=(Z, +, 0, 1, f)$ where $f : x \to \lfloor{\alpha} x \rfloor $ is a unary function with $\alpha$ a fixed transcendental number. When $\alpha$ is…
We state and prove Kuhn's equivalence theorem for a new representation of games, the intrinsic form. First, we introduce games in intrinsic form where information is represented by $\sigma$-fields over a product set. For this purpose, we…
We consider a dynamic game with asymmetric information where each player observes privately a noisy version of a (hidden) state of the world V, resulting in dependent private observations. We study structured perfect Bayesian equilibria…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…
Coverage Types provide a suitable type mechanism that integrates under-approximation logic to support Property-Based Testing. They are used to type the return value of a function that represents an input test generator. This allows us to…
We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant…
The set of all m-tuples of compatible full conditional distributions on discrete random variables is an algebraic set whose defining ideal is a unimodular toric ideal. We identify the defining polynomials of these ideals with closed walks…
The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal."…