Related papers: A Game-Theoretic Computational Interpretation of P…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…
We provide a new approach to training neural models to exhibit transparency in a well-defined, functional manner. Our approach naturally operates over structured data and tailors the predictor, functionally, towards a chosen family of…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
There is a growing concern about typically opaque decision-making with high-performance machine learning algorithms. Providing an explanation of the reasoning process in domain-specific terms can be crucial for adoption in risk-sensitive…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose…
In this work, we present a logic based on first-order CTL, namely Game Analysis Logic (GAL), in order to reason about games. We relate models and solution concepts of Game Theory as models and formulas of GAL, respectively. Precisely, we…
Arithmetic functions in Number Theory meet the Sprague-Grundy function from Combinatorial Game Theory. We study a variety of 2-player games induced by standard arithmetic functions, such as Euclidian division, divisors, remainders and…
We investigate quantitative extensions of modal logic and the modal mu-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
Due to the increasing use of machine learning in practice it becomes more and more important to be able to explain the prediction and behavior of machine learning models. An instance of explanations are counterfactual explanations which…
CZF is a system of set theory which, over classical logic, is equivalent to ZF, while over intuitionistic logic, it has a well-known constructive type-theoretic interpretation. This article introduces a simpler, intuitive family of…
While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the…
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical…
This paper proposes a new approach to power in Game Theory. Cooperation and conflict are simulated with a mechanism of payoff alteration, called F-game. Using convex combinations of preferences, an F-game can measure players' attitude to…
Real artificial intelligence always has been focused on by many machine learning researchers, especially in the area of deep learning. However deep neural network is hard to be understood and explained, and sometimes, even metaphysics. The…
For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a consequence, completeness of PC yields completeness of IPC.
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…