Related papers: An Introduction to Mechanized Reasoning
Large-scale behavioral datasets enable researchers to use complex machine learning algorithms to better predict human behavior, yet this increased predictive power does not always lead to a better understanding of the behavior in question.…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic.…
The main objective of explanations is to transmit knowledge to humans. This work proposes to construct informative explanations for predictions made from machine learning models. Motivated by the observations from social sciences, our…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
The importance of algorithmic fairness grows with the increasing impact machine learning has on people's lives. Recent work on fairness metrics shows the need for causal reasoning in fairness constraints. In this work, a practical method…
Economic theory has provided an estimable intuition in understanding the perplexing ideologies in law, in the areas of economic law, tort law, contract law, procedural law and many others. Most legal systems require the parties involved in…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
Regression plays a key role in many research areas and its variable selection is a classic and major problem. This study emphasizes cost of predictors to be purchased for future use, when we select a subset of them. Its economic aspect is…
The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
This study aims to examine the challenges and applications of machine learning for financial research. Machine learning algorithms have been developed for certain data environments which substantially differ from the one we encounter in…
Axiomatic approach has demonstrated its power in mathematics. The main goal of this preprint is to show that axiomatic methods are also very efficient for computer science. It is possible to apply these methods to many problems in computer…
In this paper an interesting application of mathematics in economics is presented: the formulation of the theory of consumer basic problem, grounded on the concept of preferences relation and operationalized with optimization tools.
A number of generalizations of stochastic and information-theoretic randomness are known in the literature. However, they are not compatible with handling meaning in vague and dynamic contexts of rough reasoning (and therefore explainable…
Prediction markets are designed to elicit information from multiple agents in order to predict (obtain probabilities for) future events. A good prediction market incentivizes agents to reveal their information truthfully; such incentive…
The emergence and continued reliance on the Internet and related technologies has resulted in the generation of large amounts of data that can be made available for analyses. However, humans do not possess the cognitive capabilities to…
Recent literature highlights the advantages of implementing social rules via dynamic game forms. We characterize when truth-telling remains a dominant strategy in gradual mechanisms implementing strategy-proof social rules, where agents…
This paper presents Abduction and Argumentation as two principled forms for reasoning, and fleshes out the fundamental role that they can play within Machine Learning. It reviews the state-of-the-art work over the past few decades on the…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…