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Martingales constitute a basic tool in stochastic analysis; this paper considers their application to counting processes. We use this tool to revisit a renewal theorem and its extensions for various counting processes. We first consider a…

Probability · Mathematics 2018-12-27 Daryl J. Daley , Masakiyo Miyazawa

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may ask whether composing the inversions of the component…

Category Theory · Mathematics 2020-07-29 Toby St. Clere Smithe

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…

Computation and Language · Computer Science 2024-05-24 Linlu Qiu , Liwei Jiang , Ximing Lu , Melanie Sclar , Valentina Pyatkin , Chandra Bhagavatula , Bailin Wang , Yoon Kim , Yejin Choi , Nouha Dziri , Xiang Ren

In earlier work, we introduced flexible inference and decision-theoretic metareasoning to address the intractability of normative inference. Here, rather than pursuing the task of computing beliefs and actions with decision models composed…

Artificial Intelligence · Computer Science 2013-02-21 Eric J. Horvitz , Adrian Klein

For AI systems to garner widespread public acceptance, we must develop methods capable of explaining the decisions of black-box models such as neural networks. In this work, we identify two issues of current explanatory methods. First, we…

Computation and Language · Computer Science 2019-12-06 Oana-Maria Camburu , Eleonora Giunchiglia , Jakob Foerster , Thomas Lukasiewicz , Phil Blunsom

The paper proposes a fresh look at the concept of goal and advances that motivational attitudes like desire, goal and intention are just facets of the broader notion of (acceptable) outcome. We propose to encode the preferences of an agent…

Logic in Computer Science · Computer Science 2022-09-13 Guido Governatori , Francesco Olivieri , Simone Scannapieco , Antonino Rotolo , Matteo Cristani

Conceptual analysis -- proposing definitions and refining them through counterexamples -- is central to philosophical methodology. We study whether language models can perform this task through iterated analysis and repair chains: one model…

Computation and Language · Computer Science 2026-05-06 Daniel Drucker , Kyle Mahowald

While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…

Computation and Language · Computer Science 2022-10-14 Britta Grusdt , Daniel Lassiter , Michael Franke

Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…

Artificial Intelligence · Computer Science 2013-04-15 Marvin S. Cohen

Prominent approaches to belief revision prescribe the adoption of a new belief that is as close as possible to the prior belief, in a process that, even in the standard case, can be described as attempting to minimize surprise. Here we…

Artificial Intelligence · Computer Science 2021-11-23 Adrian Haret

Language is not only used to transmit neutral information; we often seek to persuade by arguing in favor of a particular view. Persuasion raises a number of challenges for classical accounts of belief updating, as information cannot be…

Computation and Language · Computer Science 2022-09-15 Samuel A. Barnett , Thomas L. Griffiths , Robert D. Hawkins

While recent years have witnessed the emergence of various explainable methods in machine learning, to what degree the explanations really represent the reasoning process behind the model prediction -- namely, the faithfulness of…

Computation and Language · Computer Science 2021-09-07 Yingqiang Ge , Shuchang Liu , Zelong Li , Shuyuan Xu , Shijie Geng , Yunqi Li , Juntao Tan , Fei Sun , Yongfeng Zhang

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…

Logic in Computer Science · Computer Science 2025-09-08 Ramana Nagasamudram , Anindya Banerjee , David A. Naumann

Starting from two case histories, where only after thorough Failure Analysis the suddenly appearance of a failure was linked to much earlier events, the possibility of improving the reliability and of adjusting the reliability prediction…

Other Condensed Matter · Physics 2007-09-17 G. Mura , G. Cassanelli

We present a tool for modelling and reasoning with knowledge from various diverse (and possibly conflicting) viewpoints. The theoretical underpinnings are provided by enhancing base logics by standpoints according to a recently introduced…

Artificial Intelligence · Computer Science 2023-05-02 Florian Emmrich , Lucía Gómez Álvarez , Hannes Strass

This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational…

Computer Science and Game Theory · Computer Science 2025-02-04 Georgios Amanatidis , Michael Lampis , Evangelos Markakis , Georgios Papasotiropoulos

Following Hoare's seminal invention, now called Hoare logic, to reason about correctness of computer programs, we advocate a related but fundamentally different approach to reason about access security of computer programs such as access…

Logic in Computer Science · Computer Science 2026-04-01 Arnold Beckmann , Anton Setzer

Iterated admissibility (IA) can be seen as exhibiting a minimal criterion of rationality in games. In order to make this intuition more precise, the epistemic characterization of this game-theoretic solution has been actively investigated…

Logic · Mathematics 2013-04-19 Fernando Tohmè , Gianluca Caterina , Rocco Gangle

Belief revision is the process in which an agent incorporates a new piece of information together with a pre-existing set of beliefs. When the new information comes in the form of a report from another agent, then it is clear that we must…

Artificial Intelligence · Computer Science 2014-05-02 Aaron Hunter

Weighted abduction computes hypotheses that explain input observations. A reasoner of weighted abduction first generates possible hypotheses and then selects the hypothesis that is the most plausible. Since a reasoner employs parameters,…

Logic in Computer Science · Computer Science 2025-02-17 Shota Motoura , Ayako Hoshino , Itaru Hosomi , Kunihiko Sadamasa
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