Related papers: Relevant Consequence Relations: An Invitation
We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called…
Axiomatization has been widely used for testing logical implications. This paper suggests a non-axiomatic method, the chase, to test if a new dependency follows from a given set of probabilistic dependencies. Although the chase computation…
Probabilities of causation provide explanatory information on the observed occurrence (causal necessity) and non-occurrence (causal sufficiency) of events. Here, we adapt these probabilities (probability of necessity, probability of…
The ability to accurately interpret implied meanings plays a crucial role in human communication and language use, and language models are also expected to possess this capability. This study demonstrates that providing language models with…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
It is claimed that a variety of facts concerning ellipsis, event reference, and interclausal coherence can be explained by two features of the linguistic form in question: (1) whether the form leaves behind an empty constituent in the…
As complex machine learning models continue to find applications in high-stakes decision-making scenarios, it is crucial that we can explain and understand their predictions. Post-hoc explanation methods provide useful insights by…
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…
Case-based reasoning is known to play an important role in several legal settings. In this paper we focus on a recent approach to case-based reasoning, supported by an instantiation of abstract argumentation whereby arguments represent…
Exposure mappings facilitate investigations of complex causal effects when units interact in experiments. Current methods require experimenters to use the same exposure mappings both to define the effect of interest and to impose…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
Accurately predicting the relevance of items to users is crucial to the success of many social platforms. Conventional approaches train models on logged historical data; but recommendation systems, media services, and online marketplaces…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…
Logical relations (LR) have been around for many years, and today they are used in many formal results. However, it can be difficult to LR beginners to find a good place to start to learn. Papers often use highly specialized LRs that use…
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…
This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.