Related papers: Commonly Knowing Whether
An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to…
A concept of "guessability" is defined for sets of sequences of naturals. Eventually, these sets are thoroughly characterized. To do this, a nonstandard logic is developed, a logic containing symbols for the ellipsis as well as for…
Given an arbitrary statistical theory, different from quantum mechanics, how to decide which are the nonclassical correlations? We present a formal framework which allows for a definition of nonclassical correlations in such theories,…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
Recently, the community has achieved substantial progress on many commonsense reasoning benchmarks. However, it is still unclear what is learned from the training process: the knowledge, inference capability, or both? We argue that due to…
The paper proposes to treat agent awareness as a form of knowledge, breaking the tradition in the existing literature on awareness. It distinguishes the de re and de dicto forms of such knowledge. The work introduces two modalities…
The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by…
This paper proposes to revisit the Turing test through the concept of normality. Its core argument is that the Turing test is a test of normal intelligence as assessed by a normal judge. First, in the sense that the Turing test targets…
A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique"…
We present a natural extension of the process of taking a group quotient to arbitrary subgroups. We first review basic concepts from group theory. This will allow us to see the relationship between our new, more general quotient operation…
Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…
A researcher observes a finite sequence of choices made by multiple agents in a binary-state environment. Agents maximize expected utilities that depend on their chosen alternative and the unknown underlying state. Agents learn about the…
Language provides simple ways of communicating generalizable knowledge to each other (e.g., "Birds fly", "John hikes", "Fire makes smoke"). Though found in every language and emerging early in development, the language of generalization is…
One purpose -- quite a few thinkers would say the main purpose -- of seeking knowledge about the world is to enhance our ability to make good decisions. An item of knowledge that can make no conceivable difference with regard to anything we…
Through set-theoretic formalization of the notion of common knowledge, Aumann proved that if two agents have the common priors, and their posteriors for a given event are common knowledge, then their posteriors must be equal. In this paper…
(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…
There are things we know, things we know we don't know, and then there are things we don't know we don't know. In this paper we address the latter two issues in a Bayesian framework, introducing the notion of doubt to quantify the degree of…
Information pooling has been extensively formalised across various logical frameworks in distributed systems, characterized by diverse information-sharing patterns. These approaches generally adopt an intersection perspective, aggregating…
This paper considers the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a…
Multiple-choice question answering (MCQA) becomes particularly challenging when all choices are relevant to the question and are semantically similar. Yet this setting of MCQA can potentially provide valuable clues for choosing the right…