Related papers: Who Is Guilty?
In this paper, we generalize epistemic logic so that it can help reason about ways of combining common knowledge and distributed knowledge such as "common distributed knowledge", "distributed common knowledge", "distributed common…
The liar paradox is widely seen as not a serious problem. I try to explain why this view is mistaken.
We propose a constructive interpretation of truth which resolves the standard semantic paradoxes.
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
In this paper we concentrate on the nature of the liar paradox as a cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model [Aerts, Broekaert, Smets 1999] that has been…
We investigate the complexity of a puzzle that turns out to be NL-complete.
While there exist several reasoners for Description Logics, very few of them can cope with uncertainty. BUNDLE is an inference framework that can exploit several OWL (non-probabilistic) reasoners to perform inference over Probabilistic…
The main subjects of this text are: (1) Generalization of concepts and operations, like distance and size, to situations where they are not definable in the usual way. (2) A pragmatic theory of handling contradictions using reliability of…
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…
People often ask questions with false assumptions, a type of question that does not have regular answers. Answering such questions requires first identifying the false assumptions. Large Language Models (LLMs) often generate misleading…
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the…
When a student fails an exam, do we tend to blame their effort or the test's difficulty? Attribution, defined as how reasons are assigned to event outcomes, shapes perceptions, reinforces stereotypes, and influences decisions. Attribution…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
The fact that the famous Godel incompleteness theorem and the archetype of all logical paradoxes, that of the Liar, are related closely is, of course, not only well known, but is a part of the common knowledge of logician community.…
This article seeks to encourage a mathematical dialog regarding a possible solution to Beals Conjecture. It breaks down one of the worlds most difficult math problems into laymans terms and encourages people to question some of the most…
We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…
Large language models (LLMs) are trained on extensive datasets that encapsulate substantial world knowledge. However, their outputs often include confidently stated inaccuracies. Earlier works suggest that LLMs encode truthfulness as a…
A large-scale conversational agent can suffer from understanding user utterances with various ambiguities such as ASR ambiguity, intent ambiguity, and hypothesis ambiguity. When ambiguities are detected, the agent should engage in a…