Related papers: The Problem Of Grue Isn't
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
Maybe the first inverse problem presented in the history of the occidental thought is described in the book Republic, written by Plato. The problem is posed in the Book VII in a text known as the Allegory of the Cave. That text motivated us…
Traditional symbolic reasoning engines, while attractive for their precision and explicability, have a few major drawbacks: the use of brittle inference procedures that rely on exact matching (unification) of logical terms, an inability to…
This paper introduces a Theory of Troubleshooting that is rooted in cognitive science. This theory helps software developers explain the challenges they face and the project risks that emerge as troubleshooting becomes difficult. We define…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
Although the halting problem is undecidable, imperfect testers that fail on some instances are possible. Such instances are called hard for the tester. One variant of imperfect testers replies "I don't know" on hard instances, another…
Asking questions is a pervasive human activity, but little is understood about what makes them difficult to answer. An analysis of a pair of large databases, of New York Times crosswords and questions from the quiz-show Jeopardy,…
The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do calculus is required has been…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
Gray (2015) argued that the Fermi paradox (FP) is a misnomer, and it is not a valid paradox. Gray also speculated that the argument was misattributed to Fermi, whose lunchtime remarks did not pertain to the existence of extraterrestrial…
Standard expositions of Goedel's 1931 paper on undecidable arithmetical propositions are based on two presumptions in Goedel's 1931 interpretation of his own, formal, reasoning - one each in Theorem VI and in Theorem XI - which do not meet…
In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge; Brouwer disagrees on both…
Chalmer's famously identified pinpointing an explanation for our subjective experience as the "hard problem of consciousness". He argued that subjective experience constitutes a "hard problem" in the sense that its explanation will…
The Sorites paradox is the name of a class of paradoxes that arise when vague predicates are considered. Vague predicates lack sharp boundaries in extension and is therefore not clear exactly when such predicates apply. Several approaches…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
The toss of a coin is usually regarded as the epitome of randomness, and has been used for ages as a means to resolve disputes in a simple, fair way. Perhaps as ancient as consulting objects such as coins and dice is the art of maliciously…
We study the problem of learning Granger causality between event types from asynchronous, interdependent, multi-type event sequences. Existing work suffers from either limited model flexibility or poor model explainability and thus fails to…
The science of consciousness has been successful over the last decades. Yet, it seems that some of the key questions remain unanswered. Perhaps, as a science of consciousness, we cannot move forward using the same theoretical commitments…
After Bayes, the oldest Bayesian account of enumerative induction is given by Laplace's so-called rule of succession: if all $n$ observed instances of a phenomenon to date exhibit a given character, the probability that the next instance of…