We study impurity-based decision tree algorithms such as CART, C4.5, etc., so as to better understand their theoretical underpinnings. We consider such algorithms on special forms of functions and distributions. We deal with the uniform distribution and functions that can be described as unate functions, linear threshold functions and readonce DNF. For unate functions we show that that maximal ...

The saturation assumption is widely used in computational science and engineering, usually without any rigorous theoretical justification and even despite of counterexamples for some coarse meshes known in the mathematical literature. On the other hand, there is overwhelming numerical evidence at least in an asymptotic regime for the validity of the saturation. In the generalized form, the assu...

The combination generator, first proposed by Wichmann and Hill (1982), is constructed by taking the fractional part of the sum of several random number generators. It is probably one of the most popular random number generators used. Its empirical performance is superior to the classical Lehmer congruential generator. However, its theoretical justification is somewhat primitive. In this paper, ...

Sir Roger Penrose, Nobel Laureate, has described them as “useless” for physics, yet the old uncle locked up in the attic, as John Baez describes them, play a fundamental role in the physics of the Universe, according to Vedic Physics theory. This paper explains why.

Justification logics are modal-like logics that provide a framework for reasoning about epistemic justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the method due to Sara Negri, we internalize the Kripke-style semantics of justification logics, known as Fitting models, within the syntax of the sequent ...

In this note we study the effect of adding fixed points to justification logics. We introduce two extensions of justification logics: extensions by fixed point (or diagonal) operators, and extensions by least fixed points. The former is a justification version of Smoryǹski’s Diagonalization Operator Logic, and the latter is a justification version of Kozen’s modal μcalculus. We also introduce f...

Justification logics are propositional modal-like logics that instead of statements A is known include statements of the form A is known for reason t where the term t can represent an informal justification for A or a formal proof of A. In our present work, we introduce model-theoretic tools, namely: filtrations and a certain form of generated submodels, in the context of justification logic in...

Justification Awareness Models, JAMs, were proposed by S. Artemov as a tool for modelling epistemic scenarios like Russel’s Prime Minister example. It was demonstrated that the sharpness and the injective property of a model play essential role in the epistemic usage of JAMs. The problem to axiomatize these properties using the propositional justification language was left opened. We propose th...

The Justification Hypothesis (JH; Henriques, 2003) is a basic, general, and macro-level construct that is highly compelling. However, it needs greater specification (i.e., justification) regarding what it is, how it might be operationalized and measured, and what it does and does not predict in the real world. In the present analysis, the act of "justification" is conceptualized as the ongoing ...