43,130 research outputs found
Classification over a predicate -- the general case. Part I -- structure theory
We begin the development of structure theory for a first order theory stable
over a monadic predicate
Paradoxes and Their Resolutions
Paradoxes and their Resolutions is a ‘thematic compilation’ by Avi Sion. It collects in one volume the essays that he has written in the past (over a period of some 27 years) on this subject. It comprises expositions and resolutions of many (though not all) ancient and modern paradoxes, including: the Protagoras-Euathlus paradox (Athens, 5th Cent. BCE), the Liar paradox and the Sorites paradox (both attributed to Eubulides of Miletus, 4th Cent. BCE), Russell’s paradox (UK, 1901) and its derivatives the Barber paradox and the Master Catalogue paradox (also by Russell), Grelling’s paradox (Germany, 1908), Hempel's paradox of confirmation (USA, 1940s), and Goodman’s paradox of prediction (USA, 1955). This volume also presents and comments on some of the antinomic discourse found in some Buddhist texts (namely, in Nagarjuna, India, 2nd Cent. CE; and in the Diamond Sutra, date unknown, but probably in an early century CE)
Model theoretic stability and definability of types, after A. Grothendieck
We point out how the "Fundamental Theorem of Stability Theory", namely the
equivalence between the "non order property" and definability of types, proved
by Shelah in the 1970s, is in fact an immediate consequence of Grothendieck's
"Crit{\`e}res de compacit{\'e}" from 1952. The familiar forms for the defining
formulae then follow using Mazur's Lemma regarding weak convergence in Banach
spaces
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An information-based approach to integrating empirical and explanation-based learning
We describe a new approach to integrating explanation-based and empirical learning methods for learning relational concepts. The approach uses an information-based heuristic to evaluate components of a hypothesis that are proposed either by explanation-based or empirical methods. Providing domain knowledge to the integrated system can decrease the amount of search required during learning and increase the accuracy of learned concepts, even when the domain knowledge is incorrect and incomplete and there is noise in the training data
Induction of Non-Monotonic Logic Programs to Explain Boosted Tree Models Using LIME
We present a heuristic based algorithm to induce \textit{nonmonotonic} logic
programs that will explain the behavior of XGBoost trained classifiers. We use
the technique based on the LIME approach to locally select the most important
features contributing to the classification decision. Then, in order to explain
the model's global behavior, we propose the LIME-FOLD algorithm ---a
heuristic-based inductive logic programming (ILP) algorithm capable of learning
non-monotonic logic programs---that we apply to a transformed dataset produced
by LIME. Our proposed approach is agnostic to the choice of the ILP algorithm.
Our experiments with UCI standard benchmarks suggest a significant improvement
in terms of classification evaluation metrics. Meanwhile, the number of induced
rules dramatically decreases compared to ALEPH, a state-of-the-art ILP system
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