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1

An Improved Set-based Reasoner for the Description Logic 𝒟ℒD4,×

Cantone Domenico, Nicolosi-Asmundo Marianna, Santamaria Daniele Francesco

Fundamenta Informaticae

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2021

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Vol. 178, nr 4

315--346

EN

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic 𝒟ℒ〈4LQSR,×〉(D ) (𝒟 ℒD 4,×, for short). Our application solves the main TBox and ABox reasoning problems for 𝒟 ℒ D 4,×. In particular, it solves the consistency and the classification problems for 𝒟 ℒD 4,× -knowledge bases represented in set-theoretic terms, and a generalization of the Conjunctive Query Answering problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and improves a previous version, is implemented in C++. It supports 𝒟 ℒ D 4,×-knowledge bases serialized in the OWL/XML format and it admits also rules expressed in SWRL (Semantic Web Rule Language).

2

An Algorithmic Solution of a Birkhoff Type Problem

Simson D., Wojewódzki M.

Fundamenta Informaticae

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2008

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Vol. 83, nr 4

389-410

EN

We give an algorithmic solution in a simple combinatorial data of Birkhoff?s type problem studied in [22] and [25], for the category repft(I, K[t]/(tm)) of filtered I-chains of modules over the K-algebra K[t]/(tm) of K-dimension m < ?, where m ^(3) 2, I is a finite poset with a unique maximal element, and K is an algebraically closed field. The problem is to decide when the indecomposable objects of the category repft(I, K[t]/(tm)) admit a classification by means of a suitable parametrisation. A complete solution of this important problem of the modern representation theory is contained in Theorems 2.4 and 2.5. We show that repft(I, K[t]/(tm)) admits such a classification if and only if (I, m) is one of the pairs of the finite list presented in Theorem 2.4, and such a classification does not exist for repft(I, K[t]/(tm)) if and only if the pair (I, m) is bigger than or equal to one of the minimal pairs of the finite list presented in Theorem 2.5. The finite lists are constructed by producing computer accessible algorithms and computational programs written in MAPLE and involving essentially the package CREP (see Section 4). On this way the lists are obtained as an effect of computer computations. In particular, the solution we get shows an importance of the computer algebra technique and computer computations in solving difficult and important problems of modern algebra.

3

Automatyczna redukcja wymiaru danych wejściowych dla problemów klasyfikacji

Horzyk A.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2004

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T. 8, z. 3

487-496

PL

Problem redundancji danych wejściowych - znany również jako problem przekleństwa wymiaru danych wejściowych - dla różnego rodzaju algorytmów uczących jest dobrze znany. Skutki takiej nadmiarowości prowadzą zazwyczaj do niekorzystnych zjawisk w procesie adaptacji parametrów konstruowanych systemów. Ponadto wpływają niekorzystnie na wydłużenia czasu obliczeń i złożoności konstruowanego modelu heurystycznego. W artykule tym zaprezentowano nową metodę pozwalającą automatycznie dokonać redukcji wymiaru danych wejściowych z uwzględnieniem istoty poszczególnych danych wejściowych dla problemów klasyfikacji.

EN

Reduction of data dimension is one of the important problems known as curse of dimensionality problem. Redundant input data dimension almost always disturbs the process of train or adaptation of constructed classification system. Moreover, the constructed heuristic model is more complex and the training time is much longer. This paper presents a new method able to reduce input data dimension in such a way to remove the less important and discriminative features.