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Wnioskowanie logiczne za pomocą DNA. Reguła kontrapozycji

Rogowski Łukasz

Studia i Materiały Informatyki Stosowanej

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2013

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nr 12

11--18

PL

Obliczenia DNA (z ang. DNA computing) to nowa dziedzina informatyki, będąca alternatywą dla tradycyjnych systemów komputerowych, polegająca na wykorzystaniu cząsteczek molekularnych do rozwiązywania problemów algorytmicznych, matematycznych i logicznych. Niniejszy artykuł przedstawia istniejące implementacje systemów wnioskowania realizowanych za pomocą DNA oraz nową koncepcję takiego systemu, uwzględniającą nowe elementy: negację i regułę kontrapozycji w implikacji.

EN

DNA computing is one of new computational paradigms which are alternative to traditional computer systems. Biological molecules in special laboratory conditions can be used to solve mathematical, logical and algorithmic purposes. This paper describes some already existing models of logical inference systems and the new proposal – DNA deduction system using new elements: negation and rule of contraposition.

2

Computing Implications with Negation from a Formal Context

Missaoui R., Nourine L., Renaud Y.

Fundamenta Informaticae

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2012

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Vol. 115, nr 4

357-375

EN

The objective of this article is to define an approach towards generating implications with (or without) negation when only a formal context K = (G,M, I) is provided. To that end, we define a two-step procedure which first (i) computes implications whose premise is a key in the context K| K representing the apposition of the context K and its complementary �K with attributes in M (negative attributes), and then (ii) uses an inference axiom we have defined to produce the whole set of implications.

3

Unifying Framework for Rule Semantics: Application to Gene Expression Data

Agier M., Petit J-M., Suzuki E.

Fundamenta Informaticae

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2007

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Vol. 78, nr 4

543-559

EN

The notion of rules is very popular and appears in different flavors, for example as association rules in data mining or as functional dependencies in databases. Their syntax is the same but their semantics widely differs. In the context of gene expression data mining, we introduce three typical examples of rule semantics and for each one, we point out that Armstrong's axioms are sound and complete. In this setting, we propose a unifying framework in which any "well-formed" semantics for rules may be integrated. We do not focus on the underlying data mining problems posed by the discovery of rules, rather we prefer to discuss the expressiveness of our contribution in a particular application domain: the understanding of gene regulatory networks from gene expression data. The key idea is that biologists have the opportunity to choose - among some predefined semantics - or to define the meaning of their rules which best fits into their requirements. Our proposition has been implemented and integrated into an existing open-source system named MeV of the TIGR environment devoted to microarray data interpretation. An application has been performed on expression profiles of a sub-sample of genes from breast cancer tumors.

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A Generalization Model Based on OI-implication for Ideal Theory Refinement

Esposito F., Fanizzi N., Ferilli S., Semeraro G.

Fundamenta Informaticae

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2001

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Vol. 47, nr 1,2

15-33

EN

A framework for theory refinement is presented pursuing the efficiency and effectiveness of learning regarded as a search process. A refinement operator satisfying these requirements is formally defined as ideal. Past results have demonstrated the impossibility of specifying ideal operators in search spaces where standard generalization models, like logical implication or q-subsumption, are adopted. By assuming the object identity bias over a space defined by a clausal language ordered by logical implication, a novel generalization model, named OI-implication, is derived and we prove that ideal operators can be defined for the resulting search space.