Automated Comparative Study of Some Generalized Rough Approximations

Adam Grabowski

doi:10.3233/fi-2021-2019

Automated Comparative Study of Some Generalized Rough Approximations

Fundamenta Informaticae ◽

10.3233/fi-2021-2019 ◽

2021 ◽

Vol 179 (2) ◽

pp. 165-182

Author(s):

Adam Grabowski

Keyword(s):

Comparative Study ◽

Binary Relation ◽

Mathematical Knowledge ◽

Rationality Postulates

The paper contains some remarks on building automated counterpart of a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to arbitrary binary relation. Our focus was on translating rationality postulates for such operators by means of the Mizar system – the software and the database which allows for expressing and checking mathematical knowledge for the logical correctness. The main objective was the formal (and machine-checked) proof of Theorem 4.1 from A. Gomolińska’s paper “A Comparative Study of Some Generalized Rough Approximations”, hence the present title. We provide also the discussion on how to make the presentation more efficient to reuse the reasoning techniques of the Mizar verifier.

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On normality of a closure space generated from a tree by relation

Asian-European Journal of Mathematics ◽

10.1142/s1793557122501108 ◽

2021 ◽

pp. 2250110

Author(s):

A. K. Das ◽

Ria Gupta

Keyword(s):

Comparative Study ◽

Binary Relation ◽

Applied Mathematics ◽

Closure Space ◽

Topological Properties ◽

Closure Spaces

Binary relation plays a prominent role in the study of mathematics in particular applied mathematics. Recently, some authors generated closure spaces through relation and made a comparative study of topological properties in the space by varying the property on the relation. In this paper, we have studied closure spaces generated from a tree through binary relation and observed that under certain situation the space generated from a tree is normal.

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A Comparative Study of Some Central Notions of ASPIC+ and DeLP

Theory and Practice of Logic Programming ◽

10.1017/s1471068419000437 ◽

2019 ◽

Vol 20 (3) ◽

pp. 358-390

Author(s):

ALEJANDRO J. GARCÍA ◽

HENRY PRAKKEN ◽

GUILLERMO R. SIMARI

Keyword(s):

Comparative Study ◽

Closure Properties ◽

Rule Based ◽

Special Cases ◽

Rationality Postulates ◽

Grounded Semantics ◽

Better Than

AbstractThis paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure properties. As for differences in the definitions of arguments and attack, it turns out that DeLP’s definitions are intuitively appealing but that they may not fully comply with Caminada and Amgoud’s rationality postulates of strict closure and indirect consistency. For some special cases, the DeLP definitions are shown to fare better than ASPIC+. Next, it is argued that there are reasons to consider a variant of DeLP with grounded semantics, since in some examples its current notion of warrant arguably has counterintuitive consequences and may lead to sets of warranted arguments that are not admissible. Finally, under some minimality and consistency assumptions on ASPIC+ arguments, a one-to-many correspondence between ASPIC+ arguments and DeLP arguments is identified in such a way that if the DeLP warranting procedure is changed to grounded semantics, then ’s DeLP notion of warrant and ASPIC+ ’s notion of justification are equivalent. This result is proven for three alternative definitions of attack.

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