A world of individual assertion allows the rich and powerful to dominate the poor and weak, as happened on the early 19th-century frontier, in Gilded Age cities and in the recent American economy.
An individual assertion in (mathcal {L}_{Sigma,Phi }) is of the form (A(a)), ((B = c)(a)), (r a,b)) or (sigma (a,d)), where (a,b in Sigma _I), (A in Sigma _C), (B in Sigma _A!setminus !Sigma _C), (c in range (B)), (r in Sigma _{oR}), (sigma in Sigma _{dR}) and (d in range (sigma )).
(mathcal {A}) is a finite set, called the ABox (assertion box) of (mathcal {KB}), consisting of individual assertions.
The first part contains individual assertions, called the ABox, while the second part contains terminological axioms, called the TBox.
It is a model of an ABox (mathcal {A}), denoted by (mathcal {I}models mathcal {A}), if it satisfies all the individual assertions of (mathcal {A}).
However, it is perfectly possible to see some candidate norms as ideals, while the evaluations of individual assertions may take into account various relations between the assertion and the norm over and above conformity.
This suggests that despite the quotability of individual assertions in the Meditations, we should approach them by studying their 'therapeutic' context, that is, by asking: what psychological effect(s) is Marcus trying to achieve by saying this?
One can allow ABoxes to contain individual assertions of the form (a = b), where (a,b in Sigma _I), with the semantics that an interpretation (mathcal {I}) satisfies (a = b) if (a^mathcal {I}= b^mathcal {I}).
(Knowledge Base) An acyclic knowledge base in (mathcal {L}_{Sigma,Phi }) is a pair (mathcal {KB}= leftlangle mathcal {T},mathcal {A}rightrangle,), where: (mathcal {A}) is a finite set, called the ABox (assertion box) of (mathcal {KB}), consisting of individual assertions.
Others go farther, arguing for the abandonment of the article as the core unit of knowledge transfer, for nano-publication of individual assertions [6], for the publication of figures or data rather than articles [7], for the rise of wiki science and the end of peer review entirely [8].
Sure, philosophical thinking clarifies conceptual distinctions and specifies the significance of individual assertions.
