inversivity

Finally, we should mention some recent work by Emde, Habel, and Rollinger [10] that also involves the discovery of qualitative laws. In this case, the focus is on determining whether predicates obey certain relations, such as transitivity or inversivity.

1984 September 1, Pat Langley, Jan Zytkow, Herbert A[lexander] Simon, Gary L. Bradshaw, “Comments on GLAUBER”, in The Search for Regularity: Four Aspects of Scientific Discovery (CMU-RI-TR-84-20), Pittsburgh, Pa.: Robotics Institute, →OCLC, chapter 3 (Discovering Qualitative Empirical Laws), page 16

Some more recent work by Emde, Habel, and Rollinger (1983) addresses a problem very similar to Brown’s task. In this case, the method examines whether predicates obey certain higher-level relations, such as transitivity or inversivity.

1985 July 15, Pat Langley, Herbert A[lexander] Simon, Jan M[ikołaj] Zytkow, Douglas H. Fisher, “Some Other Discovery Systems”, in Discovering Qualitative Empirical Laws (AD-A159 235), Irvine, Calif.: University of California, Irvine, →OCLC, page 20

one motivation for a ring is the role in plays in formalising the concepts of associativity, commutativity, distributivity, identity, inversivity, that is displayed by the "familiar" real numbers under addition and multiplication.

2001 June 30, maky m., “Can you help me, please?”, in sci.math (Usenet), archived from the original on 22 Jul 2026

The notion of non-inversivity includes thermodynamic irreversibility, but inversive dislocation motions (i.e., motions in which the loading and the unloading paths coincide) are not necessarily thermodynamically reversible. […] Table 1 summarizes the preceding discussion in terms of three dichotomies that must be clearly distinguished because they belong to different levels of description: reversibility vs. irreversibility (thermodynamic), inversivity vs. non-inversivity (kinematic) and stationarity vs. non-stationarity (statistical).

2002, Michael Zaiser, Alfred Seeger, “Long-range Internal Stresses, Dislocation Patterning and Work-hardening in Crystal Plasticity”, in F. R. N. Nabarro, M. S. Duesbery, editors, Dislocations in Solids, volume 11, Amsterdam: North-Holland, →ISBN, section 2 (General aspects of crystal plasticity and work-hardening), subsection 3 (Classification of dislocation motions), pages 10–11

Let D′ = D⊗ₖK. Let L′ be a difference field extending K. Let e = ∑dᵢ⊗cᵢ be a nonzero element of D′⊗_KL′, with dᵢ ∈ D, cᵢ ∈ L′. We may choose the cᵢ linearly independent over K′. It follows (using inversivity) that the σ(cᵢ) are linearly independent over K′.

2004 February 5, Ehud Hrushovski, “Components”, in The Elementary Theory of the Frobenius Automorphisms, part I (Difference schemes), chapter 3 (Definition of difference schemes), page 24