Signed ordered knotlike quandle presentations

Signed ordered knotlike quandle presentations

We define enhanced presentations of quandles via generators and relations with additional information comprising signed operations and an order structure on the set of generators. Such a presentation determines a virtual link diagram up to virtual moves. We list formal Reidemeister moves in which Tietze moves on the presented quandle are accompanied by corresponding changes to the order structu...

Signed Interval Logi on Totally Ordered Domains

Belief Revision and Ordered Theory Presentations

The standard theory of belief revision|known as the AGM theory after its authors, C. Al-chourrr on, P. GG ardenfors and D. Makinson 3]|suuers from at least two disadvantages. One is that it represents belief states as innnite objects, namely deductively closed sets of sentences. Another is that existing belief revision models make too strong assumptions about what information is available to gu...

Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology

Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Graña. We specialize that theory to the case when there is a group action on the coefficients. First, quandle modules are used to generalize Burau representations and Alexander modules for classical knots. Second, 2-cocycles valued in non-abelian groups are us...

Generalized quandle polynomials

We define a family of generalizations of the two-variable quandle polynomial. These polynomial invariants generalize in a natural way to eight-variable polynomial invariants of finite biquandles. We use these polynomials to define a family of link invariants which further generalize the quandle counting invariant.