10,199 research outputs found
Admissibility via Natural Dualities
It is shown that admissible clauses and quasi-identities of quasivarieties
generated by a single finite algebra, or equivalently, the quasiequational and
universal theories of their free algebras on countably infinitely many
generators, may be characterized using natural dualities. In particular,
axiomatizations are obtained for the admissible clauses and quasi-identities of
bounded distributive lattices, Stone algebras, Kleene algebras and lattices,
and De Morgan algebras and lattices.Comment: 22 pages; 3 figure
Remarks on Cyclotomic and Degenerate Cyclotomic BMW Algebras
We relate the structure of cyclotomic and degenerate cyclotomic BMW algebras,
for arbitrary parameter values, to that for admissible parameter values. In
particular, we show that these algebras are cellular. We characterize those
parameter sets for affine BMW algebras over an algebraically closed field that
permit the algebras to have non--trivial cyclotomic quotients.Comment: Rewrote introduction. Minor revisions and corrections. Published in
Journal of Algebr
When Structural Principles Hold Merely Locally
In substructural logics, structural principles may hold in some fragments of a consequence relation without holding globally. I look at this phenomenon in my preferred substructural logic, in which Weakening and Cut fail but which is supra-intuitionistic. I introduce object language operators that keep track of the admissibility of Weakening and of intuitionistic implications. I end with some ideas about local transitivity
A Gauge-Independent Mechanism for Confinement and Mass Gap: Part I -- The General Framework
We propose a gauge-independent mechanism for the area-law behavior of Wilson
loop expectation values in terms of worldsheets spanning Wilson loops
interacting with the spin foams that contribute to the vacuum partition
function. The method uses an exact transformation of lattice-regularized
Yang-Mills theory that is valid for all couplings. Within this framework, some
natural conjectures can be made as to what physical mechanism enforces the
confinement property in the continuum (weak coupling) limit. Details for the
SU(2) case in three dimensions are provided in a companion paper.Comment: 16 pages, 4 figure
AC-KBO Revisited
Equational theories that contain axioms expressing associativity and
commutativity (AC) of certain operators are ubiquitous. Theorem proving methods
in such theories rely on well-founded orders that are compatible with the AC
axioms. In this paper we consider various definitions of AC-compatible
Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are
revisited. The former is enhanced to a more powerful version, and we modify the
latter to amend its lack of monotonicity on non-ground terms. We further
present new complexity results. An extension reflecting the recent proposal of
subterm coefficients in standard Knuth-Bendix orders is also given. The various
orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming
(TPLP) special issue for the 12th International Symposium on Functional and
Logic Programming (FLOPS 2014
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