816 research outputs found
The hyper Tableaux calculus with equality and an application to finite model computation
In most theorem proving applications, a proper treatment of equational theories or equality is mandatory. In this article we show how to integrate a modern treatment of equality in the hyper tableau calculus. It is based on splitting of positive clauses and an adapted version of the superposition inference rule, where equations used for superposition are drawn (only) from a set of positive unit clauses, and superposition inferences into positive literals is restricted into (positive) unit clauses only. The calculus also features a generic, semantically justified simplification rule which covers many redundancy elimination techniques known from superposition theorem proving. Our main results are soundness and completeness of the calculus, but we also show how to apply the calculus for finite model computation, and we briefly describe the implementation
Combinatorial Morse theory and minimality of hyperplane arrangements
We find an explicit combinatorial gradient vector field on the well known
complex S (Salvetti complex) which models the complement to an arrangement of
complexified hyperplanes. The argument uses a total ordering on the facets of
the stratification of R^n associated to the arrangement, which is induced by a
generic system of polar coordinates. We give a combinatorial description of the
singular facets, finding also an algebraic complex which computes local
homology. We also give a precise construction in the case of the braid
arrangement.Comment: 29 page
Set of support, demodulation, paramodulation: a historical perspective
This article is a tribute to the scientific legacy of automated reasoning pioneer and JAR founder Lawrence T. (Larry) Wos. Larry's main technical contributions were the set-of-support strategy for resolution theorem proving, and the demodulation and paramodulation inference rules for building equality into resolution. Starting from the original definitions of these concepts in Larry's papers, this survey traces their evolution, unearthing the often forgotten trails that connect Larry's original definitions to those that became standard in the field
A generalized boundary condition applied to Lieb-Schultz-Mattis type ingappabilities and many-body Chern numbers
We introduce a new boundary condition which renders the flux-insertion
argument for the Lieb-Schultz-Mattis type theorems in two or higher dimensions
free from the specific choice of system sizes. It also enables a formulation of
the Lieb-Schultz-Mattis type theorems in arbitrary dimensions in terms of the
anomaly in field theories of dimensions with a bulk correspondence as a
BF-theory in 2+1 dimensions. Furthermore, we apply the anomaly-based
formulation to the constraints on a half-filled spinless fermion on a square
lattice with flux, utilizing time-reversal, the magnetic translation and
on-site internal symmetries. This demonstrates the role of time-reversal
anomaly on the ingappabilities of a lattice model.Comment: 4 figure
Range-Restricted Interpolation through Clausal Tableaux
We show how variations of range-restriction and also the Horn property can be
passed from inputs to outputs of Craig interpolation in first-order logic. The
proof system is clausal tableaux, which stems from first-order ATP. Our results
are induced by a restriction of the clausal tableau structure, which can be
achieved in general by a proof transformation, also if the source proof is by
resolution/paramodulation. Primarily addressed applications are query synthesis
and reformulation with interpolation. Our methodical approach combines
operations on proof structures with the immediate perspective of feasible
implementation through incorporating highly optimized first-order provers
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