Efficient decision procedures for locally finite theories II

1989 ◽  
pp. 390-401 ◽  
Author(s):  
Volker Weispfenning
Keyword(s):  
Decision Procedures ◽  
Locally Finite

Examples of theories of presheaf type

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Finite Groups ◽  
Linear Independence ◽  
Geometric Theory ◽  
Vector Spaces ◽  
Linear Orders ◽  
Locally Finite ◽  
Strong Unit ◽  
Locally Finite Groups ◽  
Simplicial Sets ◽  
Separable Extensions

This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

Existentially closed central extensions of locally finite p-groups

1986 ◽  
Vol 100 (2) ◽  
pp. 281-301 ◽  
Author(s):  
Felix Leinen ◽  
Richard E. Phillips
Keyword(s):  
Central Extensions ◽  
Locally Finite ◽  
Existentially Closed ◽  
Image Position

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

Monotonic and Non-Monotonic Logics of Knowledge1

1991 ◽  
Vol 15 (3-4) ◽  
pp. 255-274
Author(s):  
Rohit Parikh
Keyword(s):  
Model Theory ◽  
Decision Procedures ◽  
Logic Of Knowledge

We study monotonic and non-monotonic Logics of Knowledge, giving decision procedures and completeness results. In particular we develop a model theory for a non-monotonic Logic of Knowledge and show that it corresponds exactly to normal applications of a non-monotonic rule of inference due to McCarthy.

scholarly journals GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR

2021 ◽  
pp. 1-54
Author(s):  
MANUEL L. REYES ◽  
DANIEL ROGALSKI
Keyword(s):  
Regularity Property ◽  
Graded Algebra ◽  
General Study ◽  
Locally Finite ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Dimension 2 ◽  
Separable Algebras ◽  
Gk Dimension

Abstract This is a general study of twisted Calabi–Yau algebras that are $\mathbb {N}$ -graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi–Yau algebras of dimension 0 as separable k-algebras, and we similarly characterize graded twisted Calabi–Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi–Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension.

scholarly journals Locally-finite quantities in sYM

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Jacob L. Bourjaily ◽  
Cameron Langer ◽  
Kokkimidis Patatoukos
Keyword(s):  
Locally Finite ◽  
Yang Mills

Abstract A locally-finite quantity is one for which there is no region of divergence anywhere in the space of real loop momenta; it can therefore be computed (in principle) without regularization. In this work, we prove that all two-loop ratio functions in planar, maximally supersymmetric Yang-Mills theory are locally-finite.

Deciding Clause Classes by Semantic Clash Resolution

1993 ◽  
Vol 18 (2-4) ◽  
pp. 163-182
Author(s):  
Alexander Leitsch
Keyword(s):  
Decision Procedure ◽  
Decision Procedures ◽  
General Concept ◽  
Complexity Measure ◽  
Syntactical Structure

It is investigated, how semantic clash resolution can be used to decide some classes of clause sets. Because semantic clash resolution is complete, the termination of the resolution procedure on a class Γ gives a decision procedure for Γ. Besides generalizing earlier results we investigate the relation between termination and clause complexity. For this purpose we define the general concept of atom complexity measure and show some general results about termination in terms of such measures. Moreover, rather than using fixed resolution refinements we define an algorithmic generator for decision procedures, which constructs appropriate semantic refinements out of the syntactical structure of the clause sets. This method is applied to the Bernays – Schönfinkel class, where it gives an efficient (resolution) decision procedure.

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