scholarly journals Product representation for default bilattices: An application of natural duality theory

2015 ◽  
Vol 219 (7) ◽  
pp. 2962-2988 ◽  
Author(s):  
L.M. Cabrer ◽  
A.P.K. Craig ◽  
H.A. Priestley
Keyword(s):  
Duality Theory ◽  
Natural Duality ◽  
Product Representation

scholarly journals Non-involutive twist-structures

2018 ◽  
Vol 28 (5) ◽  
pp. 973-999 ◽  
Author(s):  
Umberto Rivieccio ◽  
Paulo Maia ◽  
Achim Jung
Keyword(s):  
Duality Theory ◽  
Paraconsistent Logic ◽  
Point Of View ◽  
Representation Theorems ◽  
Product Representation ◽  
Logical Point ◽  
Bitopological Spaces ◽  
First Time ◽  
Algebraic Counterpart

Abstract A recent paper by Jakl, Jung and Pultr (2016, Electron. Notes Theor. Comput. Sci., 325, 201–219) succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices (the algebraic counterpart of Nelson’s paraconsistent logic) to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We provide product representation theorems for these algebras, as well as completeness, algebraizability (and some non-algebraizability) results for the corresponding logics.

THE LATTICE OF ALTER EGOS

2012 ◽  
Vol 22 (01) ◽  
pp. 1250007 ◽  
Author(s):  
BRIAN A. DAVEY ◽  
JANE G. PITKETHLY ◽  
ROSS WILLARD
Keyword(s):  
Duality Theory ◽  
Finite Algebra ◽  
Galois Connection ◽  
Natural Duality ◽  
Algebraic Lattice ◽  
Finite Set ◽  
Partial Algebras ◽  
Quasi Order ◽  
Basic Concepts

We introduce a new Galois connection for partial operations on a finite set, which induces a natural quasi-order on the collection of all partial algebras on this set. The quasi-order is compatible with the basic concepts of natural duality theory, and we use it to turn the set of all alter egos of a given finite algebra into a doubly algebraic lattice. The Galois connection provides a framework for us to develop further the theory of natural dualities for partial algebras. The development unifies several fundamental concepts from duality theory and reveals a new understanding of full dualities, particularly at the finite level.

scholarly journals Distributive bilattices from the perspective of natural duality theory

2015 ◽  
Vol 73 (2) ◽  
pp. 103-141 ◽  
Author(s):  
L. M. Cabrer ◽  
H. A. Priestley
Keyword(s):  
Duality Theory ◽  
Natural Duality

UNCOUNTABLY MANY DUALISABLE ALGEBRAS

2011 ◽  
Vol 21 (05) ◽  
pp. 825-839 ◽  
Author(s):  
JANE G. PITKETHLY
Keyword(s):  
Finite Type ◽  
Duality Theory ◽  
Natural Duality ◽  
Type Problem ◽  
Finite Algebras ◽  
Finite Set ◽  
Term Functions

Fix a finite set M with at least three elements. We find uncountably many different clones on M, each of which is the clone of term functions of a strongly dualisable algebra. This provides a solution to the Finite Type Problem of natural duality theory: there are finite algebras that are dualisable but not via a structure of finite type.

HOW FINITE IS A THREE-ELEMENT UNARY ALGEBRA?

2005 ◽  
Vol 15 (02) ◽  
pp. 217-254 ◽  
Author(s):  
J. HYNDMAN ◽  
J. G. PITKETHLY
Keyword(s):  
Finite Rank ◽  
Duality Theory ◽  
Equational Theory ◽  
Unary Algebra ◽  
Natural Duality ◽  
Finitely Based ◽  
Injectivity Condition ◽  
Tight Connection ◽  
Algebraic Operations

We show that, within the class of three-element unary algebras, there is a tight connection between a finitely based quasi-equational theory, finite rank, enough algebraic operations (from natural duality theory) and a special injectivity condition.

scholarly journals Fully distributed actor-critic architecture for multitask deep reinforcement learning

2021 ◽  
Vol 36 ◽  
Author(s):  
Sergio Valcarcel Macua ◽  
Ian Davies ◽  
Aleksi Tukiainen ◽  
Enrique Munoz de Cote
Keyword(s):  
Neural Network ◽  
Reinforcement Learning ◽  
Duality Theory ◽  
Deep Neural Network ◽  
Original Problem ◽  
Almost Sure Convergence ◽  
Continuous Control ◽  
Access Data ◽  
Central Station ◽  
Common Policy

Abstract We propose a fully distributed actor-critic architecture, named diffusion-distributed-actor-critic Diff-DAC, with application to multitask reinforcement learning (MRL). During the learning process, agents communicate their value and policy parameters to their neighbours, diffusing the information across a network of agents with no need for a central station. Each agent can only access data from its local task, but aims to learn a common policy that performs well for the whole set of tasks. The architecture is scalable, since the computational and communication cost per agent depends on the number of neighbours rather than the overall number of agents. We derive Diff-DAC from duality theory and provide novel insights into the actor-critic framework, showing that it is actually an instance of the dual-ascent method. We prove almost sure convergence of Diff-DAC to a common policy under general assumptions that hold even for deep neural network approximations. For more restrictive assumptions, we also prove that this common policy is a stationary point of an approximation of the original problem. Numerical results on multitask extensions of common continuous control benchmarks demonstrate that Diff-DAC stabilises learning and has a regularising effect that induces higher performance and better generalisation properties than previous architectures.

Sign in / Sign up

Export Citation Format

Share Document