Probability over Płonka sums of Boolean algebras: States, metrics and topology

The paper introduces the notion of state for involutive bisemilattices, a variety which plays the role of algebraic counterpart of weak Kleene logics and whose elements are represented as Płonka sums of Boolean algebras. We investigate the relations between states over an involutive bisemilattice an...

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Detalles Bibliográficos
Autores: Bonzio, Stefano, Loi, Andrea
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/253045
Acceso en línea:http://hdl.handle.net/10261/253045
Access Level:acceso abierto
Palabra clave:Involutive bisemilattice
Płonka sum
Boolean algebra
Probability measures
Pseudometric
Descripción
Sumario:The paper introduces the notion of state for involutive bisemilattices, a variety which plays the role of algebraic counterpart of weak Kleene logics and whose elements are represented as Płonka sums of Boolean algebras. We investigate the relations between states over an involutive bisemilattice and probability measures over the (Boolean) algebras in the Płonka sum representation and, the direct limit of these algebras. Moreover, we study the metric completion of involutive bisemilattices, as pseudometric spaces, and the topology induced by the pseudometric.