Search results for "Formal topology"

showing 4 items of 4 documents

A constructive semantics for non-deducibility

2008

This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

AlgebraLogicSemantics (computer science)Binary numberPredicate (mathematical logic)Formal topologyTopological semanticsFirst orderConstructiveMathematicsMLQ
researchProduct

Heyting-valued interpretations for Constructive Set Theory

2006

AbstractWe define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory (CZF). These interpretations provide models for CZF that are analogous to Boolean-valued models for ZF and to Heyting-valued models for IZF. Heyting-valued interpretations are defined here using set-generated frames and formal topologies. As applications of Heyting-valued interpretations, we present a relative consistency result and an independence proof.

Discrete mathematicsLogicConstructive set theoryFormal topologyHeyting-valued modelsConstructive set theoryHeyting algebraConsistency (knowledge bases)ConstructiveAlgebraMathematics::LogicPointfree topologyConstructive set theory Heyting algebras independence proofsMathematics::Category TheoryComputer Science::Logic in Computer ScienceIndependence (mathematical logic)Heyting algebraFrame (artificial intelligence)FrameSet theoryFormal topologyMathematicsAnnals of Pure and Applied Logic
researchProduct

Spatiality for formal topologies

2007

We define what it means for a formal topology to be spatial, and investigate properties related to spatiality both in general and in examples.

Pointfree topology formal topology spatialityMathematics (miscellaneous)Theoretical computer scienceComputer scienceFormal topologyNetwork topologyComputer Science ApplicationsMathematical Structures in Computer Science
researchProduct

Finitary formal topologies and Stone’s representation theorem

2008

AbstractWe study the concept of finitary formal topology, a point-free version of a topological space with a basis of compact open subsets. The notion of finitary formal topology is defined from the perspective of the Basic Picture (introduced by the second author) and thus it is endowed with a binary positivity relation. As an application, we prove a constructive version of Stone’s representation theorem for distributive lattices. We work within the framework of a minimalist foundation (as proposed by Maria Emilia Maietti and the second author). Both inductive and co-inductive methods are used in most proofs.

Stone's representationGeneral Computer ScienceRelation (database)Representation theoremFormal topologyformal topology; positivity; Stone's representation; constructive methodsPositivityBasis (universal algebra)Topological spaceStone’s representationMathematical proofConstructiveTheoretical Computer ScienceConstructive methodsAlgebraDistributive propertyFinitaryComputer Science(all)MathematicsTheoretical Computer Science
researchProduct