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Archive for Mathematical Logic

, Volume 56, Issue 5–6, pp 585–605 | Cite as

A predicate extension of real valued logic

  • Stefano BaratellaEmail author
Article
  • 65 Downloads

Abstract

We study a predicate extension of an unbounded real valued propositional logic that has been recently introduced. The latter, in turn, can be regarded as an extension of both the abelian logic and of the propositional continuous logic. Among other results, we prove that our predicate extension satisfies the property of weak completeness (the equivalence between satisfiability and consistency) and, under an additional assumption on the set of premisses, the property of strong completeness (the equivalence between logical consequence and provability). Eventually we discuss some topological properties of the space of types in our logic.

Keywords

Many-valued logic Unbounded truth values Real-valued logic Abelian logic Continuous logic 

Mathematics Subject Classification

03B50 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TrentoPovoItaly

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