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.

A predicate extension of real valued logic / Baratella, Stefano. - In: ARCHIVE FOR MATHEMATICAL LOGIC. - ISSN 0933-5846. - ELETTRONICO. - 56:5-6(2017), pp. 585-605. [10.1007/s00153-017-0558-3]

A predicate extension of real valued logic

Baratella, Stefano
2017-01-01

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.
2017
5-6
Baratella, Stefano
A predicate extension of real valued logic / Baratella, Stefano. - In: ARCHIVE FOR MATHEMATICAL LOGIC. - ISSN 0933-5846. - ELETTRONICO. - 56:5-6(2017), pp. 585-605. [10.1007/s00153-017-0558-3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/194162
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