Uniform Definability in Propositional Dependence Logic

Fan Yang

doi:10.1017/S1755020316000459

Uniform Definability in Propositional Dependence Logic

Fan Yang^*

^*Corresponding author for this work

Delft University of Technology

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language of propositional dependence logic without these two connectives. We show that although such a (non-compositional) translation exists, neither intuitionistic disjunction nor intuitionistic implication is uniformly definable in propositional dependence logic.

Original language	English
Pages (from-to)	65-79
Journal	Review of Symbolic Logic
Volume	10
Issue number	1
DOIs	https://doi.org/10.1017/S1755020316000459
Publication status	Published - 1 Mar 2017
Externally published	Yes

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10.1017/S1755020316000459

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AB - Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language of propositional dependence logic without these two connectives. We show that although such a (non-compositional) translation exists, neither intuitionistic disjunction nor intuitionistic implication is uniformly definable in propositional dependence logic.

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Uniform Definability in Propositional Dependence Logic

Abstract

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