In this paper we expand Kit Fine’s truthmaker semantics for intuitionistic logic with a containment operator that allows us to define the connectives of analytic implication and analytic equivalence. Analytic implication reflects in the object language the Egli-Milner preorder of propositions: A analytically implies B iff every truthmaker of A contains a truthmaker of B and every truthmaker of B is contained in a truthmaker of A. We focus on one version of the semantics where it is required that every atomic formula has a unique truthmaker. This restriction allows us to employ techniques from inquisitive semantics and show that this setting determines a logic that can be characterized by an elegant axiomatic system.

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Analytic Implication and Equivalence in Truthmaker Semantics for Intuitionistic Logic

  • Vít Punčochář,
  • Thomas Ferguson

摘要

In this paper we expand Kit Fine’s truthmaker semantics for intuitionistic logic with a containment operator that allows us to define the connectives of analytic implication and analytic equivalence. Analytic implication reflects in the object language the Egli-Milner preorder of propositions: A analytically implies B iff every truthmaker of A contains a truthmaker of B and every truthmaker of B is contained in a truthmaker of A. We focus on one version of the semantics where it is required that every atomic formula has a unique truthmaker. This restriction allows us to employ techniques from inquisitive semantics and show that this setting determines a logic that can be characterized by an elegant axiomatic system.