Kit Fine’s truthmaker semantics allows us to distinguish between implying and containing: A implies B iff every truthmaker of A includes (as a part) a truthmaker of B, and A contains B iff every truthmaker of B is included (as a part) in a truthmaker of A. These are two different notions that can both be transformed into a proper object language connective. While the former notion amounts to the usual notion of implication, the latter one leads to a novel connective with interesting logical properties. In this paper we put forward a truthmaker semantics for the implication of the relevant logic \(\mathsf {R}\) and we accompany it with the corresponding “containing” operator. This framework will allow us to relate two seemingly very different kinds of relevant implication that has so far been studied separately, namely the implication of the logic \(\mathsf {R}\) and Angell’s analytic containment. Our approach semantically determines a logic that we call \(\mathsf {RAC}\) . We explore its connection to \(\mathsf {R}\) , the logic of analytic containment \(\mathsf {AC}\) , Urquhart’s operational semantics and inquisitive semantics.

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Implying and Containing in Truthmaker Semantics

  • Vít Punčochář,
  • Thomas M. Ferguson

摘要

Kit Fine’s truthmaker semantics allows us to distinguish between implying and containing: A implies B iff every truthmaker of A includes (as a part) a truthmaker of B, and A contains B iff every truthmaker of B is included (as a part) in a truthmaker of A. These are two different notions that can both be transformed into a proper object language connective. While the former notion amounts to the usual notion of implication, the latter one leads to a novel connective with interesting logical properties. In this paper we put forward a truthmaker semantics for the implication of the relevant logic \(\mathsf {R}\) and we accompany it with the corresponding “containing” operator. This framework will allow us to relate two seemingly very different kinds of relevant implication that has so far been studied separately, namely the implication of the logic \(\mathsf {R}\) and Angell’s analytic containment. Our approach semantically determines a logic that we call \(\mathsf {RAC}\) . We explore its connection to \(\mathsf {R}\) , the logic of analytic containment \(\mathsf {AC}\) , Urquhart’s operational semantics and inquisitive semantics.