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<p>The paper introduces a relevant containment logic according to which the analytic implication <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varphi \twoheadrightarrow \psi\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>φ</mi> <mo>↠</mo> <mi>ψ</mi> </mrow> </math></EquationSource> </InlineEquation> is analyzed as the conjunction of two theses: <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varphi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation> contextually entails <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\psi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varphi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>φ</mi> </math></EquationSource> </InlineEquation> contextually contains <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\psi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>. By doing so, we are able to extend the ternary semantics of relevant logic to the analysis of topic containment, thus lifting some limitations of Richard Sylvan’s relevant containment logic. We offer a ternary account of topic containment, in that led by the consideration that topic inclusions are evaluated <i>in situ</i>, i.e. with respect to the discursive context fixed by an information state. The main technical result of the paper is a sound and complete axiomatisation of relevant containment logic. Finally, Sylvan’s logic turns out as a special case of our relevant containment logic.</p>

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Contextual Entailment and Containment: A Ternary Approach to Information and Topic Inclusion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月10日

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  • Pietro Vigiani,
  • Thomas Macaulay Ferguson

摘要

The paper introduces a relevant containment logic according to which the analytic implication \(\varphi \twoheadrightarrow \psi\) φ ↠ ψ is analyzed as the conjunction of two theses: \(\varphi\) φ contextually entails \(\psi\) ψ and \(\varphi\) φ contextually contains \(\psi\) ψ . By doing so, we are able to extend the ternary semantics of relevant logic to the analysis of topic containment, thus lifting some limitations of Richard Sylvan’s relevant containment logic. We offer a ternary account of topic containment, in that led by the consideration that topic inclusions are evaluated in situ, i.e. with respect to the discursive context fixed by an information state. The main technical result of the paper is a sound and complete axiomatisation of relevant containment logic. Finally, Sylvan’s logic turns out as a special case of our relevant containment logic.