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• W2106310727 abstract "We investigate properties of the formula $p to Box p$ in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins $phi to Boxphi / phi, negphi$, and as a consequence, we obtain various negative results about admissibility and unification in K. We describe a complete set of unifiers (i.e., substitutions making the formula provable) of $p to Box p$, and use it to establish that K has the worst possible unification type: nullary. In well-behaved transitive modal logics, admissibility and unification can be analyzed in terms of projective formulas, introduced by Ghilardi; in particular, projective formulas coincide for these logics with formulas that are admissibly saturated (i.e., derive all their multiple-conclusion admissible consequences) or exact (i.e., axiomatize a theory of a substitution). In contrast, we show that in K, the formula $p to Box p$ is admissibly saturated, but neither projective nor exact. All our results for K also apply to the basic description logic ALC." @default.
• W2106310727 created "2016-06-24" @default.
• W2106310727 creator A5091882087 @default.
• W2106310727 date "2013-11-06" @default.
• W2106310727 modified "2023-10-12" @default.
• W2106310727 title "Blending margins: the modal logic K has nullary unification type" @default.
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• W2106310727 doi "https://doi.org/10.1093/logcom/ext055" @default.
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