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arXiv · 1406.5700

A dichotomy for some elementarily generated modal logics

Stanislav Kikot
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Abstract

In this paper we consider the normal modal logics of elementary classes defined by first-order formulas of the form $\forall x_0 \exists x_1 \dots \exists x_n \bigwedge x_i R_λx_j$. We prove that many properties of these logics, such as finite axiomatisability, elementarity, axiomatisability by a set of canonical formulas or by a single generalised Sahlqvist formula, together with modal definability of the initial formula, either simultaneously hold or simultaneously do not hold.

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Stanislav Kikot. 2015-02-27. A dichotomy for some elementarily generated modal logics. https://arxiv.org/abs/1406.5700

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