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arXiv · 1712.00317

Effective Completeness for S4.3.1-Theories with Respect to Discrete Linear Models

David Nichols
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Abstract

The computable model theory of modal logic was initiated by Suman Ganguli and Anil Nerode in [4]. They use an effective Henkin-type construction to effectivize various completeness theorems from classical modal logic. This construction has the feature of only producing models whose frames can be obtained by adding edges to a tree digraph. Consequently, this construction cannot prove an effective version of a well-known completeness theorem which states that every $\mathsf{S4.3.1}$-theory has a model whose accessibility relation is a linear order of order type $\omega$. We prove an effectivization of that theorem by means of a new construction adapted from that of Ganguli and Nerode.

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David Nichols. 2017-12-01. Effective Completeness for S4.3.1-Theories with Respect to Discrete Linear Models. https://arxiv.org/abs/1712.00317

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