The Poset of All Logics I: Interpretations and Lattice Structure

2019/11/21 by Ramón Jansana, Tommaso Moraschini, Jansana, R. +1
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.1911.09394

openalex publication_date 2019/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A notion of interpretation between arbitrary logics is introduced, and the poset Log of all logics ordered under interpretability is studied. It is shown that in Log infima of arbitrarily large sets exist, but binary suprema in general do not. On the other hand, the existence of suprema of sets of equivalential logics is established. The relations between Log and the lattice of interpretability types of varieties are investigated.

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