Completeness-via-canonicity for coalgebraic logics
Fredrik Dahlqvist
TL;DR
This thesis develops a generalized method based on completeness-via-canonicity to establish completeness results for coalgebraic logics with complex axioms, extending classical modal logic techniques.
Contribution
It introduces a suite of techniques to generalize completeness-via-canonicity for coalgebraic logics with arbitrary rank axioms.
Findings
Generalized completeness-via-canonicity for coalgebraic logics
Applicable to axioms of arbitrary rank
Provides a systematic approach for completeness proofs
Abstract
This thesis aims to provide a suite of techniques to generate completeness results for coalgebraic logics with axioms of arbitrary rank. We have chosen to investigate the possibility to generalize what is arguably one of the most successful methods to prove completeness results in `classical' modal logic, namely completeness-via-canonicity. This technique is particularly well-suited to a coalgebraic generalization because of its clean and abstract algebraic formalism.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Logic, programming, and type systems · Advanced Algebra and Logic