Doctoral Dissertation — Interactive Guide
A Formal Theory of Phonological Equivalence
Alexandre Menezes Barroso
Institute of Language Studies — UNICAMP, 2027
Advisor: Prof. Dr. Maria Filomena Spatti Sandalo
What is this guide?
This guide accompanies the dissertation for readers familiar with phonology and constraint-based grammars but without mathematical training. We start with problems and examples; notation comes gradually. Numbered equations have symbol-by-symbol explanations, worked calculations and small comprehension checks. Panels let you change one thing at a time and observe the consequence. The theory joins the construction of grammars retaining input information with comparison of what their representations, parameters and observations can distinguish. You need not run code to follow the argument; programs remain available for inspecting the details.
Lean 4
Computer-verified formal proofs
Python 3
Runnable exact calculations
Wolfram
Symbolic algebra
Dissertation Structure
The problem of phonological equivalence
What a grammar preserves and what a comparison distinguishes
Representation, evaluation and equivalence
Responses, transports and sufficient information
Typed requirements and preservation of input information
Subjects, contexts, and initial or created violations
Interaction, composition and limits of grammar
Dependencies, exclusions, computation and identification
Variation, probability and identification
Base mass, normalization and shared parameters
Continuity and the evaluation domain
Persistence, discretization and information about the law
Comparison of analyses and explanatory scope
Results about representation, mechanisms and observations
Variable opacity in Uyghur
Joint prediction of raising and harmony
Grammatical information, equivalence and empirical scope
Consequences, commitments and routes to inspection
Appendix L · Data comparisons and PhonoScript
Portuguese, English and Mandarin: what each observation preserves
References
Complete dissertation bibliography