This paper presents an algebraic treatment of logic, aiming to further the project of a "subjective semantics" for quantification, identity, and modality. Semantics has largely concentrated on truth and reference, the relation of language to the world, and this is part of its usual definition. It has also been the discipline which offers theories to explain the logical behavior of various sorts of expressions traditionally studied in logic: connectors, modalities, quantifiers, abstractors, the identity predicate, and so forth. Recently a number of studies have concentrated on the relation between language and the states of mind (generally epistemic or doxastic attitudes) of its users, to provide such explanations, and the term "semantics" has also been used there.' The present study will be among these. Truth and reference will be eschewed. Intuitive descriptions of the framework will be given, albeit briefly, in terms of mental operations on propositions (regarded therefore as the sort of thing which we can vary or modify in imagination). Generality will be part of the aim; neutrality with respect to certain nonclassical logics will be guarded. The Appendix will show how standard semantic analyses can fit into this general framework. The algebraic (latticewith-transformations) analysis of modality, quantification and identity given here may therefore be of some interest outside 'subjective semantics' as well.