A Topical Approach to Implication-in-Fiction and Analytic Containment Logics

Abstract We develop a topical framework for implication-in-fiction by representing topics as subalgebras, following [12]. We propose an account where those propositions follow within the fiction which (1) follow tout court and (2) are on topic. This is formally modeled in an algebra of propositions as the intersection of a subalgebra and a filter, both of which are generated by the values of the premises under some interpretation of the language in the algebra. We then show how this notion generalises to a Tarskian consequence relation over classes of algebras, and show that in some cases this consequence relation satisfies the Proscriptive Principle ( PP ), and thus is appropriate for logics of analytic containment.