Uno Studio di Logiche a Quattro Valori tramite Proposizionalità

This work presents an analysis of the logics arising from the four-valued semantics studied in Martínez-Fernández and Martí (2021) as a way to account for the semantic difference between sentences that are neither true nor false but express a proposition and those that do not. The main idea here is to use these formal tools in order to model an interesting inferential property, namely preservation of propositionality. At a formal level it is in fact possible to capture and impose the intuitive requirement for an argument that if the premises are all propositions, then the conclusion has to express a proposition too. What emerges from this investigation is that preservation of propositionality corresponds to a constraint that can be seen as desirable even from another point of view, namely a purely relevantist interest. The analysis of the logics arising from this motivation, concerns the characterization of their consequence relations with respect to well-known three valued logics and the syntactic property of variable inclusion, which can be regarded as a minimal formal requirement to capture some meaning-connection between premises and conclusion of an argument. Moreover, this work studies what principles of conditional logic are validated and invalidated by the logics that preserve propositionality, and an assessment regarding their adequacy in the way they model indicative conditionals in ordinary language is carried out.