MLC Seminar

Speaker: Pablo Rivas-Robledo
Title: Modal Logic and Modality without Possible Worlds: Semantics, Correspondence and Modal Normativism
Date:
Time: 16:00 - 17:30
Location: SP107 F1.15 (ILLC Seminar Room)

In this talk I present a modular semantics for a wide range of modal logics, which I call Non-deterministic Semantics via Snapshots (NDSS), building on work by Coniglio, Omori, Pawłowski and Skurt. Unlike relational semantics, which evaluates formulas at possible worlds, NDSS assigns every formula a snapshot: a pair of truth values, the first recording whether the formula is true and the second whether it is necessary. I show how, with tools from the literature on non-deterministic semantics (refinements of non-deterministic matrices, restricted non-deterministic matrices and level valuations), one obtains the familiar normal modal logics, non-normal ones, and even logics too weak to be closed under replacement of equivalents. On this basis I prove a single modular soundness and completeness theorem covering all the systems discussed. I then turn to two current developments. First, I give a tentative account of how modal correspondence theory changes when the focus shifts from possible worlds to snapshots. Second, I discuss the philosophical interpretation of the formalism and its connection to modal normativism, a form of non-descriptivism according to which modal discourse does not function to describe states of affairs at this or any other possible world, and modal truths need no modal features of the world as truthmakers. The talk covers some known results, some new ones and some work in progress. Possible-world enthusiasts are welcome.